def get_zero_op(self, kernel, **knl_kwargs): u_sym = sym.var("u") dn_u_sym = sym.var("dn_u") return ( sym.S(kernel, dn_u_sym, qbx_forced_limit=-1, **knl_kwargs) - sym.D(kernel, u_sym, qbx_forced_limit="avg", **knl_kwargs) - 0.5*u_sym)
def get_zero_op(self, kernel, **knl_kwargs): d = kernel.dim u_sym = sym.var("u") grad_u_sym = sym.make_sym_mv("grad_u", d) dn_u_sym = sym.var("dn_u") return ( d1.resolve(d1.dnabla(d) * d1(sym.S(kernel, dn_u_sym, qbx_forced_limit="avg", **knl_kwargs))) - d2.resolve(d2.dnabla(d) * d2(sym.D(kernel, u_sym, qbx_forced_limit="avg", **knl_kwargs))) - 0.5*grad_u_sym )
def __init__(self, domain_n_exprs, ne, interfaces, use_l2_weighting=None): """ :attr interfaces: a tuple of tuples ``(outer_domain, inner_domain, interface_id)``, where *outer_domain* and *inner_domain* are indices into *domain_k_names*, and *interface_id* is a symbolic name for the discretization of the interface. 'outer' designates the side of the interface to which the normal points. :attr domain_n_exprs: a tuple of variable names of the Helmholtz parameter *k*, to be used inside each part of the source geometry. May also be a tuple of strings, which will be transformed into variable references of the corresponding names. :attr beta: A symbolic expression for the wave number in the :math:`z` direction. May be a string, which will be interpreted as a variable name. """ self.interfaces = interfaces ne = sym.var(ne) self.ne = sym.cse(ne, "ne") self.domain_n_exprs = [ sym.var(n_expr) for idom, n_expr in enumerate(domain_n_exprs)] del domain_n_exprs import pymbolic.primitives as p def upper_half_square_root(x): return p.If( p.Comparison( (x**0.5).a.imag, "<", 0), 1j*(-x)**0.5, x**0.5) self.domain_K_exprs = [ sym.cse( upper_half_square_root(n_expr**2-ne**2), "K%d" % i) for i, n_expr in enumerate(self.domain_n_exprs)] from sumpy.kernel import HelmholtzKernel self.kernel = HelmholtzKernel(2, allow_evanescent=True)
def main(): cl_ctx = cl.create_some_context() queue = cl.CommandQueue(cl_ctx) target_order = 10 from functools import partial nelements = 30 qbx_order = 4 from sumpy.kernel import LaplaceKernel from meshmode.mesh.generation import ( # noqa ellipse, cloverleaf, starfish, drop, n_gon, qbx_peanut, make_curve_mesh) mesh = make_curve_mesh(partial(ellipse, 1), np.linspace(0, 1, nelements+1), target_order) from meshmode.discretization import Discretization from meshmode.discretization.poly_element import \ InterpolatoryQuadratureSimplexGroupFactory density_discr = Discretization(cl_ctx, mesh, InterpolatoryQuadratureSimplexGroupFactory(target_order)) from pytential.qbx import QBXLayerPotentialSource qbx = QBXLayerPotentialSource(density_discr, 4*target_order, qbx_order, fmm_order=False) from pytools.obj_array import join_fields sig_sym = sym.var("sig") knl = LaplaceKernel(2) op = join_fields( sym.tangential_derivative(mesh.ambient_dim, sym.D(knl, sig_sym, qbx_forced_limit=+1)).as_scalar(), sym.tangential_derivative(mesh.ambient_dim, sym.D(knl, sig_sym, qbx_forced_limit=-1)).as_scalar(), ) nodes = density_discr.nodes().with_queue(queue) angle = cl.clmath.atan2(nodes[1], nodes[0]) n = 10 sig = cl.clmath.sin(n*angle) dt_sig = n*cl.clmath.cos(n*angle) res = bind(qbx, op)(queue, sig=sig) extval = res[0].get() intval = res[1].get() pv = 0.5*(extval + intval) dt_sig_h = dt_sig.get() import matplotlib.pyplot as pt pt.plot(extval, label="+num") pt.plot(pv + dt_sig_h*0.5, label="+ex") pt.legend(loc="best") pt.show()
def get_zero_op(self, kernel, **knl_kwargs): assert isinstance(kernel, LaplaceKernel) assert not knl_kwargs u_sym = sym.var("u") return ( -sym.Dp(kernel, sym.S(kernel, u_sym)) - 0.25*u_sym + sym.Sp(kernel, sym.Sp(kernel, u_sym)) )
def test_unregularized_off_surface_fmm_vs_direct(ctx_getter): cl_ctx = ctx_getter() queue = cl.CommandQueue(cl_ctx) nelements = 300 target_order = 8 fmm_order = 4 mesh = make_curve_mesh(WobblyCircle.random(8, seed=30), np.linspace(0, 1, nelements+1), target_order) from pytential.unregularized import UnregularizedLayerPotentialSource from meshmode.discretization import Discretization from meshmode.discretization.poly_element import \ InterpolatoryQuadratureSimplexGroupFactory density_discr = Discretization( cl_ctx, mesh, InterpolatoryQuadratureSimplexGroupFactory(target_order)) direct = UnregularizedLayerPotentialSource( density_discr, fmm_order=False, ) fmm = direct.copy( fmm_level_to_order=lambda kernel, kernel_args, tree, level: fmm_order) sigma = density_discr.zeros(queue) + 1 fplot = FieldPlotter(np.zeros(2), extent=5, npoints=100) from pytential.target import PointsTarget ptarget = PointsTarget(fplot.points) from sumpy.kernel import LaplaceKernel op = sym.D(LaplaceKernel(2), sym.var("sigma"), qbx_forced_limit=None) direct_fld_in_vol = bind((direct, ptarget), op)(queue, sigma=sigma) fmm_fld_in_vol = bind((fmm, ptarget), op)(queue, sigma=sigma) err = cl.clmath.fabs(fmm_fld_in_vol - direct_fld_in_vol) linf_err = cl.array.max(err).get() print("l_inf error:", linf_err) assert linf_err < 5e-3
def test_unregularized_with_ones_kernel(ctx_getter): cl_ctx = ctx_getter() queue = cl.CommandQueue(cl_ctx) nelements = 10 order = 8 mesh = make_curve_mesh(partial(ellipse, 1), np.linspace(0, 1, nelements+1), order) from meshmode.discretization import Discretization from meshmode.discretization.poly_element import \ InterpolatoryQuadratureSimplexGroupFactory discr = Discretization(cl_ctx, mesh, InterpolatoryQuadratureSimplexGroupFactory(order)) from pytential.unregularized import UnregularizedLayerPotentialSource lpot_src = UnregularizedLayerPotentialSource(discr) from sumpy.kernel import one_kernel_2d expr = sym.IntG(one_kernel_2d, sym.var("sigma"), qbx_forced_limit=None) from pytential.target import PointsTarget op_self = bind(lpot_src, expr) op_nonself = bind((lpot_src, PointsTarget(np.zeros((2, 1), dtype=float))), expr) with cl.CommandQueue(cl_ctx) as queue: sigma = cl.array.zeros(queue, discr.nnodes, dtype=float) sigma.fill(1) sigma.finish() result_self = op_self(queue, sigma=sigma) result_nonself = op_nonself(queue, sigma=sigma) assert np.allclose(result_self.get(), 2 * np.pi) assert np.allclose(result_nonself.get(), 2 * np.pi)
def test_identities(ctx_getter, zero_op_name, curve_name, curve_f, qbx_order, k): cl_ctx = ctx_getter() queue = cl.CommandQueue(cl_ctx) # prevent cache 'splosion from sympy.core.cache import clear_cache clear_cache() target_order = 7 u_sym = sym.var("u") grad_u_sym = sym.VectorVariable("grad_u") dn_u_sym = sym.var("dn_u") if k == 0: k_sym = 0 else: k_sym = "k" zero_op_table = { "green": sym.S(k_sym, dn_u_sym) - sym.D(k_sym, u_sym) - 0.5*u_sym, "green_grad": d1.nabla * d1(sym.S(k_sym, dn_u_sym)) - d2.nabla * d2(sym.D(k_sym, u_sym)) - 0.5*grad_u_sym, # only for k==0: "zero_calderon": -sym.Dp(0, sym.S(0, u_sym)) - 0.25*u_sym + sym.Sp(0, sym.Sp(0, u_sym)) } order_table = { "green": qbx_order, "green_grad": qbx_order-1, "zero_calderon": qbx_order-1, } zero_op = zero_op_table[zero_op_name] from pytools.convergence import EOCRecorder eoc_rec = EOCRecorder() for nelements in [30, 50, 70]: mesh = make_curve_mesh(curve_f, np.linspace(0, 1, nelements+1), target_order) from meshmode.discretization import Discretization from meshmode.discretization.poly_element import \ InterpolatoryQuadratureSimplexGroupFactory from pytential.qbx import QBXLayerPotentialSource density_discr = Discretization( cl_ctx, mesh, InterpolatoryQuadratureSimplexGroupFactory(target_order)) qbx = QBXLayerPotentialSource(density_discr, 4*target_order, qbx_order, # Don't use FMM for now fmm_order=False) # {{{ compute values of a solution to the PDE nodes_host = density_discr.nodes().get(queue) normal = bind(density_discr, sym.normal())(queue).as_vector(np.object) normal_host = [normal[0].get(), normal[1].get()] if k != 0: angle = 0.3 wave_vec = np.array([np.cos(angle), np.sin(angle)]) u = np.exp(1j*k*np.tensordot(wave_vec, nodes_host, axes=1)) grad_u = 1j*k*wave_vec[:, np.newaxis]*u else: center = np.array([3, 1]) diff = nodes_host - center[:, np.newaxis] dist_squared = np.sum(diff**2, axis=0) dist = np.sqrt(dist_squared) u = np.log(dist) grad_u = diff/dist_squared dn_u = normal_host[0]*grad_u[0] + normal_host[1]*grad_u[1] # }}} u_dev = cl.array.to_device(queue, u) dn_u_dev = cl.array.to_device(queue, dn_u) grad_u_dev = cl.array.to_device(queue, grad_u) key = (qbx_order, curve_name, nelements, zero_op_name) bound_op = bind(qbx, zero_op) error = bound_op( queue, u=u_dev, dn_u=dn_u_dev, grad_u=grad_u_dev, k=k) if 0: pt.plot(error) pt.show() l2_error_norm = norm(density_discr, queue, error) print(key, l2_error_norm) eoc_rec.add_data_point(1/nelements, l2_error_norm) print(eoc_rec) tgt_order = order_table[zero_op_name] assert eoc_rec.order_estimate() > tgt_order - 1.3
def test_ellipse_eigenvalues(ctx_getter, ellipse_aspect, mode_nr, qbx_order): logging.basicConfig(level=logging.INFO) print("ellipse_aspect: %s, mode_nr: %d, qbx_order: %d" % ( ellipse_aspect, mode_nr, qbx_order)) cl_ctx = ctx_getter() queue = cl.CommandQueue(cl_ctx) target_order = 7 from meshmode.discretization import Discretization from meshmode.discretization.poly_element import \ InterpolatoryQuadratureSimplexGroupFactory from pytential.qbx import QBXLayerPotentialSource from pytools.convergence import EOCRecorder s_eoc_rec = EOCRecorder() d_eoc_rec = EOCRecorder() sp_eoc_rec = EOCRecorder() if ellipse_aspect != 1: nelements_values = [60, 100, 150, 200] else: nelements_values = [30, 70] # See # # [1] G. J. Rodin and O. Steinbach, "Boundary Element Preconditioners # for Problems Defined on Slender Domains", SIAM Journal on Scientific # Computing, Vol. 24, No. 4, pg. 1450, 2003. # http://dx.doi.org/10.1137/S1064827500372067 for nelements in nelements_values: mesh = make_curve_mesh(partial(ellipse, ellipse_aspect), np.linspace(0, 1, nelements+1), target_order) fmm_order = qbx_order if fmm_order > 3: # FIXME: for now fmm_order = False density_discr = Discretization( cl_ctx, mesh, InterpolatoryQuadratureSimplexGroupFactory(target_order)) qbx = QBXLayerPotentialSource(density_discr, 4*target_order, qbx_order, fmm_order=fmm_order) nodes = density_discr.nodes().with_queue(queue) if 0: # plot geometry, centers, normals centers = qbx.centers(density_discr, 1) nodes_h = nodes.get() centers_h = [centers[0].get(), centers[1].get()] pt.plot(nodes_h[0], nodes_h[1], "x-") pt.plot(centers_h[0], centers_h[1], "o") normal = bind(qbx, sym.normal())(queue).as_vector(np.object) pt.quiver(nodes_h[0], nodes_h[1], normal[0].get(), normal[1].get()) pt.gca().set_aspect("equal") pt.show() angle = cl.clmath.atan2(nodes[1]*ellipse_aspect, nodes[0]) ellipse_fraction = ((1-ellipse_aspect)/(1+ellipse_aspect))**mode_nr # (2.6) in [1] J = cl.clmath.sqrt( # noqa cl.clmath.sin(angle)**2 + (1/ellipse_aspect)**2 * cl.clmath.cos(angle)**2) # {{{ single layer sigma = cl.clmath.cos(mode_nr*angle)/J s_sigma_op = bind(qbx, sym.S(0, sym.var("sigma"))) s_sigma = s_sigma_op(queue=queue, sigma=sigma) # SIGN BINGO! :) s_eigval = 1/(2*mode_nr) * (1 + (-1)**mode_nr * ellipse_fraction) # (2.12) in [1] s_sigma_ref = s_eigval*J*sigma if 0: #pt.plot(s_sigma.get(), label="result") #pt.plot(s_sigma_ref.get(), label="ref") pt.plot((s_sigma_ref-s_sigma).get(), label="err") pt.legend() pt.show() s_err = ( norm(density_discr, queue, s_sigma - s_sigma_ref) / norm(density_discr, queue, s_sigma_ref)) s_eoc_rec.add_data_point(1/nelements, s_err) # }}} # {{{ double layer sigma = cl.clmath.cos(mode_nr*angle) d_sigma_op = bind(qbx, sym.D(0, sym.var("sigma"))) d_sigma = d_sigma_op(queue=queue, sigma=sigma) # SIGN BINGO! :) d_eigval = -(-1)**mode_nr * 1/2*ellipse_fraction d_sigma_ref = d_eigval*sigma if 0: pt.plot(d_sigma.get(), label="result") pt.plot(d_sigma_ref.get(), label="ref") pt.legend() pt.show() if ellipse_aspect == 1: d_ref_norm = norm(density_discr, queue, sigma) else: d_ref_norm = norm(density_discr, queue, d_sigma_ref) d_err = ( norm(density_discr, queue, d_sigma - d_sigma_ref) / d_ref_norm) d_eoc_rec.add_data_point(1/nelements, d_err) # }}} if ellipse_aspect == 1: # {{{ S' sigma = cl.clmath.cos(mode_nr*angle) sp_sigma_op = bind(qbx, sym.Sp(0, sym.var("sigma"))) sp_sigma = sp_sigma_op(queue=queue, sigma=sigma) sp_eigval = 0 sp_sigma_ref = sp_eigval*sigma sp_err = ( norm(density_discr, queue, sp_sigma - sp_sigma_ref) / norm(density_discr, queue, sigma)) sp_eoc_rec.add_data_point(1/nelements, sp_err) # }}} print("Errors for S:") print(s_eoc_rec) required_order = qbx_order + 1 assert s_eoc_rec.order_estimate() > required_order - 1.5 print("Errors for D:") print(d_eoc_rec) required_order = qbx_order assert d_eoc_rec.order_estimate() > required_order - 1.5 if ellipse_aspect == 1: print("Errors for S':") print(sp_eoc_rec) required_order = qbx_order assert sp_eoc_rec.order_estimate() > required_order - 1.5
def find_mode(): import warnings warnings.simplefilter("error", np.ComplexWarning) cl_ctx = cl.create_some_context() queue = cl.CommandQueue(cl_ctx) k0 = 1.4447 k1 = k0*1.02 beta_sym = sym.var("beta") from pytential.symbolic.pde.scalar import ( # noqa DielectricSRep2DBoundaryOperator as SRep, DielectricSDRep2DBoundaryOperator as SDRep) pde_op = SDRep( mode="te", k_vacuum=1, interfaces=((0, 1, sym.DEFAULT_SOURCE),), domain_k_exprs=(k0, k1), beta=beta_sym, use_l2_weighting=False) u_sym = pde_op.make_unknown("u") op = pde_op.operator(u_sym) # {{{ discretization setup from meshmode.mesh.generation import ellipse, make_curve_mesh curve_f = partial(ellipse, 1) target_order = 7 qbx_order = 4 nelements = 30 from meshmode.mesh.processing import affine_map mesh = make_curve_mesh(curve_f, np.linspace(0, 1, nelements+1), target_order) lambda_ = 1.55 circle_radius = 3.4*2*np.pi/lambda_ mesh = affine_map(mesh, A=circle_radius*np.eye(2)) from meshmode.discretization import Discretization from meshmode.discretization.poly_element import \ InterpolatoryQuadratureSimplexGroupFactory from pytential.qbx import QBXLayerPotentialSource density_discr = Discretization( cl_ctx, mesh, InterpolatoryQuadratureSimplexGroupFactory(target_order)) qbx = QBXLayerPotentialSource(density_discr, 4*target_order, qbx_order, # Don't use FMM for now fmm_order=False) # }}} x_vec = np.random.randn(len(u_sym)*density_discr.nnodes) y_vec = np.random.randn(len(u_sym)*density_discr.nnodes) def muller_solve_func(beta): from pytential.symbolic.execution import build_matrix mat = build_matrix( queue, qbx, op, u_sym, context={"beta": beta}).get() return 1/x_vec.dot(la.solve(mat, y_vec)) starting_guesses = (1+0j)*( k0 + (k1-k0) * np.random.rand(3)) from pytential.muller import muller beta, niter = muller(muller_solve_func, z_start=starting_guesses) print("beta")
InterpolatoryQuadratureSimplexGroupFactory density_discr = Discretization( cl_ctx, mesh, InterpolatoryQuadratureSimplexGroupFactory(target_order)) qbx = QBXLayerPotentialSource(density_discr, 4*target_order, qbx_order, fmm_order=qbx_order) nodes = density_discr.nodes().with_queue(queue) angle = cl.clmath.atan2(nodes[1], nodes[0]) from pytential import bind, sym d = sym.Derivative() #op = d.nabla[0] * d(sym.S(kernel, sym.var("sigma"))) op = sym.D(kernel, sym.var("sigma")) #op = sym.S(kernel, sym.var("sigma")) sigma = cl.clmath.cos(mode_nr*angle) if 0: sigma = 0*angle from random import randrange for i in range(5): sigma[randrange(len(sigma))] = 1 if isinstance(kernel, HelmholtzKernel): sigma = sigma.astype(np.complex128) bound_bdry_op = bind(qbx, op) #mlab.figure(bgcolor=(1, 1, 1)) if 1:
def __init__(self, mode, k_vacuum, domain_k_exprs, beta, interfaces, use_l2_weighting=None): """ :attr mode: one of 'te', 'tm', 'tem' :attr k_vacuum: A symbolic expression for the wave number in vacuum. May be a string, which will be interpreted as a variable name. :attr interfaces: a tuple of tuples ``(outer_domain, inner_domain, interface_id)``, where *outer_domain* and *inner_domain* are indices into *domain_k_names*, and *interface_id* is a symbolic name for the discretization of the interface. 'outer' designates the side of the interface to which the normal points. :attr domain_k_exprs: a tuple of variable names of the Helmholtz parameter *k*, to be used inside each part of the source geometry. May also be a tuple of strings, which will be transformed into variable references of the corresponding names. :attr beta: A symbolic expression for the wave number in the :math:`z` direction. May be a string, which will be interpreted as a variable name. """ if use_l2_weighting is None: use_l2_weighting = False super(Dielectric2DBoundaryOperatorBase, self).__init__( use_l2_weighting=use_l2_weighting) if mode == "te": self.ez_enabled = False self.hz_enabled = True elif mode == "tm": self.ez_enabled = True self.hz_enabled = False elif mode == "tem": self.ez_enabled = True self.hz_enabled = True else: raise ValueError("invalid mode '%s'" % mode) self.interfaces = interfaces fk_e = self.field_kind_e fk_h = self.field_kind_h dir_none = self.dir_none dir_normal = self.dir_normal dir_tangential = self.dir_tangential if isinstance(beta, str): beta = sym.var(beta) beta = sym.cse(beta, "beta") if isinstance(k_vacuum, str): k_vacuum = sym.var(k_vacuum) k_vacuum = sym.cse(k_vacuum, "k_vac") self.domain_k_exprs = [ sym.var(k_expr) if isinstance(k_expr, str) else sym.cse(k_expr, "k%d" % idom) for idom, k_expr in enumerate(domain_k_exprs)] del domain_k_exprs # Note the case of k/K! # "K" is the 2D Helmholtz parameter. # "k" is the 3D Helmholtz parameter. self.domain_K_exprs = [ sym.cse((k_expr**2-beta**2)**0.5, "K%d" % i) for i, k_expr in enumerate(self.domain_k_exprs)] from sumpy.kernel import HelmholtzKernel self.kernel = HelmholtzKernel(2, allow_evanescent=True) # {{{ build bc list # list of tuples, where each tuple consists of BCTermDescriptor instances all_bcs = [] for i_interface, (outer_domain, inner_domain, _) in ( enumerate(self.interfaces)): k_outer = self.domain_k_exprs[outer_domain] k_inner = self.domain_k_exprs[inner_domain] all_bcs += [ ( # [E] = 0 self.BCTermDescriptor( i_interface=i_interface, direction=dir_none, field_kind=fk_e, coeff_outer=1, coeff_inner=-1), ), ( # [H] = 0 self.BCTermDescriptor( i_interface=i_interface, direction=dir_none, field_kind=fk_h, coeff_outer=1, coeff_inner=-1), ), ( self.BCTermDescriptor( i_interface=i_interface, direction=dir_tangential, field_kind=fk_e, coeff_outer=beta/(k_outer**2-beta**2), coeff_inner=-beta/(k_inner**2-beta**2)), self.BCTermDescriptor( i_interface=i_interface, direction=dir_normal, field_kind=fk_h, coeff_outer=sym.cse(-k_vacuum/(k_outer**2-beta**2)), coeff_inner=sym.cse(k_vacuum/(k_inner**2-beta**2))), ), ( self.BCTermDescriptor( i_interface=i_interface, direction=dir_tangential, field_kind=fk_h, coeff_outer=beta/(k_outer**2-beta**2), coeff_inner=-beta/(k_inner**2-beta**2)), self.BCTermDescriptor( i_interface=i_interface, direction=dir_normal, field_kind=fk_e, coeff_outer=sym.cse( (k_outer**2/k_vacuum)/(k_outer**2-beta**2)), coeff_inner=sym.cse( -(k_inner**2/k_vacuum) / (k_inner**2-beta**2))) ), ] del k_outer del k_inner self.bcs = [] for bc in all_bcs: any_significant_e = any( term.field_kind == fk_e and term.direction in [dir_normal, dir_none] for term in bc) any_significant_h = any( term.field_kind == fk_h and term.direction in [dir_normal, dir_none] for term in bc) is_necessary = ( (self.ez_enabled and any_significant_e) or (self.hz_enabled and any_significant_h)) # Only keep tangential modes for TEM. Otherwise, # no jump in H already implies jump condition on # tangential derivative. is_tem = self.ez_enabled and self.hz_enabled terms = tuple( term for term in bc if term.direction != dir_tangential or is_tem) if is_necessary: self.bcs.append(terms) assert (len(all_bcs) * (int(self.ez_enabled) + int(self.hz_enabled)) // 2 == len(self.bcs))
def get_qbx_center_neighborhood_sizes(lpot_source, radius): queue = cl.CommandQueue(lpot_source.cl_context) def inspect_geo_data(insn, bound_expr, geo_data): nonlocal sizes, nsources, ncenters tree = geo_data.tree().with_queue(queue) from boxtree.area_query import PeerListFinder plf = PeerListFinder(queue.context) pl, evt = plf(queue, tree) # Perform an area query around each QBX center, counting the # neighborhood sizes. knl = NeighborhoodCounter.generate( queue.context, tree.dimensions, tree.coord_dtype, tree.box_id_dtype, tree.box_id_dtype, tree.nlevels, extra_type_aliases=(('particle_id_t', tree.particle_id_dtype),)) centers = geo_data.centers() search_radii = radius * geo_data.expansion_radii().with_queue(queue) ncenters = len(search_radii) nsources = tree.nsources sizes = cl.array.zeros(queue, ncenters, np.int32) assert nsources == lpot_source.quad_stage2_density_discr.nnodes coords = [] coords.extend(tree.sources) coords.extend(centers) evt = knl( *NeighborhoodCounter.unwrap_args( tree, pl, tree.box_source_starts, tree.box_source_counts_cumul, search_radii, sizes, *coords), range=slice(ncenters), queue=queue, wait_for=[evt]) cl.wait_for_events([evt]) return False # no need to do the actual FMM sizes = None nsources = None ncenters = None lpot_source = lpot_source.copy(geometry_data_inspector=inspect_geo_data) density_discr = lpot_source.density_discr nodes = density_discr.nodes().with_queue(queue) sigma = cl.clmath.sin(10 * nodes[0]) # The kernel doesn't really matter here from sumpy.kernel import LaplaceKernel sigma_sym = sym.var('sigma') k_sym = LaplaceKernel(lpot_source.ambient_dim) sym_op = sym.S(k_sym, sigma_sym, qbx_forced_limit=+1) bound_op = bind(lpot_source, sym_op) bound_op(queue, sigma=sigma) return (sizes.get(queue), nsources, ncenters)
raise ValueError("invalid mesh dim") # }}} # {{{ set up operator knl = case.knl_class(ambient_dim) op = case.get_operator(ambient_dim) if knl.is_complex_valued: dtype = np.complex128 else: dtype = np.float64 sym_u = op.get_density_var("u") sym_bc = op.get_density_var("bc") sym_charges = sym.var("charges") sym_op_u = op.operator(sym_u) # }}} # {{{ set up test data np.random.seed(22) source_charges = np.random.randn(point_source.ndofs) source_charges[-1] = -np.sum(source_charges[:-1]) source_charges = source_charges.astype(dtype) assert np.sum(source_charges) < 1.0e-15 source_charges_dev = actx.from_numpy(source_charges)
from pytential import bind, sym import faulthandler from six.moves import range faulthandler.enable() target_order = 16 qbx_order = 3 nelements = 60 mode_nr = 3 k = 0 if k: kernel = HelmholtzKernel(2) kernel_kwargs = {"k": sym.var("k")} else: kernel = LaplaceKernel(2) kernel_kwargs = {} #kernel = OneKernel() def main(): import logging logging.basicConfig(level=logging.WARNING) # INFO for more progress info cl_ctx = cl.create_some_context() queue = cl.CommandQueue(cl_ctx) from meshmode.mesh.generation import ( # noqa make_curve_mesh, starfish, ellipse, drop)
def main(mesh_name="torus", visualize=False): import logging logging.basicConfig(level=logging.WARNING) # INFO for more progress info cl_ctx = cl.create_some_context() queue = cl.CommandQueue(cl_ctx) actx = PyOpenCLArrayContext(queue) if mesh_name == "torus": rout = 10 rin = 1 from meshmode.mesh.generation import generate_torus base_mesh = generate_torus(rout, rin, 40, 4, mesh_order) from meshmode.mesh.processing import affine_map, merge_disjoint_meshes # nx = 1 # ny = 1 nz = 1 dz = 0 meshes = [ affine_map(base_mesh, A=np.diag([1, 1, 1]), b=np.array([0, 0, iz * dz])) for iz in range(nz) ] mesh = merge_disjoint_meshes(meshes, single_group=True) if visualize: from meshmode.mesh.visualization import draw_curve draw_curve(mesh) import matplotlib.pyplot as plt plt.show() else: raise ValueError("unknown mesh name: {}".format(mesh_name)) pre_density_discr = Discretization( actx, mesh, InterpolatoryQuadratureSimplexGroupFactory(bdry_quad_order)) from pytential.qbx import (QBXLayerPotentialSource, QBXTargetAssociationFailedException) qbx = QBXLayerPotentialSource( pre_density_discr, fine_order=bdry_ovsmp_quad_order, qbx_order=qbx_order, fmm_order=fmm_order, ) from sumpy.visualization import FieldPlotter fplot = FieldPlotter(np.zeros(3), extent=20, npoints=50) targets = actx.from_numpy(fplot.points) from pytential import GeometryCollection places = GeometryCollection( { "qbx": qbx, "qbx_target_assoc": qbx.copy(target_association_tolerance=0.2), "targets": PointsTarget(targets) }, auto_where="qbx") density_discr = places.get_discretization("qbx") # {{{ describe bvp from sumpy.kernel import LaplaceKernel kernel = LaplaceKernel(3) sigma_sym = sym.var("sigma") #sqrt_w = sym.sqrt_jac_q_weight(3) sqrt_w = 1 inv_sqrt_w_sigma = sym.cse(sigma_sym / sqrt_w) # -1 for interior Dirichlet # +1 for exterior Dirichlet loc_sign = +1 bdry_op_sym = (loc_sign * 0.5 * sigma_sym + sqrt_w * (sym.S(kernel, inv_sqrt_w_sigma, qbx_forced_limit=+1) + sym.D(kernel, inv_sqrt_w_sigma, qbx_forced_limit="avg"))) # }}} bound_op = bind(places, bdry_op_sym) # {{{ fix rhs and solve from meshmode.dof_array import thaw, flatten, unflatten nodes = thaw(actx, density_discr.nodes()) source = np.array([rout, 0, 0]) def u_incoming_func(x): from pytools.obj_array import obj_array_vectorize x = obj_array_vectorize(actx.to_numpy, flatten(x)) x = np.array(list(x)) # return 1/cl.clmath.sqrt( (x[0] - source[0])**2 # +(x[1] - source[1])**2 # +(x[2] - source[2])**2 ) return 1.0 / la.norm(x - source[:, None], axis=0) bc = unflatten(actx, density_discr, actx.from_numpy(u_incoming_func(nodes))) bvp_rhs = bind(places, sqrt_w * sym.var("bc"))(actx, bc=bc) from pytential.solve import gmres gmres_result = gmres(bound_op.scipy_op(actx, "sigma", dtype=np.float64), bvp_rhs, tol=1e-14, progress=True, stall_iterations=0, hard_failure=True) sigma = bind(places, sym.var("sigma") / sqrt_w)(actx, sigma=gmres_result.solution) # }}} from meshmode.discretization.visualization import make_visualizer bdry_vis = make_visualizer(actx, density_discr, 20) bdry_vis.write_vtk_file("laplace.vtu", [ ("sigma", sigma), ]) # {{{ postprocess/visualize repr_kwargs = dict(source="qbx_target_assoc", target="targets", qbx_forced_limit=None) representation_sym = (sym.S(kernel, inv_sqrt_w_sigma, **repr_kwargs) + sym.D(kernel, inv_sqrt_w_sigma, **repr_kwargs)) try: fld_in_vol = actx.to_numpy( bind(places, representation_sym)(actx, sigma=sigma)) except QBXTargetAssociationFailedException as e: fplot.write_vtk_file("laplace-dirichlet-3d-failed-targets.vts", [ ("failed", e.failed_target_flags.get(queue)), ]) raise #fplot.show_scalar_in_mayavi(fld_in_vol.real, max_val=5) fplot.write_vtk_file("laplace-dirichlet-3d-potential.vts", [ ("potential", fld_in_vol), ])
def main(): # cl.array.to_device(queue, numpy_array) from meshmode.mesh.io import generate_gmsh, FileSource from meshmode.mesh.generation import generate_icosphere from meshmode.mesh.refinement import Refiner mesh = generate_icosphere(1, target_order) refinement_increment = 1 refiner = Refiner(mesh) for i in range(refinement_increment): flags = np.ones(mesh.nelements, dtype=bool) refiner.refine(flags) mesh = refiner.get_current_mesh() from meshmode.mesh.processing import perform_flips # Flip elements--gmsh generates inside-out geometry. mesh = perform_flips(mesh, np.ones(mesh.nelements)) print("%d elements" % mesh.nelements) from meshmode.mesh.processing import find_bounding_box bbox_min, bbox_max = find_bounding_box(mesh) bbox_center = 0.5 * (bbox_min + bbox_max) bbox_size = max(bbox_max - bbox_min) / 2 logger.info("%d elements" % mesh.nelements) from pytential.qbx import QBXLayerPotentialSource from meshmode.discretization import Discretization from meshmode.discretization.poly_element import \ InterpolatoryQuadratureSimplexGroupFactory density_discr = Discretization( cl_ctx, mesh, InterpolatoryQuadratureSimplexGroupFactory(target_order)) qbx = QBXLayerPotentialSource(density_discr, 4 * target_order, qbx_order, fmm_order=False, fmm_backend="fmmlib") from pytential.symbolic.pde.maxwell import MuellerAugmentedMFIEOperator pde_op = MuellerAugmentedMFIEOperator( omega=1.0, epss=[1.0, 1.0], mus=[1.0, 1.0], ) from pytential import bind, sym unk = pde_op.make_unknown("sigma") sym_operator = pde_op.operator(unk) sym_rhs = pde_op.rhs(sym.make_sym_vector("Einc", 3), sym.make_sym_vector("Hinc", 3)) sym_repr = pde_op.representation(1, unk) if 1: expr = sym_repr print(sym.pretty(expr)) print("#" * 80) from pytential.target import PointsTarget tgt_points = np.zeros((3, 1)) tgt_points[0, 0] = 100 tgt_points[1, 0] = -200 tgt_points[2, 0] = 300 bound_op = bind((qbx, PointsTarget(tgt_points)), expr) print(bound_op.code) if 1: def green3e(x, y, z, source, strength, k): # electric field corresponding to dyadic green's function # due to monochromatic electric dipole located at "source". # "strength" is the the intensity of the dipole. # E = (I + Hess)(exp(ikr)/r) dot (strength) # dx = x - source[0] dy = y - source[1] dz = z - source[2] rr = np.sqrt(dx**2 + dy**2 + dz**2) fout = np.exp(1j * k * rr) / rr evec = fout * strength qmat = np.zeros((3, 3), dtype=np.complex128) qmat[0, 0] = (2 * dx**2 - dy**2 - dz**2) * (1 - 1j * k * rr) qmat[1, 1] = (2 * dy**2 - dz**2 - dx**2) * (1 - 1j * k * rr) qmat[2, 2] = (2 * dz**2 - dx**2 - dy**2) * (1 - 1j * k * rr) qmat[0, 0] = qmat[0, 0] + (-k**2 * dx**2 * rr**2) qmat[1, 1] = qmat[1, 1] + (-k**2 * dy**2 * rr**2) qmat[2, 2] = qmat[2, 2] + (-k**2 * dz**2 * rr**2) qmat[0, 1] = (3 - k**2 * rr**2 - 3 * 1j * k * rr) * (dx * dy) qmat[1, 2] = (3 - k**2 * rr**2 - 3 * 1j * k * rr) * (dy * dz) qmat[2, 0] = (3 - k**2 * rr**2 - 3 * 1j * k * rr) * (dz * dx) qmat[1, 0] = qmat[0, 1] qmat[2, 1] = qmat[1, 2] qmat[0, 2] = qmat[2, 0] fout = np.exp(1j * k * rr) / rr**5 / k**2 fvec = fout * np.dot(qmat, strength) evec = evec + fvec return evec def green3m(x, y, z, source, strength, k): # magnetic field corresponding to dyadic green's function # due to monochromatic electric dipole located at "source". # "strength" is the the intensity of the dipole. # H = curl((I + Hess)(exp(ikr)/r) dot (strength)) = # strength \cross \grad (exp(ikr)/r) # dx = x - source[0] dy = y - source[1] dz = z - source[2] rr = np.sqrt(dx**2 + dy**2 + dz**2) fout = (1 - 1j * k * rr) * np.exp(1j * k * rr) / rr**3 fvec = np.zeros(3, dtype=np.complex128) fvec[0] = fout * dx fvec[1] = fout * dy fvec[2] = fout * dz hvec = np.cross(strength, fvec) return hvec def dipole3e(x, y, z, source, strength, k): # # evalaute electric and magnetic field due # to monochromatic electric dipole located at "source" # with intensity "strength" evec = green3e(x, y, z, source, strength, k) evec = evec * 1j * k hvec = green3m(x, y, z, source, strength, k) # print(hvec) # print(strength) return evec, hvec def dipole3m(x, y, z, source, strength, k): # # evalaute electric and magnetic field due # to monochromatic magnetic dipole located at "source" # with intensity "strength" evec = green3m(x, y, z, source, strength, k) hvec = green3e(x, y, z, source, strength, k) hvec = -hvec * 1j * k return evec, hvec def dipole3eall(x, y, z, sources, strengths, k): ns = len(strengths) evec = np.zeros(3, dtype=np.complex128) hvec = np.zeros(3, dtype=np.complex128) for i in range(ns): evect, hvect = dipole3e(x, y, z, sources[i], strengths[i], k) evec = evec + evect hvec = hvec + hvect nodes = density_discr.nodes().with_queue(queue).get() source = [0.01, -0.03, 0.02] # source = cl.array.to_device(queue,np.zeros(3)) # source[0] = 0.01 # source[1] =-0.03 # source[2] = 0.02 strength = np.ones(3) # evec = cl.array.to_device(queue,np.zeros((3,len(nodes[0])),dtype=np.complex128)) # hvec = cl.array.to_device(queue,np.zeros((3,len(nodes[0])),dtype=np.complex128)) evec = np.zeros((3, len(nodes[0])), dtype=np.complex128) hvec = np.zeros((3, len(nodes[0])), dtype=np.complex128) for i in range(len(nodes[0])): evec[:, i], hvec[:, i] = dipole3e(nodes[0][i], nodes[1][i], nodes[2][i], source, strength, k) print(np.shape(hvec)) print(type(evec)) print(type(hvec)) evec = cl.array.to_device(queue, evec) hvec = cl.array.to_device(queue, hvec) bvp_rhs = bind(qbx, sym_rhs)(queue, Einc=evec, Hinc=hvec) print(np.shape(bvp_rhs)) print(type(bvp_rhs)) # print(bvp_rhs) 1 / -1 bound_op = bind(qbx, sym_operator) from pytential.solve import gmres if 1: gmres_result = gmres(bound_op.scipy_op(queue, "sigma", dtype=np.complex128, k=k), bvp_rhs, tol=1e-8, progress=True, stall_iterations=0, hard_failure=True) sigma = gmres_result.solution fld_at_tgt = bind((qbx, PointsTarget(tgt_points)), sym_repr)(queue, sigma=sigma, k=k) fld_at_tgt = np.array([fi.get() for fi in fld_at_tgt]) print(fld_at_tgt) fld_exact_e, fld_exact_h = dipole3e(tgt_points[0, 0], tgt_points[1, 0], tgt_points[2, 0], source, strength, k) print(fld_exact_e) print(fld_exact_h) 1 / 0 # }}} #mlab.figure(bgcolor=(1, 1, 1)) if 1: from meshmode.discretization.visualization import make_visualizer bdry_vis = make_visualizer(queue, density_discr, target_order) bdry_normals = bind(density_discr, sym.normal(3))(queue)\ .as_vector(dtype=object) bdry_vis.write_vtk_file("source.vtu", [ ("sigma", sigma), ("bdry_normals", bdry_normals), ]) fplot = FieldPlotter(bbox_center, extent=2 * bbox_size, npoints=(150, 150, 1)) qbx_stick_out = qbx.copy(target_stick_out_factor=0.1) from pytential.target import PointsTarget from pytential.qbx import QBXTargetAssociationFailedException rho_sym = sym.var("rho") try: fld_in_vol = bind((qbx_stick_out, PointsTarget(fplot.points)), sym.make_obj_array([ sym.S(pde_op.kernel, rho_sym, k=sym.var("k"), qbx_forced_limit=None), sym.d_dx( 3, sym.S(pde_op.kernel, rho_sym, k=sym.var("k"), qbx_forced_limit=None)), sym.d_dy( 3, sym.S(pde_op.kernel, rho_sym, k=sym.var("k"), qbx_forced_limit=None)), sym.d_dz( 3, sym.S(pde_op.kernel, rho_sym, k=sym.var("k"), qbx_forced_limit=None)), ]))(queue, jt=jt, rho=rho, k=k) except QBXTargetAssociationFailedException as e: fplot.write_vtk_file( "failed-targets.vts", [("failed_targets", e.failed_target_flags.get(queue))]) raise fld_in_vol = sym.make_obj_array([fiv.get() for fiv in fld_in_vol]) #fplot.show_scalar_in_mayavi(fld_in_vol.real, max_val=5) fplot.write_vtk_file("potential.vts", [ ("potential", fld_in_vol[0]), ("grad", fld_in_vol[1:]), ])
def test_cost_model_correctness(actx_factory, dim, off_surface, use_target_specific_qbx): """Check that computed cost matches that of a constant-one FMM.""" actx = actx_factory() queue = actx.queue cost_model = QBXCostModel( translation_cost_model_factory=OpCountingTranslationCostModel) lpot_source = get_lpot_source(actx, dim).copy( cost_model=cost_model, _use_target_specific_qbx=use_target_specific_qbx) # Construct targets. if off_surface: from pytential.target import PointsTarget from boxtree.tools import make_uniform_particle_array ntargets = 10**3 targets = PointsTarget( make_uniform_particle_array(queue, ntargets, dim, np.float64)) target_discrs_and_qbx_sides = ((targets, 0), ) qbx_forced_limit = None else: targets = lpot_source.density_discr target_discrs_and_qbx_sides = ((targets, 1), ) qbx_forced_limit = 1 places = GeometryCollection((lpot_source, targets)) source_dd = places.auto_source density_discr = places.get_discretization(source_dd.geometry) # Construct bound op, run cost model. sigma_sym = sym.var("sigma") k_sym = LaplaceKernel(lpot_source.ambient_dim) sym_op_S = sym.S(k_sym, sigma_sym, qbx_forced_limit=qbx_forced_limit) op_S = bind(places, sym_op_S) sigma = get_density(actx, density_discr) modeled_time, _ = op_S.cost_per_stage("constant_one", sigma=sigma) modeled_time, = modeled_time.values() # Run FMM with ConstantOneWrangler. This can't be done with pytential's # high-level interface, so call the FMM driver directly. from pytential.qbx.fmm import drive_fmm geo_data = lpot_source.qbx_fmm_geometry_data( places, source_dd.geometry, target_discrs_and_qbx_sides=target_discrs_and_qbx_sides) wrangler = ConstantOneQBXExpansionWrangler( TreeIndependentDataForWrangler(), queue, geo_data, use_target_specific_qbx) quad_stage2_density_discr = places.get_discretization( source_dd.geometry, sym.QBX_SOURCE_QUAD_STAGE2) ndofs = quad_stage2_density_discr.ndofs src_weights = np.ones(ndofs) timing_data = {} potential = drive_fmm(wrangler, (src_weights, ), timing_data, traversal=wrangler.trav)[0][geo_data.ncenters:] # Check constant one wrangler for correctness. assert np.all(potential == ndofs) # Check that the cost model matches the timing data returned by the # constant one wrangler. mismatches = [] for stage in timing_data: if stage not in modeled_time: assert timing_data[stage]["ops_elapsed"] == 0 else: if timing_data[stage]["ops_elapsed"] != modeled_time[stage]: mismatches.append((stage, timing_data[stage]["ops_elapsed"], modeled_time[stage])) assert not mismatches, "\n".join(str(s) for s in mismatches) # {{{ Test per-box cost total_cost = 0.0 for stage in timing_data: total_cost += timing_data[stage]["ops_elapsed"] per_box_cost, _ = op_S.cost_per_box("constant_one", sigma=sigma) logging.info(per_box_cost) per_box_cost, = per_box_cost.values() total_aggregate_cost = cost_model.aggregate_over_boxes(per_box_cost) assert total_cost == (total_aggregate_cost + modeled_time["coarsen_multipoles"] + modeled_time["refine_locals"])
def test_target_specific_qbx(ctx_factory, op, helmholtz_k, qbx_order): logging.basicConfig(level=logging.INFO) cl_ctx = ctx_factory() queue = cl.CommandQueue(cl_ctx) actx = PyOpenCLArrayContext(queue) target_order = 4 fmm_tol = 1e-3 from meshmode.mesh.generation import generate_icosphere mesh = generate_icosphere(1, target_order) from meshmode.discretization import Discretization from meshmode.discretization.poly_element import \ InterpolatoryQuadratureSimplexGroupFactory from pytential.qbx import QBXLayerPotentialSource pre_density_discr = Discretization( actx, mesh, InterpolatoryQuadratureSimplexGroupFactory(target_order)) from sumpy.expansion.level_to_order import SimpleExpansionOrderFinder qbx = QBXLayerPotentialSource( pre_density_discr, 4 * target_order, qbx_order=qbx_order, fmm_level_to_order=SimpleExpansionOrderFinder(fmm_tol), fmm_backend="fmmlib", _expansions_in_tree_have_extent=True, _expansion_stick_out_factor=0.9, _use_target_specific_qbx=False, ) kernel_length_scale = 5 / abs(helmholtz_k) if helmholtz_k else None places = { "qbx": qbx, "qbx_target_specific": qbx.copy(_use_target_specific_qbx=True) } from pytential.qbx.refinement import refine_geometry_collection places = GeometryCollection(places, auto_where="qbx") places = refine_geometry_collection( places, kernel_length_scale=kernel_length_scale) density_discr = places.get_discretization("qbx") from meshmode.dof_array import thaw nodes = thaw(actx, density_discr.nodes()) u_dev = actx.np.sin(nodes[0]) if helmholtz_k == 0: kernel = LaplaceKernel(3) kernel_kwargs = {} else: kernel = HelmholtzKernel(3, allow_evanescent=True) kernel_kwargs = {"k": sym.var("k")} u_sym = sym.var("u") if op == "S": op = sym.S elif op == "D": op = sym.D elif op == "Sp": op = sym.Sp else: raise ValueError("unknown operator: '%s'" % op) expr = op(kernel, u_sym, qbx_forced_limit=-1, **kernel_kwargs) from meshmode.dof_array import flatten bound_op = bind(places, expr) pot_ref = actx.to_numpy(flatten(bound_op(actx, u=u_dev, k=helmholtz_k))) bound_op = bind(places, expr, auto_where="qbx_target_specific") pot_tsqbx = actx.to_numpy(flatten(bound_op(actx, u=u_dev, k=helmholtz_k))) assert np.allclose(pot_tsqbx, pot_ref, atol=1e-13, rtol=1e-13)
def test_3d_jump_relations(ctx_factory, relation, visualize=False): # logging.basicConfig(level=logging.INFO) cl_ctx = ctx_factory() queue = cl.CommandQueue(cl_ctx) if relation == "div_s": target_order = 3 else: target_order = 4 qbx_order = target_order from pytools.convergence import EOCRecorder eoc_rec = EOCRecorder() for nel_factor in [6, 10, 14]: from meshmode.mesh.generation import generate_torus mesh = generate_torus(5, 2, order=target_order, n_major=2 * nel_factor, n_minor=nel_factor) from meshmode.discretization import Discretization from meshmode.discretization.poly_element import \ InterpolatoryQuadratureSimplexGroupFactory pre_discr = Discretization( cl_ctx, mesh, InterpolatoryQuadratureSimplexGroupFactory(3)) from pytential.qbx import QBXLayerPotentialSource qbx, _ = QBXLayerPotentialSource( pre_discr, fine_order=4 * target_order, qbx_order=qbx_order, fmm_order=qbx_order + 5, fmm_backend="fmmlib").with_refinement() from sumpy.kernel import LaplaceKernel knl = LaplaceKernel(3) def nxcurlS(qbx_forced_limit): return sym.n_cross( sym.curl( sym.S(knl, sym.cse(sym.tangential_to_xyz(density_sym), "jxyz"), qbx_forced_limit=qbx_forced_limit))) x, y, z = qbx.density_discr.nodes().with_queue(queue) m = cl.clmath if relation == "nxcurls": density_sym = sym.make_sym_vector("density", 2) jump_identity_sym = ( nxcurlS(+1) - (nxcurlS("avg") + 0.5 * sym.tangential_to_xyz(density_sym))) # The tangential coordinate system is element-local, so we can't just # conjure up some globally smooth functions, interpret their values # in the tangential coordinate system, and be done. Instead, generate # an XYZ function and project it. density = bind( qbx, sym.xyz_to_tangential(sym.make_sym_vector("jxyz", 3)))( queue, jxyz=sym.make_obj_array([ m.cos(0.5 * x) * m.cos(0.5 * y) * m.cos(0.5 * z), m.sin(0.5 * x) * m.cos(0.5 * y) * m.sin(0.5 * z), m.sin(0.5 * x) * m.cos(0.5 * y) * m.cos(0.5 * z), ])) elif relation == "sp": density = m.cos(2 * x) * m.cos(2 * y) * m.cos(z) density_sym = sym.var("density") jump_identity_sym = ( sym.Sp(knl, density_sym, qbx_forced_limit=+1) - (sym.Sp(knl, density_sym, qbx_forced_limit="avg") - 0.5 * density_sym)) elif relation == "div_s": density = m.cos(2 * x) * m.cos(2 * y) * m.cos(z) density_sym = sym.var("density") jump_identity_sym = ( sym.div( sym.S(knl, sym.normal(3).as_vector() * density_sym, qbx_forced_limit="avg")) + sym.D(knl, density_sym, qbx_forced_limit="avg")) else: raise ValueError("unexpected value of 'relation': %s" % relation) bound_jump_identity = bind(qbx, jump_identity_sym) jump_identity = bound_jump_identity(queue, density=density) h_max = bind(qbx, sym.h_max(qbx.ambient_dim))(queue) err = (norm(qbx, queue, jump_identity, np.inf) / norm(qbx, queue, density, np.inf)) print("ERROR", h_max, err) eoc_rec.add_data_point(h_max, err) # {{{ visualization if visualize and relation == "nxcurls": nxcurlS_ext = bind(qbx, nxcurlS(+1))(queue, density=density) nxcurlS_avg = bind(qbx, nxcurlS("avg"))(queue, density=density) jtxyz = bind(qbx, sym.tangential_to_xyz(density_sym))(queue, density=density) from meshmode.discretization.visualization import make_visualizer bdry_vis = make_visualizer(queue, qbx.density_discr, target_order + 3) bdry_normals = bind(qbx, sym.normal(3))(queue)\ .as_vector(dtype=object) bdry_vis.write_vtk_file("source-%s.vtu" % nel_factor, [ ("jt", jtxyz), ("nxcurlS_ext", nxcurlS_ext), ("nxcurlS_avg", nxcurlS_avg), ("bdry_normals", bdry_normals), ]) if visualize and relation == "sp": sp_ext = bind(qbx, sym.Sp(knl, density_sym, qbx_forced_limit=+1))(queue, density=density) sp_avg = bind(qbx, sym.Sp(knl, density_sym, qbx_forced_limit="avg"))(queue, density=density) from meshmode.discretization.visualization import make_visualizer bdry_vis = make_visualizer(queue, qbx.density_discr, target_order + 3) bdry_normals = bind(qbx, sym.normal(3))(queue)\ .as_vector(dtype=object) bdry_vis.write_vtk_file("source-%s.vtu" % nel_factor, [ ("density", density), ("sp_ext", sp_ext), ("sp_avg", sp_avg), ("bdry_normals", bdry_normals), ]) # }}} print(eoc_rec) assert eoc_rec.order_estimate() >= qbx_order - 1.5
def run_dielectric_test(cl_ctx, queue, nelements, qbx_order, op_class, mode, k0=3, k1=2.9, mesh_order=10, bdry_quad_order=None, bdry_ovsmp_quad_order=None, use_l2_weighting=False, fmm_order=None, visualize=False): if fmm_order is None: fmm_order = qbx_order * 2 if bdry_quad_order is None: bdry_quad_order = mesh_order if bdry_ovsmp_quad_order is None: bdry_ovsmp_quad_order = 4*bdry_quad_order from meshmode.mesh.generation import ellipse, make_curve_mesh from functools import partial mesh = make_curve_mesh( partial(ellipse, 3), np.linspace(0, 1, nelements+1), mesh_order) density_discr = Discretization( cl_ctx, mesh, InterpolatoryQuadratureSimplexGroupFactory(bdry_quad_order)) logger.info("%d elements" % mesh.nelements) # from meshmode.discretization.visualization import make_visualizer # bdry_vis = make_visualizer(queue, density_discr, 20) # {{{ solve bvp from sumpy.kernel import HelmholtzKernel, AxisTargetDerivative kernel = HelmholtzKernel(2) beta = 2.5 K0 = np.sqrt(k0**2-beta**2) # noqa K1 = np.sqrt(k1**2-beta**2) # noqa pde_op = op_class( mode, k_vacuum=1, interfaces=((0, 1, sym.DEFAULT_SOURCE),), domain_k_exprs=(k0, k1), beta=beta, use_l2_weighting=use_l2_weighting) op_unknown_sym = pde_op.make_unknown("unknown") representation0_sym = pde_op.representation(op_unknown_sym, 0) representation1_sym = pde_op.representation(op_unknown_sym, 1) from pytential.qbx import QBXLayerPotentialSource qbx = QBXLayerPotentialSource( density_discr, fine_order=bdry_ovsmp_quad_order, qbx_order=qbx_order, fmm_order=fmm_order ).with_refinement() #print(sym.pretty(pde_op.operator(op_unknown_sym))) #1/0 bound_pde_op = bind(qbx, pde_op.operator(op_unknown_sym)) e_factor = float(pde_op.ez_enabled) h_factor = float(pde_op.hz_enabled) e_sources_0 = make_obj_array(list(np.array([ [0.1, 0.2] ]).T.copy())) e_strengths_0 = np.array([1*e_factor]) e_sources_1 = make_obj_array(list(np.array([ [4, 4] ]).T.copy())) e_strengths_1 = np.array([1*e_factor]) h_sources_0 = make_obj_array(list(np.array([ [0.2, 0.1] ]).T.copy())) h_strengths_0 = np.array([1*h_factor]) h_sources_1 = make_obj_array(list(np.array([ [4, 5] ]).T.copy())) h_strengths_1 = np.array([1*h_factor]) kernel_grad = [ AxisTargetDerivative(i, kernel) for i in range(density_discr.ambient_dim)] from sumpy.p2p import P2P pot_p2p = P2P(cl_ctx, [kernel], exclude_self=False) pot_p2p_grad = P2P(cl_ctx, kernel_grad, exclude_self=False) normal = bind(density_discr, sym.normal())(queue).as_vector(np.object) tangent = bind( density_discr, sym.pseudoscalar()/sym.area_element())(queue).as_vector(np.object) _, (E0,) = pot_p2p(queue, density_discr.nodes(), e_sources_0, [e_strengths_0], out_host=False, k=K0) _, (E1,) = pot_p2p(queue, density_discr.nodes(), e_sources_1, [e_strengths_1], out_host=False, k=K1) _, (grad0_E0, grad1_E0) = pot_p2p_grad( queue, density_discr.nodes(), e_sources_0, [e_strengths_0], out_host=False, k=K0) _, (grad0_E1, grad1_E1) = pot_p2p_grad( queue, density_discr.nodes(), e_sources_1, [e_strengths_1], out_host=False, k=K1) _, (H0,) = pot_p2p(queue, density_discr.nodes(), h_sources_0, [h_strengths_0], out_host=False, k=K0) _, (H1,) = pot_p2p(queue, density_discr.nodes(), h_sources_1, [h_strengths_1], out_host=False, k=K1) _, (grad0_H0, grad1_H0) = pot_p2p_grad( queue, density_discr.nodes(), h_sources_0, [h_strengths_0], out_host=False, k=K0) _, (grad0_H1, grad1_H1) = pot_p2p_grad( queue, density_discr.nodes(), h_sources_1, [h_strengths_1], out_host=False, k=K1) E0_dntarget = (grad0_E0*normal[0] + grad1_E0*normal[1]) # noqa E1_dntarget = (grad0_E1*normal[0] + grad1_E1*normal[1]) # noqa H0_dntarget = (grad0_H0*normal[0] + grad1_H0*normal[1]) # noqa H1_dntarget = (grad0_H1*normal[0] + grad1_H1*normal[1]) # noqa E0_dttarget = (grad0_E0*tangent[0] + grad1_E0*tangent[1]) # noqa E1_dttarget = (grad0_E1*tangent[0] + grad1_E1*tangent[1]) # noqa H0_dttarget = (grad0_H0*tangent[0] + grad1_H0*tangent[1]) # noqa H1_dttarget = (grad0_H1*tangent[0] + grad1_H1*tangent[1]) # noqa sqrt_w = bind(density_discr, sym.sqrt_jac_q_weight())(queue) bvp_rhs = np.zeros(len(pde_op.bcs), dtype=np.object) for i_bc, terms in enumerate(pde_op.bcs): for term in terms: assert term.i_interface == 0 if term.field_kind == pde_op.field_kind_e: if term.direction == pde_op.dir_none: bvp_rhs[i_bc] += ( term.coeff_outer * E0 + term.coeff_inner * E1) elif term.direction == pde_op.dir_normal: bvp_rhs[i_bc] += ( term.coeff_outer * E0_dntarget + term.coeff_inner * E1_dntarget) elif term.direction == pde_op.dir_tangential: bvp_rhs[i_bc] += ( term.coeff_outer * E0_dttarget + term.coeff_inner * E1_dttarget) else: raise NotImplementedError("direction spec in RHS") elif term.field_kind == pde_op.field_kind_h: if term.direction == pde_op.dir_none: bvp_rhs[i_bc] += ( term.coeff_outer * H0 + term.coeff_inner * H1) elif term.direction == pde_op.dir_normal: bvp_rhs[i_bc] += ( term.coeff_outer * H0_dntarget + term.coeff_inner * H1_dntarget) elif term.direction == pde_op.dir_tangential: bvp_rhs[i_bc] += ( term.coeff_outer * H0_dttarget + term.coeff_inner * H1_dttarget) else: raise NotImplementedError("direction spec in RHS") if use_l2_weighting: bvp_rhs[i_bc] *= sqrt_w scipy_op = bound_pde_op.scipy_op(queue, "unknown", domains=[sym.DEFAULT_TARGET]*len(pde_op.bcs), K0=K0, K1=K1, dtype=np.complex128) if mode == "tem" or op_class is SRep: from sumpy.tools import vector_from_device, vector_to_device from pytential.solve import lu unknown = lu(scipy_op, vector_from_device(queue, bvp_rhs)) unknown = vector_to_device(queue, unknown) else: from pytential.solve import gmres gmres_result = gmres(scipy_op, bvp_rhs, tol=1e-14, progress=True, hard_failure=True, stall_iterations=0) unknown = gmres_result.solution # }}} targets_0 = make_obj_array(list(np.array([ [3.2 + t, -4] for t in [0, 0.5, 1] ]).T.copy())) targets_1 = make_obj_array(list(np.array([ [t*-0.3, t*-0.2] for t in [0, 0.5, 1] ]).T.copy())) from pytential.target import PointsTarget from sumpy.tools import vector_from_device F0_tgt = vector_from_device(queue, bind( # noqa (qbx, PointsTarget(targets_0)), representation0_sym)(queue, unknown=unknown, K0=K0, K1=K1)) F1_tgt = vector_from_device(queue, bind( # noqa (qbx, PointsTarget(targets_1)), representation1_sym)(queue, unknown=unknown, K0=K0, K1=K1)) _, (E0_tgt_true,) = pot_p2p(queue, targets_0, e_sources_0, [e_strengths_0], out_host=True, k=K0) _, (E1_tgt_true,) = pot_p2p(queue, targets_1, e_sources_1, [e_strengths_1], out_host=True, k=K1) _, (H0_tgt_true,) = pot_p2p(queue, targets_0, h_sources_0, [h_strengths_0], out_host=True, k=K0) _, (H1_tgt_true,) = pot_p2p(queue, targets_1, h_sources_1, [h_strengths_1], out_host=True, k=K1) err_F0_total = 0 # noqa err_F1_total = 0 # noqa i_field = 0 def vec_norm(ary): return la.norm(ary.reshape(-1)) def field_kind_to_string(field_kind): return {pde_op.field_kind_e: "E", pde_op.field_kind_h: "H"}[field_kind] for field_kind in pde_op.field_kinds: if not pde_op.is_field_present(field_kind): continue if field_kind == pde_op.field_kind_e: F0_tgt_true = E0_tgt_true # noqa F1_tgt_true = E1_tgt_true # noqa elif field_kind == pde_op.field_kind_h: F0_tgt_true = H0_tgt_true # noqa F1_tgt_true = H1_tgt_true # noqa else: assert False abs_err_F0 = vec_norm(F0_tgt[i_field] - F0_tgt_true) # noqa abs_err_F1 = vec_norm(F1_tgt[i_field] - F1_tgt_true) # noqa rel_err_F0 = abs_err_F0/vec_norm(F0_tgt_true) # noqa rel_err_F1 = abs_err_F1/vec_norm(F1_tgt_true) # noqa err_F0_total = max(rel_err_F0, err_F0_total) # noqa err_F1_total = max(rel_err_F1, err_F1_total) # noqa print("Abs Err %s0" % field_kind_to_string(field_kind), abs_err_F0) print("Abs Err %s1" % field_kind_to_string(field_kind), abs_err_F1) print("Rel Err %s0" % field_kind_to_string(field_kind), rel_err_F0) print("Rel Err %s1" % field_kind_to_string(field_kind), rel_err_F1) i_field += 1 if visualize: from sumpy.visualization import FieldPlotter fplot = FieldPlotter(np.zeros(2), extent=5, npoints=300) from pytential.target import PointsTarget fld0 = bind( (qbx, PointsTarget(fplot.points)), representation0_sym)(queue, unknown=unknown, K0=K0) fld1 = bind( (qbx, PointsTarget(fplot.points)), representation1_sym)(queue, unknown=unknown, K1=K1) comp_fields = [] i_field = 0 for field_kind in pde_op.field_kinds: if not pde_op.is_field_present(field_kind): continue fld_str = field_kind_to_string(field_kind) comp_fields.extend([ ("%s_fld0" % fld_str, fld0[i_field].get()), ("%s_fld1" % fld_str, fld1[i_field].get()), ]) i_field += 0 low_order_qbx = QBXLayerPotentialSource( density_discr, fine_order=bdry_ovsmp_quad_order, qbx_order=2, fmm_order=3).with_refinement() from sumpy.kernel import LaplaceKernel from pytential.target import PointsTarget ones = (cl.array.empty(queue, (density_discr.nnodes,), dtype=np.float64) .fill(1)) ind_func = - bind((low_order_qbx, PointsTarget(fplot.points)), sym.D(LaplaceKernel(2), sym.var("u")))( queue, u=ones).get() _, (e_fld0_true,) = pot_p2p( queue, fplot.points, e_sources_0, [e_strengths_0], out_host=True, k=K0) _, (e_fld1_true,) = pot_p2p( queue, fplot.points, e_sources_1, [e_strengths_1], out_host=True, k=K1) _, (h_fld0_true,) = pot_p2p( queue, fplot.points, h_sources_0, [h_strengths_0], out_host=True, k=K0) _, (h_fld1_true,) = pot_p2p( queue, fplot.points, h_sources_1, [h_strengths_1], out_host=True, k=K1) #fplot.show_scalar_in_mayavi(fld_in_vol.real, max_val=5) fplot.write_vtk_file( "potential-n%d.vts" % nelements, [ ("e_fld0_true", e_fld0_true), ("e_fld1_true", e_fld1_true), ("h_fld0_true", h_fld0_true), ("h_fld1_true", h_fld1_true), ("ind", ind_func), ] + comp_fields ) return err_F0_total, err_F1_total
def op(**kwargs): kwargs.update(kernel_kwargs) #op = sym.d_dx(sym.S(kernel, sym.var("sigma"), **kwargs)) return sym.D(kernel, sym.var("sigma"), **kwargs)
mesh = make_curve_mesh(starfish, np.linspace(0, 1, nelements+1), target_order) from pytential.discretization.qbx import make_upsampling_qbx_discr discr = make_upsampling_qbx_discr( cl_ctx, mesh, target_order, qbx_order) nodes = discr.nodes().with_queue(queue) angle = cl.clmath.atan2(nodes[1], nodes[0]) from pytential import bind, sym representation = sym.D(0, sym.var("sigma")) op = representation - 0.5*sym.var("sigma") bc = cl.clmath.cos(mode_nr*angle) bound_op = bind(discr, op) from pytential.gmres import gmres gmres_result = gmres( bound_op.scipy_op(queue, "sigma"), bc, tol=1e-14, progress=True, hard_failure=True) import sys sys.exit() sigma = gmres_result.solution
def test_cost_model_correctness(ctx_factory, dim, off_surface, use_target_specific_qbx): """Check that computed cost matches that of a constant-one FMM.""" cl_ctx = ctx_factory() queue = cl.CommandQueue(cl_ctx) actx = PyOpenCLArrayContext(queue) cost_model = ( CostModel( translation_cost_model_factory=OpCountingTranslationCostModel)) lpot_source = get_lpot_source(actx, dim).copy( cost_model=cost_model, _use_target_specific_qbx=use_target_specific_qbx) # Construct targets. if off_surface: from pytential.target import PointsTarget from boxtree.tools import make_uniform_particle_array ntargets = 10 ** 3 targets = PointsTarget( make_uniform_particle_array(queue, ntargets, dim, np.float)) target_discrs_and_qbx_sides = ((targets, 0),) qbx_forced_limit = None else: targets = lpot_source.density_discr target_discrs_and_qbx_sides = ((targets, 1),) qbx_forced_limit = 1 places = GeometryCollection((lpot_source, targets)) source_dd = places.auto_source density_discr = places.get_discretization(source_dd.geometry) # Construct bound op, run cost model. sigma_sym = sym.var("sigma") k_sym = LaplaceKernel(lpot_source.ambient_dim) sym_op_S = sym.S(k_sym, sigma_sym, qbx_forced_limit=qbx_forced_limit) op_S = bind(places, sym_op_S) sigma = get_density(actx, density_discr) from pytools import one cost_S = one(op_S.get_modeled_cost(actx, sigma=sigma).values()) # Run FMM with ConstantOneWrangler. This can't be done with pytential's # high-level interface, so call the FMM driver directly. from pytential.qbx.fmm import drive_fmm geo_data = lpot_source.qbx_fmm_geometry_data( places, source_dd.geometry, target_discrs_and_qbx_sides=target_discrs_and_qbx_sides) wrangler = ConstantOneQBXExpansionWrangler( queue, geo_data, use_target_specific_qbx) quad_stage2_density_discr = places.get_discretization( source_dd.geometry, sym.QBX_SOURCE_QUAD_STAGE2) ndofs = quad_stage2_density_discr.ndofs src_weights = np.ones(ndofs) timing_data = {} potential = drive_fmm(wrangler, src_weights, timing_data, traversal=wrangler.trav)[0][geo_data.ncenters:] # Check constant one wrangler for correctness. assert (potential == ndofs).all() modeled_time = cost_S.get_predicted_times(merge_close_lists=True) # Check that the cost model matches the timing data returned by the # constant one wrangler. mismatches = [] for stage in timing_data: if timing_data[stage]["ops_elapsed"] != modeled_time[stage]: mismatches.append( (stage, timing_data[stage]["ops_elapsed"], modeled_time[stage])) assert not mismatches, "\n".join(str(s) for s in mismatches)
def test_off_surface_eval_vs_direct(ctx_factory, do_plot=False): logging.basicConfig(level=logging.INFO) cl_ctx = ctx_factory() queue = cl.CommandQueue(cl_ctx) # prevent cache 'splosion from sympy.core.cache import clear_cache clear_cache() nelements = 300 target_order = 8 qbx_order = 3 mesh = make_curve_mesh(WobblyCircle.random(8, seed=30), np.linspace(0, 1, nelements + 1), target_order) from pytential.qbx import QBXLayerPotentialSource from meshmode.discretization import Discretization from meshmode.discretization.poly_element import \ InterpolatoryQuadratureSimplexGroupFactory pre_density_discr = Discretization( cl_ctx, mesh, InterpolatoryQuadratureSimplexGroupFactory(target_order)) direct_qbx, _ = QBXLayerPotentialSource( pre_density_discr, 4 * target_order, qbx_order, fmm_order=False, target_association_tolerance=0.05, ).with_refinement() fmm_qbx, _ = QBXLayerPotentialSource( pre_density_discr, 4 * target_order, qbx_order, fmm_order=qbx_order + 3, _expansions_in_tree_have_extent=True, target_association_tolerance=0.05, ).with_refinement() fplot = FieldPlotter(np.zeros(2), extent=5, npoints=500) from pytential.target import PointsTarget ptarget = PointsTarget(fplot.points) from sumpy.kernel import LaplaceKernel op = sym.D(LaplaceKernel(2), sym.var("sigma"), qbx_forced_limit=None) from pytential.qbx import QBXTargetAssociationFailedException try: direct_density_discr = direct_qbx.density_discr direct_sigma = direct_density_discr.zeros(queue) + 1 direct_fld_in_vol = bind((direct_qbx, ptarget), op)(queue, sigma=direct_sigma) except QBXTargetAssociationFailedException as e: fplot.show_scalar_in_matplotlib(e.failed_target_flags.get(queue)) import matplotlib.pyplot as pt pt.show() raise fmm_density_discr = fmm_qbx.density_discr fmm_sigma = fmm_density_discr.zeros(queue) + 1 fmm_fld_in_vol = bind((fmm_qbx, ptarget), op)(queue, sigma=fmm_sigma) err = cl.clmath.fabs(fmm_fld_in_vol - direct_fld_in_vol) linf_err = cl.array.max(err).get() print("l_inf error:", linf_err) if do_plot: #fplot.show_scalar_in_mayavi(0.1*.get(queue)) fplot.write_vtk_file( "potential.vts", [("fmm_fld_in_vol", fmm_fld_in_vol.get(queue)), ("direct_fld_in_vol", direct_fld_in_vol.get(queue))]) assert linf_err < 1e-3
def main(mesh_name="ellipse", visualize=False): import logging logging.basicConfig(level=logging.WARNING) # INFO for more progress info cl_ctx = cl.create_some_context() queue = cl.CommandQueue(cl_ctx) actx = PyOpenCLArrayContext(queue) from meshmode.mesh.generation import ellipse, make_curve_mesh from functools import partial if mesh_name == "ellipse": mesh = make_curve_mesh( partial(ellipse, 1), np.linspace(0, 1, nelements+1), mesh_order) elif mesh_name == "ellipse_array": base_mesh = make_curve_mesh( partial(ellipse, 1), np.linspace(0, 1, nelements+1), mesh_order) from meshmode.mesh.processing import affine_map, merge_disjoint_meshes nx = 2 ny = 2 dx = 2 / nx meshes = [ affine_map( base_mesh, A=np.diag([dx*0.25, dx*0.25]), b=np.array([dx*(ix-nx/2), dx*(iy-ny/2)])) for ix in range(nx) for iy in range(ny)] mesh = merge_disjoint_meshes(meshes, single_group=True) if visualize: from meshmode.mesh.visualization import draw_curve draw_curve(mesh) import matplotlib.pyplot as plt plt.show() else: raise ValueError("unknown mesh name: {}".format(mesh_name)) pre_density_discr = Discretization( actx, mesh, InterpolatoryQuadratureSimplexGroupFactory(bdry_quad_order)) from pytential.qbx import ( QBXLayerPotentialSource, QBXTargetAssociationFailedException) qbx = QBXLayerPotentialSource( pre_density_discr, fine_order=bdry_ovsmp_quad_order, qbx_order=qbx_order, fmm_order=fmm_order ) from sumpy.visualization import FieldPlotter fplot = FieldPlotter(np.zeros(2), extent=5, npoints=500) targets = actx.from_numpy(fplot.points) from pytential import GeometryCollection places = GeometryCollection({ "qbx": qbx, "qbx_high_target_assoc_tol": qbx.copy(target_association_tolerance=0.05), "targets": PointsTarget(targets) }, auto_where="qbx") density_discr = places.get_discretization("qbx") # {{{ describe bvp from sumpy.kernel import LaplaceKernel, HelmholtzKernel kernel = HelmholtzKernel(2) sigma_sym = sym.var("sigma") sqrt_w = sym.sqrt_jac_q_weight(2) inv_sqrt_w_sigma = sym.cse(sigma_sym/sqrt_w) # Brakhage-Werner parameter alpha = 1j # -1 for interior Dirichlet # +1 for exterior Dirichlet loc_sign = +1 k_sym = sym.var("k") bdry_op_sym = (-loc_sign*0.5*sigma_sym + sqrt_w*( alpha*sym.S(kernel, inv_sqrt_w_sigma, k=k_sym, qbx_forced_limit=+1) - sym.D(kernel, inv_sqrt_w_sigma, k=k_sym, qbx_forced_limit="avg") )) # }}} bound_op = bind(places, bdry_op_sym) # {{{ fix rhs and solve from meshmode.dof_array import thaw nodes = thaw(actx, density_discr.nodes()) k_vec = np.array([2, 1]) k_vec = k * k_vec / la.norm(k_vec, 2) def u_incoming_func(x): return actx.np.exp( 1j * (x[0] * k_vec[0] + x[1] * k_vec[1])) bc = -u_incoming_func(nodes) bvp_rhs = bind(places, sqrt_w*sym.var("bc"))(actx, bc=bc) from pytential.solve import gmres gmres_result = gmres( bound_op.scipy_op(actx, sigma_sym.name, dtype=np.complex128, k=k), bvp_rhs, tol=1e-8, progress=True, stall_iterations=0, hard_failure=True) # }}} # {{{ postprocess/visualize repr_kwargs = dict( source="qbx_high_target_assoc_tol", target="targets", qbx_forced_limit=None) representation_sym = ( alpha*sym.S(kernel, inv_sqrt_w_sigma, k=k_sym, **repr_kwargs) - sym.D(kernel, inv_sqrt_w_sigma, k=k_sym, **repr_kwargs)) u_incoming = u_incoming_func(targets) ones_density = density_discr.zeros(actx) for elem in ones_density: elem.fill(1) indicator = actx.to_numpy( bind(places, sym.D(LaplaceKernel(2), sigma_sym, **repr_kwargs))( actx, sigma=ones_density)) try: fld_in_vol = actx.to_numpy( bind(places, representation_sym)( actx, sigma=gmres_result.solution, k=k)) except QBXTargetAssociationFailedException as e: fplot.write_vtk_file("helmholtz-dirichlet-failed-targets.vts", [ ("failed", e.failed_target_flags.get(queue)) ]) raise #fplot.show_scalar_in_mayavi(fld_in_vol.real, max_val=5) fplot.write_vtk_file("helmholtz-dirichlet-potential.vts", [ ("potential", fld_in_vol), ("indicator", indicator), ("u_incoming", actx.to_numpy(u_incoming)), ])
def main(): import logging logging.basicConfig(level=logging.WARNING) # INFO for more progress info cl_ctx = cl.create_some_context() queue = cl.CommandQueue(cl_ctx) target_order = 16 qbx_order = 3 nelements = 60 mode_nr = 0 k = 0 if k: kernel = HelmholtzKernel(2) else: kernel = LaplaceKernel(2) #kernel = OneKernel() mesh = make_curve_mesh( #lambda t: ellipse(1, t), starfish, np.linspace(0, 1, nelements+1), target_order) from pytential.qbx import QBXLayerPotentialSource from meshmode.discretization import Discretization from meshmode.discretization.poly_element import \ InterpolatoryQuadratureSimplexGroupFactory pre_density_discr = Discretization( cl_ctx, mesh, InterpolatoryQuadratureSimplexGroupFactory(target_order)) slow_qbx, _ = QBXLayerPotentialSource( pre_density_discr, fine_order=2*target_order, qbx_order=qbx_order, fmm_order=False, target_association_tolerance=.05 ).with_refinement() qbx = slow_qbx.copy(fmm_order=10) density_discr = slow_qbx.density_discr nodes = density_discr.nodes().with_queue(queue) angle = cl.clmath.atan2(nodes[1], nodes[0]) from pytential import bind, sym #op = sym.d_dx(sym.S(kernel, sym.var("sigma")), qbx_forced_limit=None) #op = sym.D(kernel, sym.var("sigma"), qbx_forced_limit=None) op = sym.S(kernel, sym.var("sigma"), qbx_forced_limit=None) sigma = cl.clmath.cos(mode_nr*angle) if isinstance(kernel, HelmholtzKernel): sigma = sigma.astype(np.complex128) fplot = FieldPlotter(np.zeros(2), extent=5, npoints=600) from pytential.target import PointsTarget fld_in_vol = bind( (slow_qbx, PointsTarget(fplot.points)), op)(queue, sigma=sigma, k=k).get() fmm_fld_in_vol = bind( (qbx, PointsTarget(fplot.points)), op)(queue, sigma=sigma, k=k).get() err = fmm_fld_in_vol-fld_in_vol import matplotlib matplotlib.use('Agg') im = fplot.show_scalar_in_matplotlib(np.log10(np.abs(err) + 1e-17)) from matplotlib.colors import Normalize im.set_norm(Normalize(vmin=-12, vmax=0)) import matplotlib.pyplot as pt from matplotlib.ticker import NullFormatter pt.gca().xaxis.set_major_formatter(NullFormatter()) pt.gca().yaxis.set_major_formatter(NullFormatter()) cb = pt.colorbar(shrink=0.9) cb.set_label(r"$\log_{10}(\mathdefault{Error})$") pt.savefig("fmm-error-order-%d.pdf" % qbx_order)
def run_exterior_stokes_2d( ctx_factory, nelements, mesh_order=4, target_order=4, qbx_order=4, fmm_order=False, # FIXME: FMM is slower than direct eval mu=1, circle_rad=1.5, visualize=False): # This program tests an exterior Stokes flow in 2D using the # compound representation given in Hsiao & Kress, # ``On an integral equation for the two-dimensional exterior Stokes problem,'' # Applied Numerical Mathematics 1 (1985). logging.basicConfig(level=logging.INFO) cl_ctx = cl.create_some_context() queue = cl.CommandQueue(cl_ctx) actx = PyOpenCLArrayContext(queue) ovsmp_target_order = 4 * target_order # {{{ geometries from meshmode.mesh.generation import ( # noqa make_curve_mesh, starfish, ellipse, drop) mesh = make_curve_mesh(lambda t: circle_rad * ellipse(1, t), np.linspace(0, 1, nelements + 1), target_order) coarse_density_discr = Discretization( actx, mesh, InterpolatoryQuadratureSimplexGroupFactory(target_order)) from pytential.qbx import QBXLayerPotentialSource target_association_tolerance = 0.05 qbx = QBXLayerPotentialSource( coarse_density_discr, fine_order=ovsmp_target_order, qbx_order=qbx_order, fmm_order=fmm_order, target_association_tolerance=target_association_tolerance, _expansions_in_tree_have_extent=True, ) def circle_mask(test_points, radius): return (test_points[0, :]**2 + test_points[1, :]**2 > radius**2) def outside_circle(test_points, radius): mask = circle_mask(test_points, radius) return np.array([row[mask] for row in test_points]) from pytential.target import PointsTarget nsamp = 30 eval_points_1d = np.linspace(-3., 3., nsamp) eval_points = np.zeros((2, len(eval_points_1d)**2)) eval_points[0, :] = np.tile(eval_points_1d, len(eval_points_1d)) eval_points[1, :] = np.repeat(eval_points_1d, len(eval_points_1d)) eval_points = outside_circle(eval_points, radius=circle_rad) point_targets = PointsTarget(eval_points) fplot = FieldPlotter(np.zeros(2), extent=6, npoints=100) plot_targets = PointsTarget(outside_circle(fplot.points, radius=circle_rad)) places = GeometryCollection({ sym.DEFAULT_SOURCE: qbx, sym.DEFAULT_TARGET: qbx.density_discr, "point_target": point_targets, "plot_target": plot_targets, }) density_discr = places.get_discretization(sym.DEFAULT_SOURCE) normal = bind(places, sym.normal(2).as_vector())(actx) path_length = bind(places, sym.integral(2, 1, 1))(actx) # }}} # {{{ describe bvp from pytential.symbolic.stokes import StressletWrapper, StokesletWrapper dim = 2 cse = sym.cse sigma_sym = sym.make_sym_vector("sigma", dim) meanless_sigma_sym = cse(sigma_sym - sym.mean(2, 1, sigma_sym)) int_sigma = sym.Ones() * sym.integral(2, 1, sigma_sym) nvec_sym = sym.make_sym_vector("normal", dim) mu_sym = sym.var("mu") # -1 for interior Dirichlet # +1 for exterior Dirichlet loc_sign = 1 stresslet_obj = StressletWrapper(dim=2) stokeslet_obj = StokesletWrapper(dim=2) bdry_op_sym = (-loc_sign * 0.5 * sigma_sym - stresslet_obj.apply( sigma_sym, nvec_sym, mu_sym, qbx_forced_limit="avg") + stokeslet_obj.apply( meanless_sigma_sym, mu_sym, qbx_forced_limit="avg") - (0.5 / np.pi) * int_sigma) # }}} bound_op = bind(places, bdry_op_sym) # {{{ fix rhs and solve def fund_soln(x, y, loc, strength): #with direction (1,0) for point source r = actx.np.sqrt((x - loc[0])**2 + (y - loc[1])**2) scaling = strength / (4 * np.pi * mu) xcomp = (-actx.np.log(r) + (x - loc[0])**2 / r**2) * scaling ycomp = ((x - loc[0]) * (y - loc[1]) / r**2) * scaling return [xcomp, ycomp] def rotlet_soln(x, y, loc): r = actx.np.sqrt((x - loc[0])**2 + (y - loc[1])**2) xcomp = -(y - loc[1]) / r**2 ycomp = (x - loc[0]) / r**2 return [xcomp, ycomp] def fund_and_rot_soln(x, y, loc, strength): #with direction (1,0) for point source r = actx.np.sqrt((x - loc[0])**2 + (y - loc[1])**2) scaling = strength / (4 * np.pi * mu) xcomp = ((-actx.np.log(r) + (x - loc[0])**2 / r**2) * scaling - (y - loc[1]) * strength * 0.125 / r**2 + 3.3) ycomp = (((x - loc[0]) * (y - loc[1]) / r**2) * scaling + (x - loc[0]) * strength * 0.125 / r**2 + 1.5) return make_obj_array([xcomp, ycomp]) from meshmode.dof_array import unflatten, flatten, thaw nodes = flatten(thaw(actx, density_discr.nodes())) fund_soln_loc = np.array([0.5, -0.2]) strength = 100. bc = unflatten( actx, density_discr, fund_and_rot_soln(nodes[0], nodes[1], fund_soln_loc, strength)) omega_sym = sym.make_sym_vector("omega", dim) u_A_sym_bdry = stokeslet_obj.apply( # noqa: N806 omega_sym, mu_sym, qbx_forced_limit=1) from pytential.utils import unflatten_from_numpy omega = unflatten_from_numpy( actx, density_discr, make_obj_array([(strength / path_length) * np.ones(len(nodes[0])), np.zeros(len(nodes[0]))])) bvp_rhs = bind(places, sym.make_sym_vector("bc", dim) + u_A_sym_bdry)(actx, bc=bc, mu=mu, omega=omega) gmres_result = gmres(bound_op.scipy_op(actx, "sigma", np.float64, mu=mu, normal=normal), bvp_rhs, x0=bvp_rhs, tol=1e-9, progress=True, stall_iterations=0, hard_failure=True) # }}} # {{{ postprocess/visualize sigma = gmres_result.solution sigma_int_val_sym = sym.make_sym_vector("sigma_int_val", 2) int_val = bind(places, sym.integral(2, 1, sigma_sym))(actx, sigma=sigma) int_val = -int_val / (2 * np.pi) print("int_val = ", int_val) u_A_sym_vol = stokeslet_obj.apply( # noqa: N806 omega_sym, mu_sym, qbx_forced_limit=2) representation_sym = ( -stresslet_obj.apply(sigma_sym, nvec_sym, mu_sym, qbx_forced_limit=2) + stokeslet_obj.apply(meanless_sigma_sym, mu_sym, qbx_forced_limit=2) - u_A_sym_vol + sigma_int_val_sym) where = (sym.DEFAULT_SOURCE, "point_target") vel = bind(places, representation_sym, auto_where=where)(actx, sigma=sigma, mu=mu, normal=normal, sigma_int_val=int_val, omega=omega) print("@@@@@@@@") plot_vel = bind(places, representation_sym, auto_where=(sym.DEFAULT_SOURCE, "plot_target"))(actx, sigma=sigma, mu=mu, normal=normal, sigma_int_val=int_val, omega=omega) def get_obj_array(obj_array): return make_obj_array([ary.get() for ary in obj_array]) exact_soln = fund_and_rot_soln(actx.from_numpy(eval_points[0]), actx.from_numpy(eval_points[1]), fund_soln_loc, strength) vel = get_obj_array(vel) err = vel - get_obj_array(exact_soln) # FIXME: Pointwise relative errors don't make sense! rel_err = err / (get_obj_array(exact_soln)) if 0: print("@@@@@@@@") print("vel[0], err[0], rel_err[0] ***** vel[1], err[1], rel_err[1]: ") for i in range(len(vel[0])): print( "{:15.8e}, {:15.8e}, {:15.8e} ***** {:15.8e}, {:15.8e}, {:15.8e}" .format(vel[0][i], err[0][i], rel_err[0][i], vel[1][i], err[1][i], rel_err[1][i])) print("@@@@@@@@") l2_err = np.sqrt((6. / (nsamp - 1))**2 * np.sum(err[0] * err[0]) + (6. / (nsamp - 1))**2 * np.sum(err[1] * err[1])) l2_rel_err = np.sqrt((6. / (nsamp - 1))**2 * np.sum(rel_err[0] * rel_err[0]) + (6. / (nsamp - 1))**2 * np.sum(rel_err[1] * rel_err[1])) print("L2 error estimate: ", l2_err) print("L2 rel error estimate: ", l2_rel_err) print("max error at sampled points: ", max(abs(err[0])), max(abs(err[1]))) print("max rel error at sampled points: ", max(abs(rel_err[0])), max(abs(rel_err[1]))) if visualize: import matplotlib.pyplot as plt full_pot = np.zeros_like(fplot.points) * float("nan") mask = circle_mask(fplot.points, radius=circle_rad) for i, vel in enumerate(plot_vel): full_pot[i, mask] = vel.get() plt.quiver(fplot.points[0], fplot.points[1], full_pot[0], full_pot[1], linewidth=0.1) plt.savefig("exterior-2d-field.pdf") # }}} h_max = bind(places, sym.h_max(qbx.ambient_dim))(actx) return h_max, l2_err
def __init__(self, k=sym.var("k")): from sumpy.kernel import HelmholtzKernel self.kernel = HelmholtzKernel(3) self.k = k
def main(): import logging logging.basicConfig(level=logging.WARNING) # INFO for more progress info cl_ctx = cl.create_some_context() queue = cl.CommandQueue(cl_ctx) actx = PyOpenCLArrayContext(queue) target_order = 16 qbx_order = 3 nelements = 60 mode_nr = 0 k = 0 if k: kernel = HelmholtzKernel(2) else: kernel = LaplaceKernel(2) mesh = make_curve_mesh( #lambda t: ellipse(1, t), starfish, np.linspace(0, 1, nelements + 1), target_order) from pytential.qbx import QBXLayerPotentialSource from meshmode.discretization import Discretization from meshmode.discretization.poly_element import \ InterpolatoryQuadratureSimplexGroupFactory pre_density_discr = Discretization( actx, mesh, InterpolatoryQuadratureSimplexGroupFactory(target_order)) unaccel_qbx = QBXLayerPotentialSource( pre_density_discr, fine_order=2 * target_order, qbx_order=qbx_order, fmm_order=False, target_association_tolerance=.05, ) from pytential.target import PointsTarget fplot = FieldPlotter(np.zeros(2), extent=5, npoints=600) from pytential import GeometryCollection places = GeometryCollection({ "unaccel_qbx": unaccel_qbx, "qbx": unaccel_qbx.copy(fmm_order=10), "targets": PointsTarget(fplot.points) }) density_discr = places.get_discretization("unaccel_qbx") nodes = thaw(actx, density_discr.nodes()) angle = actx.np.arctan2(nodes[1], nodes[0]) from pytential import bind, sym if k: kernel_kwargs = {"k": sym.var("k")} else: kernel_kwargs = {} def get_op(): kwargs = dict(qbx_forced_limit=None) kwargs.update(kernel_kwargs) # return sym.d_dx(2, sym.S(kernel, sym.var("sigma"), **kwargs)) # return sym.D(kernel, sym.var("sigma"), **kwargs) return sym.S(kernel, sym.var("sigma"), **kwargs) op = get_op() sigma = actx.np.cos(mode_nr * angle) if isinstance(kernel, HelmholtzKernel): for i, elem in np.ndenumerate(sigma): sigma[i] = elem.astype(np.complex128) fld_in_vol = bind(places, op, auto_where=("unaccel_qbx", "targets"))(actx, sigma=sigma, k=k).get() fmm_fld_in_vol = bind(places, op, auto_where=("qbx", "targets"))(actx, sigma=sigma, k=k).get() err = fmm_fld_in_vol - fld_in_vol try: import matplotlib except ImportError: return matplotlib.use("Agg") im = fplot.show_scalar_in_matplotlib(np.log10(np.abs(err) + 1e-17)) from matplotlib.colors import Normalize im.set_norm(Normalize(vmin=-12, vmax=0)) import matplotlib.pyplot as pt from matplotlib.ticker import NullFormatter pt.gca().xaxis.set_major_formatter(NullFormatter()) pt.gca().yaxis.set_major_formatter(NullFormatter()) cb = pt.colorbar(shrink=0.9) cb.set_label(r"$\log_{10}(\mathrm{Error})$") pt.savefig("fmm-error-order-%d.pdf" % qbx_order)
def timing_run(nx, ny): import logging logging.basicConfig(level=logging.WARNING) # INFO for more progress info cl_ctx = cl.create_some_context() queue = cl.CommandQueue(cl_ctx) mesh = make_mesh(nx=nx, ny=ny) density_discr = Discretization( cl_ctx, mesh, InterpolatoryQuadratureSimplexGroupFactory(bdry_quad_order)) from pytential.qbx import ( QBXLayerPotentialSource, QBXTargetAssociationFailedException) qbx = QBXLayerPotentialSource( density_discr, fine_order=bdry_ovsmp_quad_order, qbx_order=qbx_order, fmm_order=fmm_order ) # {{{ describe bvp from sumpy.kernel import HelmholtzKernel kernel = HelmholtzKernel(2) cse = sym.cse sigma_sym = sym.var("sigma") sqrt_w = sym.sqrt_jac_q_weight(2) inv_sqrt_w_sigma = cse(sigma_sym/sqrt_w) # Brakhage-Werner parameter alpha = 1j # -1 for interior Dirichlet # +1 for exterior Dirichlet loc_sign = +1 bdry_op_sym = (-loc_sign*0.5*sigma_sym + sqrt_w*( alpha*sym.S(kernel, inv_sqrt_w_sigma, k=sym.var("k")) - sym.D(kernel, inv_sqrt_w_sigma, k=sym.var("k")) )) # }}} bound_op = bind(qbx, bdry_op_sym) # {{{ fix rhs and solve mode_nr = 3 nodes = density_discr.nodes().with_queue(queue) angle = cl.clmath.atan2(nodes[1], nodes[0]) sigma = cl.clmath.cos(mode_nr*angle) # }}} # {{{ postprocess/visualize repr_kwargs = dict(k=sym.var("k"), qbx_forced_limit=+1) sym_op = sym.S(kernel, sym.var("sigma"), **repr_kwargs) bound_op = bind(qbx, sym_op) print("FMM WARM-UP RUN 1: %d elements" % mesh.nelements) bound_op(queue, sigma=sigma, k=k) print("FMM WARM-UP RUN 2: %d elements" % mesh.nelements) bound_op(queue, sigma=sigma, k=k) queue.finish() print("FMM TIMING RUN: %d elements" % mesh.nelements) from time import time t_start = time() bound_op(queue, sigma=sigma, k=k) queue.finish() elapsed = time()-t_start print("FMM TIMING RUN DONE: %d elements -> %g s" % (mesh.nelements, elapsed)) return (mesh.nelements, elapsed) if 0: from sumpy.visualization import FieldPlotter fplot = FieldPlotter(np.zeros(2), extent=5, npoints=1500) targets = cl.array.to_device(queue, fplot.points) qbx_tgt_tol = qbx.copy(target_association_tolerance=0.05) indicator_qbx = qbx_tgt_tol.copy( fmm_level_to_order=lambda lev: 7, qbx_order=2) ones_density = density_discr.zeros(queue) ones_density.fill(1) indicator = bind( (indicator_qbx, PointsTarget(targets)), sym_op)( queue, sigma=ones_density).get() qbx_stick_out = qbx.copy(target_stick_out_factor=0.1) try: fld_in_vol = bind( (qbx_stick_out, PointsTarget(targets)), sym_op)(queue, sigma=sigma, k=k).get() except QBXTargetAssociationFailedException as e: fplot.write_vtk_file( "failed-targets.vts", [ ("failed", e.failed_target_flags.get(queue)) ] ) raise #fplot.show_scalar_in_mayavi(fld_in_vol.real, max_val=5) fplot.write_vtk_file( "potential-scaling.vts", [ ("potential", fld_in_vol), ("indicator", indicator) ] )
def get_op(): kwargs = dict(qbx_forced_limit=None) kwargs.update(kernel_kwargs) # return sym.d_dx(2, sym.S(kernel, sym.var("sigma"), **kwargs)) # return sym.D(kernel, sym.var("sigma"), **kwargs) return sym.S(kernel, sym.var("sigma"), **kwargs)
extinction of the combined (incoming + scattered) field on the interior of the scatterer. """ logging.basicConfig(level=logging.INFO) actx = actx_factory() np.random.seed(12) knl_kwargs = {"k": case.k} # {{{ come up with a solution to Maxwell's equations j_sym = sym.make_sym_vector("j", 3) jt_sym = sym.make_sym_vector("jt", 2) rho_sym = sym.var("rho") from pytential.symbolic.pde.maxwell import ( PECChargeCurrentMFIEOperator, get_sym_maxwell_point_source, get_sym_maxwell_plane_wave) mfie = PECChargeCurrentMFIEOperator() test_source = case.get_source(actx) calc_patch = CalculusPatch(np.array([-3, 0, 0]), h=0.01) calc_patch_tgt = PointsTarget(actx.from_numpy(calc_patch.points)) import pyopencl.clrandom as clrandom rng = clrandom.PhiloxGenerator(actx.context, seed=12)
def main(): import logging logging.basicConfig(level=logging.INFO) cl_ctx = cl.create_some_context() queue = cl.CommandQueue(cl_ctx) from meshmode.mesh.generation import ellipse, make_curve_mesh from functools import partial mesh = make_curve_mesh( partial(ellipse, 2), np.linspace(0, 1, nelements+1), mesh_order) pre_density_discr = Discretization( cl_ctx, mesh, InterpolatoryQuadratureSimplexGroupFactory(bdry_quad_order)) from pytential.qbx import ( QBXLayerPotentialSource, QBXTargetAssociationFailedException) qbx, _ = QBXLayerPotentialSource( pre_density_discr, fine_order=bdry_ovsmp_quad_order, qbx_order=qbx_order, fmm_order=fmm_order, expansion_disks_in_tree_have_extent=True, ).with_refinement() density_discr = qbx.density_discr from pytential.symbolic.pde.cahn_hilliard import CahnHilliardOperator chop = CahnHilliardOperator( # FIXME: Constants? lambda1=1.5, lambda2=1.25, c=1) unk = chop.make_unknown("sigma") bound_op = bind(qbx, chop.operator(unk)) # {{{ fix rhs and solve nodes = density_discr.nodes().with_queue(queue) def g(xvec): x, y = xvec return cl.clmath.atan2(y, x) bc = sym.make_obj_array([ # FIXME: Realistic BC g(nodes), -g(nodes), ]) from pytential.solve import gmres gmres_result = gmres( bound_op.scipy_op(queue, "sigma", dtype=np.complex128), bc, tol=1e-8, progress=True, stall_iterations=0, hard_failure=True) # }}} # {{{ postprocess/visualize sigma = gmres_result.solution from sumpy.visualization import FieldPlotter fplot = FieldPlotter(np.zeros(2), extent=5, npoints=500) targets = cl.array.to_device(queue, fplot.points) qbx_stick_out = qbx.copy(target_association_tolerance=0.05) indicator_qbx = qbx_stick_out.copy(qbx_order=2) from sumpy.kernel import LaplaceKernel ones_density = density_discr.zeros(queue) ones_density.fill(1) indicator = bind( (indicator_qbx, PointsTarget(targets)), sym.D(LaplaceKernel(2), sym.var("sigma")))( queue, sigma=ones_density).get() try: fld_in_vol = bind( (qbx_stick_out, PointsTarget(targets)), chop.representation(unk))(queue, sigma=sigma).get() except QBXTargetAssociationFailedException as e: fplot.write_vtk_file( "failed-targets.vts", [ ("failed", e.failed_target_flags.get(queue)) ] ) raise #fplot.show_scalar_in_mayavi(fld_in_vol.real, max_val=5) fplot.write_vtk_file( "potential.vts", [ ("potential", fld_in_vol), ("indicator", indicator), ] )
def run_int_eq_test( cl_ctx, queue, curve_f, nelements, qbx_order, bc_type, loc_sign, k, target_order, source_order): mesh = make_curve_mesh(curve_f, np.linspace(0, 1, nelements+1), target_order) if 0: from pytential.visualization import show_mesh show_mesh(mesh) pt.gca().set_aspect("equal") pt.show() from pytential.qbx import QBXLayerPotentialSource from meshmode.discretization import Discretization from meshmode.discretization.poly_element import \ InterpolatoryQuadratureSimplexGroupFactory density_discr = Discretization( cl_ctx, mesh, InterpolatoryQuadratureSimplexGroupFactory(target_order)) if source_order is None: source_order = 4*target_order qbx = QBXLayerPotentialSource( density_discr, fine_order=source_order, qbx_order=qbx_order, # Don't use FMM for now fmm_order=False) # {{{ set up operator from pytential.symbolic.pde.scalar import ( DirichletOperator, NeumannOperator) from sumpy.kernel import LaplaceKernel, HelmholtzKernel, AxisTargetDerivative if k: knl = HelmholtzKernel(2) knl_kwargs = {"k": k} else: knl = LaplaceKernel(2) knl_kwargs = {} if knl.is_complex_valued: dtype = np.complex128 else: dtype = np.float64 if bc_type == "dirichlet": op = DirichletOperator((knl, knl_kwargs), loc_sign, use_l2_weighting=True) elif bc_type == "neumann": op = NeumannOperator((knl, knl_kwargs), loc_sign, use_l2_weighting=True, use_improved_operator=False) else: assert False op_u = op.operator(sym.var("u")) # }}} # {{{ set up test data inner_radius = 0.1 outer_radius = 2 if loc_sign < 0: test_src_geo_radius = outer_radius test_tgt_geo_radius = inner_radius else: test_src_geo_radius = inner_radius test_tgt_geo_radius = outer_radius point_sources = make_circular_point_group(10, test_src_geo_radius, func=lambda x: x**1.5) test_targets = make_circular_point_group(20, test_tgt_geo_radius) np.random.seed(22) source_charges = np.random.randn(point_sources.shape[1]) source_charges[-1] = -np.sum(source_charges[:-1]) source_charges = source_charges.astype(dtype) assert np.sum(source_charges) < 1e-15 # }}} if 0: # show geometry, centers, normals nodes_h = density_discr.nodes().get(queue=queue) pt.plot(nodes_h[0], nodes_h[1], "x-") normal = bind(density_discr, sym.normal())(queue).as_vector(np.object) pt.quiver(nodes_h[0], nodes_h[1], normal[0].get(queue), normal[1].get(queue)) pt.gca().set_aspect("equal") pt.show() # {{{ establish BCs from sumpy.p2p import P2P pot_p2p = P2P(cl_ctx, [knl], exclude_self=False, value_dtypes=dtype) evt, (test_direct,) = pot_p2p( queue, test_targets, point_sources, [source_charges], out_host=False, **knl_kwargs) nodes = density_discr.nodes() evt, (src_pot,) = pot_p2p( queue, nodes, point_sources, [source_charges], **knl_kwargs) grad_p2p = P2P(cl_ctx, [AxisTargetDerivative(0, knl), AxisTargetDerivative(1, knl)], exclude_self=False, value_dtypes=dtype) evt, (src_grad0, src_grad1) = grad_p2p( queue, nodes, point_sources, [source_charges], **knl_kwargs) if bc_type == "dirichlet": bc = src_pot elif bc_type == "neumann": normal = bind(density_discr, sym.normal())(queue).as_vector(np.object) bc = (src_grad0*normal[0] + src_grad1*normal[1]) # }}} # {{{ solve bound_op = bind(qbx, op_u) rhs = bind(density_discr, op.prepare_rhs(sym.var("bc")))(queue, bc=bc) from pytential.solve import gmres gmres_result = gmres( bound_op.scipy_op(queue, "u", k=k), rhs, tol=1e-14, progress=True, hard_failure=False) u = gmres_result.solution print("gmres state:", gmres_result.state) if 0: # {{{ build matrix for spectrum check from sumpy.tools import build_matrix mat = build_matrix(bound_op.scipy_op("u")) w, v = la.eig(mat) if 0: pt.imshow(np.log10(1e-20+np.abs(mat))) pt.colorbar() pt.show() #assert abs(s[-1]) < 1e-13, "h #assert abs(s[-2]) > 1e-7 #from pudb import set_trace; set_trace() # }}} # }}} # {{{ error check from pytential.target import PointsTarget bound_tgt_op = bind((qbx, PointsTarget(test_targets)), op.representation(sym.var("u"))) test_via_bdry = bound_tgt_op(queue, u=u, k=k) err = test_direct-test_via_bdry err = err.get() test_direct = test_direct.get() test_via_bdry = test_via_bdry.get() # {{{ remove effect of net source charge if k == 0 and bc_type == "neumann" and loc_sign == -1: # remove constant offset in interior Laplace Neumann error tgt_ones = np.ones_like(test_direct) tgt_ones = tgt_ones/la.norm(tgt_ones) err = err - np.vdot(tgt_ones, err)*tgt_ones # }}} rel_err_2 = la.norm(err)/la.norm(test_direct) rel_err_inf = la.norm(err, np.inf)/la.norm(test_direct, np.inf) # }}} print("rel_err_2: %g rel_err_inf: %g" % (rel_err_2, rel_err_inf)) # {{{ test tangential derivative bound_t_deriv_op = bind(qbx, op.representation( sym.var("u"), map_potentials=sym.tangential_derivative, qbx_forced_limit=loc_sign)) #print(bound_t_deriv_op.code) tang_deriv_from_src = bound_t_deriv_op(queue, u=u).as_scalar().get() tangent = bind( density_discr, sym.pseudoscalar()/sym.area_element())(queue).as_vector(np.object) tang_deriv_ref = (src_grad0 * tangent[0] + src_grad1 * tangent[1]).get() if 0: pt.plot(tang_deriv_ref.real) pt.plot(tang_deriv_from_src.real) pt.show() td_err = tang_deriv_from_src - tang_deriv_ref rel_td_err_inf = la.norm(td_err, np.inf)/la.norm(tang_deriv_ref, np.inf) print("rel_td_err_inf: %g" % rel_td_err_inf) # }}} # {{{ plotting if 0: fplot = FieldPlotter(np.zeros(2), extent=1.25*2*max(test_src_geo_radius, test_tgt_geo_radius), npoints=200) #pt.plot(u) #pt.show() evt, (fld_from_src,) = pot_p2p( queue, fplot.points, point_sources, [source_charges], **knl_kwargs) fld_from_bdry = bind( (qbx, PointsTarget(fplot.points)), op.representation(sym.var("u")) )(queue, u=u, k=k) fld_from_src = fld_from_src.get() fld_from_bdry = fld_from_bdry.get() nodes = density_discr.nodes().get(queue=queue) def prep(): pt.plot(point_sources[0], point_sources[1], "o", label="Monopole 'Point Charges'") pt.plot(test_targets[0], test_targets[1], "v", label="Observation Points") pt.plot(nodes[0], nodes[1], "k-", label=r"$\Gamma$") from matplotlib.cm import get_cmap cmap = get_cmap() cmap._init() if 0: cmap._lut[(cmap.N*99)//100:, -1] = 0 # make last percent transparent? prep() if 1: pt.subplot(131) pt.title("Field error (loc_sign=%s)" % loc_sign) log_err = np.log10(1e-20+np.abs(fld_from_src-fld_from_bdry)) log_err = np.minimum(-3, log_err) fplot.show_scalar_in_matplotlib(log_err, cmap=cmap) #from matplotlib.colors import Normalize #im.set_norm(Normalize(vmin=-6, vmax=1)) cb = pt.colorbar(shrink=0.9) cb.set_label(r"$\log_{10}(\mathdefault{Error})$") if 1: pt.subplot(132) prep() pt.title("Source Field") fplot.show_scalar_in_matplotlib( fld_from_src.real, max_val=3) pt.colorbar(shrink=0.9) if 1: pt.subplot(133) prep() pt.title("Solved Field") fplot.show_scalar_in_matplotlib( fld_from_bdry.real, max_val=3) pt.colorbar(shrink=0.9) # total field #fplot.show_scalar_in_matplotlib( #fld_from_src.real+fld_from_bdry.real, max_val=0.1) #pt.colorbar() pt.legend(loc="best", prop=dict(size=15)) from matplotlib.ticker import NullFormatter pt.gca().xaxis.set_major_formatter(NullFormatter()) pt.gca().yaxis.set_major_formatter(NullFormatter()) pt.gca().set_aspect("equal") if 0: border_factor_top = 0.9 border_factor = 0.3 xl, xh = pt.xlim() xhsize = 0.5*(xh-xl) pt.xlim(xl-border_factor*xhsize, xh+border_factor*xhsize) yl, yh = pt.ylim() yhsize = 0.5*(yh-yl) pt.ylim(yl-border_factor_top*yhsize, yh+border_factor*yhsize) #pt.savefig("helmholtz.pdf", dpi=600) pt.show() # }}} class Result(Record): pass return Result( rel_err_2=rel_err_2, rel_err_inf=rel_err_inf, rel_td_err_inf=rel_td_err_inf, gmres_result=gmres_result)
def test_perf_data_gathering(ctx_getter, n_arms=5): cl_ctx = ctx_getter() queue = cl.CommandQueue(cl_ctx) # prevent cache 'splosion from sympy.core.cache import clear_cache clear_cache() target_order = 8 starfish_func = NArmedStarfish(n_arms, 0.8) mesh = make_curve_mesh( starfish_func, np.linspace(0, 1, n_arms * 30), target_order) sigma_sym = sym.var("sigma") # The kernel doesn't really matter here from sumpy.kernel import LaplaceKernel k_sym = LaplaceKernel(mesh.ambient_dim) sym_op = sym.S(k_sym, sigma_sym, qbx_forced_limit=+1) from meshmode.discretization import Discretization from meshmode.discretization.poly_element import ( InterpolatoryQuadratureSimplexGroupFactory) pre_density_discr = Discretization( queue.context, mesh, InterpolatoryQuadratureSimplexGroupFactory(target_order)) results = [] def inspect_geo_data(insn, bound_expr, geo_data): from pytential.qbx.fmm import assemble_performance_data perf_data = assemble_performance_data(geo_data, uses_pde_expansions=True) results.append(perf_data) return False # no need to do the actual FMM from pytential.qbx import QBXLayerPotentialSource lpot_source = QBXLayerPotentialSource( pre_density_discr, 4*target_order, # qbx order and fmm order don't really matter 10, fmm_order=10, _expansions_in_tree_have_extent=True, _expansion_stick_out_factor=0.5, geometry_data_inspector=inspect_geo_data, target_association_tolerance=1e-10, ) lpot_source, _ = lpot_source.with_refinement() density_discr = lpot_source.density_discr if 0: from meshmode.discretization.visualization import draw_curve draw_curve(density_discr) import matplotlib.pyplot as plt plt.show() nodes = density_discr.nodes().with_queue(queue) sigma = cl.clmath.sin(10 * nodes[0]) bind(lpot_source, sym_op)(queue, sigma=sigma)
def main(): logging.basicConfig(level=logging.INFO) nelements = 60 qbx_order = 3 k_fac = 4 k0 = 3*k_fac k1 = 2.9*k_fac mesh_order = 10 bdry_quad_order = mesh_order bdry_ovsmp_quad_order = bdry_quad_order * 4 fmm_order = qbx_order * 2 cl_ctx = cl.create_some_context() queue = cl.CommandQueue(cl_ctx) from meshmode.mesh.generation import ellipse, make_curve_mesh from functools import partial mesh = make_curve_mesh( partial(ellipse, 3), np.linspace(0, 1, nelements+1), mesh_order) density_discr = Discretization( cl_ctx, mesh, InterpolatoryQuadratureSimplexGroupFactory(bdry_quad_order)) logger.info("%d elements" % mesh.nelements) # from meshmode.discretization.visualization import make_visualizer # bdry_vis = make_visualizer(queue, density_discr, 20) # {{{ solve bvp from sumpy.kernel import HelmholtzKernel kernel = HelmholtzKernel(2) beta = 2.5*k_fac K0 = np.sqrt(k0**2-beta**2) K1 = np.sqrt(k1**2-beta**2) from pytential.symbolic.pde.scalar import DielectricSDRep2DBoundaryOperator pde_op = DielectricSDRep2DBoundaryOperator( mode='tm', k_vacuum=1, interfaces=((0, 1, sym.DEFAULT_SOURCE),), domain_k_exprs=(k0, k1), beta=beta) op_unknown_sym = pde_op.make_unknown("unknown") representation0_sym = pde_op.representation(op_unknown_sym, 0) representation1_sym = pde_op.representation(op_unknown_sym, 1) from pytential.qbx import QBXLayerPotentialSource qbx = QBXLayerPotentialSource( density_discr, fine_order=bdry_ovsmp_quad_order, qbx_order=qbx_order, fmm_order=fmm_order ) bound_pde_op = bind(qbx, pde_op.operator(op_unknown_sym)) # in inner domain sources_1 = make_obj_array(list(np.array([ [-1.5, 0.5] ]).T.copy())) strengths_1 = np.array([1]) from sumpy.p2p import P2P pot_p2p = P2P(cl_ctx, [kernel], exclude_self=False) _, (Einc,) = pot_p2p(queue, density_discr.nodes(), sources_1, [strengths_1], out_host=False, k=K0) sqrt_w = bind(density_discr, sym.sqrt_jac_q_weight())(queue) bvp_rhs = np.zeros(len(pde_op.bcs), dtype=np.object) for i_bc, terms in enumerate(pde_op.bcs): for term in terms: assert term.i_interface == 0 assert term.field_kind == pde_op.field_kind_e if term.direction == pde_op.dir_none: bvp_rhs[i_bc] += ( term.coeff_outer * (-Einc) ) elif term.direction == pde_op.dir_normal: # no jump in normal derivative bvp_rhs[i_bc] += 0*Einc else: raise NotImplementedError("direction spec in RHS") bvp_rhs[i_bc] *= sqrt_w from pytential.solve import gmres gmres_result = gmres( bound_pde_op.scipy_op(queue, "unknown", dtype=np.complex128, domains=[sym.DEFAULT_TARGET]*2, K0=K0, K1=K1), bvp_rhs, tol=1e-6, progress=True, hard_failure=True, stall_iterations=0) # }}} unknown = gmres_result.solution # {{{ visualize from pytential.qbx import QBXLayerPotentialSource lap_qbx = QBXLayerPotentialSource( density_discr, fine_order=bdry_ovsmp_quad_order, qbx_order=qbx_order, fmm_order=qbx_order ) from sumpy.visualization import FieldPlotter fplot = FieldPlotter(np.zeros(2), extent=5, npoints=300) from pytential.target import PointsTarget fld0 = bind( (qbx, PointsTarget(fplot.points)), representation0_sym)(queue, unknown=unknown, K0=K0).get() fld1 = bind( (qbx, PointsTarget(fplot.points)), representation1_sym)(queue, unknown=unknown, K1=K1).get() ones = cl.array.empty(queue, density_discr.nnodes, np.float64) dom1_indicator = -bind( (lap_qbx, PointsTarget(fplot.points)), sym.D(0, sym.var("sigma")))( queue, sigma=ones.fill(1)).get() _, (fld_inc_vol,) = pot_p2p(queue, fplot.points, sources_1, [strengths_1], out_host=True, k=K0) #fplot.show_scalar_in_mayavi(fld_in_vol.real, max_val=5) fplot.write_vtk_file( "potential.vts", [ ("fld0", fld0), ("fld1", fld1), ("fld_inc_vol", fld_inc_vol), ("fld_total", ( (fld_inc_vol + fld0)*(1-dom1_indicator) + fld1*dom1_indicator )), ("dom1_indicator", dom1_indicator), ] )
def test_off_surface_eval(ctx_getter, use_fmm, do_plot=False): logging.basicConfig(level=logging.INFO) cl_ctx = ctx_getter() queue = cl.CommandQueue(cl_ctx) # prevent cache 'splosion from sympy.core.cache import clear_cache clear_cache() nelements = 30 target_order = 8 qbx_order = 3 if use_fmm: fmm_order = qbx_order else: fmm_order = False mesh = make_curve_mesh(partial(ellipse, 3), np.linspace(0, 1, nelements+1), target_order) from pytential.qbx import QBXLayerPotentialSource from meshmode.discretization import Discretization from meshmode.discretization.poly_element import \ InterpolatoryQuadratureSimplexGroupFactory pre_density_discr = Discretization( cl_ctx, mesh, InterpolatoryQuadratureSimplexGroupFactory(target_order)) qbx, _ = QBXLayerPotentialSource( pre_density_discr, 4*target_order, qbx_order, fmm_order=fmm_order, ).with_refinement() density_discr = qbx.density_discr from sumpy.kernel import LaplaceKernel op = sym.D(LaplaceKernel(2), sym.var("sigma"), qbx_forced_limit=-2) sigma = density_discr.zeros(queue) + 1 fplot = FieldPlotter(np.zeros(2), extent=0.54, npoints=30) from pytential.target import PointsTarget fld_in_vol = bind( (qbx, PointsTarget(fplot.points)), op)(queue, sigma=sigma) err = cl.clmath.fabs(fld_in_vol - (-1)) linf_err = cl.array.max(err).get() print("l_inf error:", linf_err) if do_plot: fplot.show_scalar_in_matplotlib(fld_in_vol.get()) import matplotlib.pyplot as pt pt.colorbar() pt.show() assert linf_err < 1e-3
def main(): import logging logging.basicConfig(level=logging.WARNING) # INFO for more progress info cl_ctx = cl.create_some_context() queue = cl.CommandQueue(cl_ctx) from meshmode.mesh.generation import generate_torus rout = 10 rin = 1 if 1: base_mesh = generate_torus( rout, rin, 40, 4, mesh_order) from meshmode.mesh.processing import affine_map, merge_disjoint_meshes # nx = 1 # ny = 1 nz = 1 dz = 0 meshes = [ affine_map( base_mesh, A=np.diag([1, 1, 1]), b=np.array([0, 0, iz*dz])) for iz in range(nz)] mesh = merge_disjoint_meshes(meshes, single_group=True) if 0: from meshmode.mesh.visualization import draw_curve draw_curve(mesh) import matplotlib.pyplot as plt plt.show() pre_density_discr = Discretization( cl_ctx, mesh, InterpolatoryQuadratureSimplexGroupFactory(bdry_quad_order)) from pytential.qbx import ( QBXLayerPotentialSource, QBXTargetAssociationFailedException) qbx, _ = QBXLayerPotentialSource( pre_density_discr, fine_order=bdry_ovsmp_quad_order, qbx_order=qbx_order, fmm_order=fmm_order ).with_refinement() density_discr = qbx.density_discr # {{{ describe bvp from sumpy.kernel import LaplaceKernel kernel = LaplaceKernel(3) cse = sym.cse sigma_sym = sym.var("sigma") #sqrt_w = sym.sqrt_jac_q_weight(3) sqrt_w = 1 inv_sqrt_w_sigma = cse(sigma_sym/sqrt_w) # -1 for interior Dirichlet # +1 for exterior Dirichlet loc_sign = +1 bdry_op_sym = (loc_sign*0.5*sigma_sym + sqrt_w*( sym.S(kernel, inv_sqrt_w_sigma) + sym.D(kernel, inv_sqrt_w_sigma) )) # }}} bound_op = bind(qbx, bdry_op_sym) # {{{ fix rhs and solve nodes = density_discr.nodes().with_queue(queue) source = np.array([rout, 0, 0]) def u_incoming_func(x): # return 1/cl.clmath.sqrt( (x[0] - source[0])**2 # +(x[1] - source[1])**2 # +(x[2] - source[2])**2 ) return 1.0/la.norm(x.get()-source[:, None], axis=0) bc = cl.array.to_device(queue, u_incoming_func(nodes)) bvp_rhs = bind(qbx, sqrt_w*sym.var("bc"))(queue, bc=bc) from pytential.solve import gmres gmres_result = gmres( bound_op.scipy_op(queue, "sigma", dtype=np.float64), bvp_rhs, tol=1e-14, progress=True, stall_iterations=0, hard_failure=True) sigma = bind(qbx, sym.var("sigma")/sqrt_w)(queue, sigma=gmres_result.solution) # }}} from meshmode.discretization.visualization import make_visualizer bdry_vis = make_visualizer(queue, density_discr, 20) bdry_vis.write_vtk_file("laplace.vtu", [ ("sigma", sigma), ]) # {{{ postprocess/visualize repr_kwargs = dict(qbx_forced_limit=None) representation_sym = ( sym.S(kernel, inv_sqrt_w_sigma, **repr_kwargs) + sym.D(kernel, inv_sqrt_w_sigma, **repr_kwargs)) from sumpy.visualization import FieldPlotter fplot = FieldPlotter(np.zeros(3), extent=20, npoints=50) targets = cl.array.to_device(queue, fplot.points) qbx_stick_out = qbx.copy(target_stick_out_factor=0.2) try: fld_in_vol = bind( (qbx_stick_out, PointsTarget(targets)), representation_sym)(queue, sigma=sigma).get() except QBXTargetAssociationFailedException as e: fplot.write_vtk_file( "failed-targets.vts", [ ("failed", e.failed_target_flags.get(queue)) ] ) raise #fplot.show_scalar_in_mayavi(fld_in_vol.real, max_val=5) fplot.write_vtk_file( "potential-laplace-3d.vts", [ ("potential", fld_in_vol), ] )
def main(): import logging logging.basicConfig(level=logging.INFO) ctx = cl.create_some_context() queue = cl.CommandQueue(ctx) mesh = generate_gmsh( FileSource("circle.step"), 2, order=mesh_order, force_ambient_dim=2, other_options=["-string", "Mesh.CharacteristicLengthMax = %g;" % h] ) logger.info("%d elements" % mesh.nelements) # {{{ discretizations and connections vol_discr = Discretization(ctx, mesh, InterpolatoryQuadratureSimplexGroupFactory(vol_quad_order)) ovsmp_vol_discr = Discretization(ctx, mesh, InterpolatoryQuadratureSimplexGroupFactory(vol_ovsmp_quad_order)) from meshmode.discretization.connection import ( make_boundary_restriction, make_same_mesh_connection) bdry_mesh, bdry_discr, bdry_connection = make_boundary_restriction( queue, vol_discr, InterpolatoryQuadratureSimplexGroupFactory(bdry_quad_order)) vol_to_ovsmp_vol = make_same_mesh_connection( queue, ovsmp_vol_discr, vol_discr) # }}} # {{{ visualizers vol_vis = make_visualizer(queue, vol_discr, 20) bdry_vis = make_visualizer(queue, bdry_discr, 20) # }}} vol_x = vol_discr.nodes().with_queue(queue) ovsmp_vol_x = ovsmp_vol_discr.nodes().with_queue(queue) rhs = rhs_func(vol_x[0], vol_x[1]) poisson_true_sol = sol_func(vol_x[0], vol_x[1]) vol_vis.write_vtk_file("volume.vtu", [("f", rhs)]) bdry_normals = bind(bdry_discr, p.normal())(queue).as_vector(dtype=object) bdry_vis.write_vtk_file("boundary.vtu", [ ("normals", bdry_normals) ]) bdry_nodes = bdry_discr.nodes().with_queue(queue) bdry_f = rhs_func(bdry_nodes[0], bdry_nodes[1]) bdry_f_2 = bdry_connection(queue, rhs) bdry_vis.write_vtk_file("y.vtu", [("f", bdry_f_2)]) if 0: vol_vis.show_scalar_in_mayavi(rhs, do_show=False) bdry_vis.show_scalar_in_mayavi(bdry_f - bdry_f_2, line_width=10, do_show=False) import mayavi.mlab as mlab mlab.colorbar() mlab.show() # {{{ compute volume potential from sumpy.qbx import LayerPotential from sumpy.expansion.local import LineTaylorLocalExpansion def get_kernel(): from sumpy.symbolic import pymbolic_real_norm_2 from pymbolic.primitives import (make_sym_vector, Variable as var) r = pymbolic_real_norm_2(make_sym_vector("d", 3)) expr = var("log")(r) scaling = 1/(2*var("pi")) from sumpy.kernel import ExpressionKernel return ExpressionKernel( dim=3, expression=expr, scaling=scaling, is_complex_valued=False) laplace_2d_in_3d_kernel = get_kernel() layer_pot = LayerPotential(ctx, [ LineTaylorLocalExpansion(laplace_2d_in_3d_kernel, order=vol_qbx_order)]) targets = cl.array.zeros(queue, (3,) + vol_x.shape[1:], vol_x.dtype) targets[:2] = vol_x center_dist = np.min( cl.clmath.sqrt( bind(vol_discr, p.area_element())(queue)).get()) centers = make_obj_array([ci.copy().reshape(vol_discr.nnodes) for ci in targets]) centers[2][:] = center_dist sources = cl.array.zeros(queue, (3,) + ovsmp_vol_x.shape[1:], ovsmp_vol_x.dtype) sources[:2] = ovsmp_vol_x ovsmp_rhs = vol_to_ovsmp_vol(queue, rhs) ovsmp_vol_weights = bind(ovsmp_vol_discr, p.area_element() * p.QWeight())(queue) evt, (vol_pot,) = layer_pot( queue, targets=targets.reshape(3, vol_discr.nnodes), centers=centers, sources=sources.reshape(3, ovsmp_vol_discr.nnodes), strengths=( (ovsmp_vol_weights*ovsmp_rhs).reshape(ovsmp_vol_discr.nnodes),) ) vol_pot_bdry = bdry_connection(queue, vol_pot) # }}} # {{{ solve bvp from sumpy.kernel import LaplaceKernel from pytential.symbolic.pde.scalar import DirichletOperator op = DirichletOperator(LaplaceKernel(2), -1, use_l2_weighting=True) sym_sigma = sym.var("sigma") op_sigma = op.operator(sym_sigma) from pytential.qbx import QBXLayerPotentialSource qbx = QBXLayerPotentialSource( bdry_discr, fine_order=bdry_ovsmp_quad_order, qbx_order=qbx_order, fmm_order=fmm_order ) bound_op = bind(qbx, op_sigma) poisson_bc = poisson_bc_func(bdry_nodes[0], bdry_nodes[1]) bvp_bc = poisson_bc - vol_pot_bdry bdry_f = rhs_func(bdry_nodes[0], bdry_nodes[1]) bvp_rhs = bind(bdry_discr, op.prepare_rhs(sym.var("bc")))(queue, bc=bvp_bc) from pytential.solve import gmres gmres_result = gmres( bound_op.scipy_op(queue, "sigma"), bvp_rhs, tol=1e-14, progress=True, hard_failure=False) sigma = gmres_result.solution print("gmres state:", gmres_result.state) # }}} bvp_sol = bind( (qbx, vol_discr), op.representation(sym_sigma))(queue, sigma=sigma) poisson_sol = bvp_sol + vol_pot poisson_err = poisson_sol-poisson_true_sol rel_err = ( norm(vol_discr, queue, poisson_err) / norm(vol_discr, queue, poisson_true_sol)) bdry_vis.write_vtk_file("poisson-boundary.vtu", [ ("vol_pot_bdry", vol_pot_bdry), ("sigma", sigma), ]) vol_vis.write_vtk_file("poisson-volume.vtu", [ ("bvp_sol", bvp_sol), ("poisson_sol", poisson_sol), ("poisson_true_sol", poisson_true_sol), ("poisson_err", poisson_err), ("vol_pot", vol_pot), ("rhs", rhs), ]) print("h = %s" % h) print("mesh_order = %s" % mesh_order) print("vol_quad_order = %s" % vol_quad_order) print("vol_ovsmp_quad_order = %s" % vol_ovsmp_quad_order) print("bdry_quad_order = %s" % bdry_quad_order) print("bdry_ovsmp_quad_order = %s" % bdry_ovsmp_quad_order) print("qbx_order = %s" % qbx_order) print("vol_qbx_order = %s" % vol_qbx_order) print("fmm_order = %s" % fmm_order) print() print("rel err: %g" % rel_err)
def test_off_surface_eval_vs_direct(ctx_getter, do_plot=False): logging.basicConfig(level=logging.INFO) cl_ctx = ctx_getter() queue = cl.CommandQueue(cl_ctx) # prevent cache 'splosion from sympy.core.cache import clear_cache clear_cache() nelements = 300 target_order = 8 qbx_order = 3 mesh = make_curve_mesh(WobblyCircle.random(8, seed=30), np.linspace(0, 1, nelements+1), target_order) from pytential.qbx import QBXLayerPotentialSource from meshmode.discretization import Discretization from meshmode.discretization.poly_element import \ InterpolatoryQuadratureSimplexGroupFactory pre_density_discr = Discretization( cl_ctx, mesh, InterpolatoryQuadratureSimplexGroupFactory(target_order)) direct_qbx, _ = QBXLayerPotentialSource( pre_density_discr, 4*target_order, qbx_order, fmm_order=False, target_association_tolerance=0.05, ).with_refinement() fmm_qbx, _ = QBXLayerPotentialSource( pre_density_discr, 4*target_order, qbx_order, fmm_order=qbx_order + 3, _expansions_in_tree_have_extent=True, target_association_tolerance=0.05, ).with_refinement() fplot = FieldPlotter(np.zeros(2), extent=5, npoints=1000) from pytential.target import PointsTarget ptarget = PointsTarget(fplot.points) from sumpy.kernel import LaplaceKernel op = sym.D(LaplaceKernel(2), sym.var("sigma"), qbx_forced_limit=None) from pytential.qbx import QBXTargetAssociationFailedException try: direct_density_discr = direct_qbx.density_discr direct_sigma = direct_density_discr.zeros(queue) + 1 direct_fld_in_vol = bind((direct_qbx, ptarget), op)( queue, sigma=direct_sigma) except QBXTargetAssociationFailedException as e: fplot.show_scalar_in_matplotlib(e.failed_target_flags.get(queue)) import matplotlib.pyplot as pt pt.show() raise fmm_density_discr = fmm_qbx.density_discr fmm_sigma = fmm_density_discr.zeros(queue) + 1 fmm_fld_in_vol = bind((fmm_qbx, ptarget), op)(queue, sigma=fmm_sigma) err = cl.clmath.fabs(fmm_fld_in_vol - direct_fld_in_vol) linf_err = cl.array.max(err).get() print("l_inf error:", linf_err) if do_plot: #fplot.show_scalar_in_mayavi(0.1*.get(queue)) fplot.write_vtk_file("potential.vts", [ ("fmm_fld_in_vol", fmm_fld_in_vol.get(queue)), ("direct_fld_in_vol", direct_fld_in_vol.get(queue)) ]) assert linf_err < 1e-3
def run_int_eq_test(cl_ctx, queue, case, resolution, visualize): mesh = case.get_mesh(resolution, case.target_order) print("%d elements" % mesh.nelements) from pytential.qbx import QBXLayerPotentialSource from meshmode.discretization import Discretization from meshmode.discretization.poly_element import \ InterpolatoryQuadratureSimplexGroupFactory pre_density_discr = Discretization( cl_ctx, mesh, InterpolatoryQuadratureSimplexGroupFactory(case.target_order)) source_order = 4*case.target_order refiner_extra_kwargs = {} qbx_lpot_kwargs = {} if case.fmm_backend is None: qbx_lpot_kwargs["fmm_order"] = False else: if hasattr(case, "fmm_tol"): from sumpy.expansion.level_to_order import SimpleExpansionOrderFinder qbx_lpot_kwargs["fmm_level_to_order"] = SimpleExpansionOrderFinder( case.fmm_tol) elif hasattr(case, "fmm_order"): qbx_lpot_kwargs["fmm_order"] = case.fmm_order else: qbx_lpot_kwargs["fmm_order"] = case.qbx_order + 5 qbx = QBXLayerPotentialSource( pre_density_discr, fine_order=source_order, qbx_order=case.qbx_order, _box_extent_norm=getattr(case, "box_extent_norm", None), _from_sep_smaller_crit=getattr(case, "from_sep_smaller_crit", None), _from_sep_smaller_min_nsources_cumul=30, fmm_backend=case.fmm_backend, **qbx_lpot_kwargs) if case.use_refinement: if case.k != 0 and getattr(case, "refine_on_helmholtz_k", True): refiner_extra_kwargs["kernel_length_scale"] = 5/case.k if hasattr(case, "scaled_max_curvature_threshold"): refiner_extra_kwargs["_scaled_max_curvature_threshold"] = \ case.scaled_max_curvature_threshold if hasattr(case, "expansion_disturbance_tolerance"): refiner_extra_kwargs["_expansion_disturbance_tolerance"] = \ case.expansion_disturbance_tolerance if hasattr(case, "refinement_maxiter"): refiner_extra_kwargs["maxiter"] = case.refinement_maxiter #refiner_extra_kwargs["visualize"] = True print("%d elements before refinement" % pre_density_discr.mesh.nelements) qbx, _ = qbx.with_refinement(**refiner_extra_kwargs) print("%d stage-1 elements after refinement" % qbx.density_discr.mesh.nelements) print("%d stage-2 elements after refinement" % qbx.stage2_density_discr.mesh.nelements) print("quad stage-2 elements have %d nodes" % qbx.quad_stage2_density_discr.groups[0].nunit_nodes) density_discr = qbx.density_discr if hasattr(case, "visualize_geometry") and case.visualize_geometry: bdry_normals = bind( density_discr, sym.normal(mesh.ambient_dim) )(queue).as_vector(dtype=object) bdry_vis = make_visualizer(queue, density_discr, case.target_order) bdry_vis.write_vtk_file("geometry.vtu", [ ("normals", bdry_normals) ]) # {{{ plot geometry if 0: if mesh.ambient_dim == 2: # show geometry, centers, normals nodes_h = density_discr.nodes().get(queue=queue) pt.plot(nodes_h[0], nodes_h[1], "x-") normal = bind(density_discr, sym.normal(2))(queue).as_vector(np.object) pt.quiver(nodes_h[0], nodes_h[1], normal[0].get(queue), normal[1].get(queue)) pt.gca().set_aspect("equal") pt.show() elif mesh.ambient_dim == 3: bdry_vis = make_visualizer(queue, density_discr, case.target_order+3) bdry_normals = bind(density_discr, sym.normal(3))(queue)\ .as_vector(dtype=object) bdry_vis.write_vtk_file("pre-solve-source-%s.vtu" % resolution, [ ("bdry_normals", bdry_normals), ]) else: raise ValueError("invalid mesh dim") # }}} # {{{ set up operator from pytential.symbolic.pde.scalar import ( DirichletOperator, NeumannOperator) from sumpy.kernel import LaplaceKernel, HelmholtzKernel if case.k: knl = HelmholtzKernel(mesh.ambient_dim) knl_kwargs = {"k": sym.var("k")} concrete_knl_kwargs = {"k": case.k} else: knl = LaplaceKernel(mesh.ambient_dim) knl_kwargs = {} concrete_knl_kwargs = {} if knl.is_complex_valued: dtype = np.complex128 else: dtype = np.float64 loc_sign = +1 if case.prob_side in [+1, "scat"] else -1 if case.bc_type == "dirichlet": op = DirichletOperator(knl, loc_sign, use_l2_weighting=True, kernel_arguments=knl_kwargs) elif case.bc_type == "neumann": op = NeumannOperator(knl, loc_sign, use_l2_weighting=True, use_improved_operator=False, kernel_arguments=knl_kwargs) else: assert False op_u = op.operator(sym.var("u")) # }}} # {{{ set up test data if case.prob_side == -1: test_src_geo_radius = case.outer_radius test_tgt_geo_radius = case.inner_radius elif case.prob_side == +1: test_src_geo_radius = case.inner_radius test_tgt_geo_radius = case.outer_radius elif case.prob_side == "scat": test_src_geo_radius = case.outer_radius test_tgt_geo_radius = case.outer_radius else: raise ValueError("unknown problem_side") point_sources = make_circular_point_group( mesh.ambient_dim, 10, test_src_geo_radius, func=lambda x: x**1.5) test_targets = make_circular_point_group( mesh.ambient_dim, 20, test_tgt_geo_radius) np.random.seed(22) source_charges = np.random.randn(point_sources.shape[1]) source_charges[-1] = -np.sum(source_charges[:-1]) source_charges = source_charges.astype(dtype) assert np.sum(source_charges) < 1e-15 source_charges_dev = cl.array.to_device(queue, source_charges) # }}} # {{{ establish BCs from pytential.source import PointPotentialSource from pytential.target import PointsTarget point_source = PointPotentialSource(cl_ctx, point_sources) pot_src = sym.IntG( # FIXME: qbx_forced_limit--really? knl, sym.var("charges"), qbx_forced_limit=None, **knl_kwargs) test_direct = bind((point_source, PointsTarget(test_targets)), pot_src)( queue, charges=source_charges_dev, **concrete_knl_kwargs) if case.bc_type == "dirichlet": bc = bind((point_source, density_discr), pot_src)( queue, charges=source_charges_dev, **concrete_knl_kwargs) elif case.bc_type == "neumann": bc = bind( (point_source, density_discr), sym.normal_derivative( qbx.ambient_dim, pot_src, where=sym.DEFAULT_TARGET) )(queue, charges=source_charges_dev, **concrete_knl_kwargs) # }}} # {{{ solve bound_op = bind(qbx, op_u) rhs = bind(density_discr, op.prepare_rhs(sym.var("bc")))(queue, bc=bc) try: from pytential.solve import gmres gmres_result = gmres( bound_op.scipy_op(queue, "u", dtype, **concrete_knl_kwargs), rhs, tol=case.gmres_tol, progress=True, hard_failure=True, stall_iterations=50, no_progress_factor=1.05) except QBXTargetAssociationFailedException as e: bdry_vis = make_visualizer(queue, density_discr, case.target_order+3) bdry_vis.write_vtk_file("failed-targets-%s.vtu" % resolution, [ ("failed_targets", e.failed_target_flags), ]) raise print("gmres state:", gmres_result.state) weighted_u = gmres_result.solution # }}} # {{{ build matrix for spectrum check if 0: from sumpy.tools import build_matrix mat = build_matrix( bound_op.scipy_op( queue, arg_name="u", dtype=dtype, k=case.k)) w, v = la.eig(mat) if 0: pt.imshow(np.log10(1e-20+np.abs(mat))) pt.colorbar() pt.show() #assert abs(s[-1]) < 1e-13, "h #assert abs(s[-2]) > 1e-7 #from pudb import set_trace; set_trace() # }}} if case.prob_side != "scat": # {{{ error check points_target = PointsTarget(test_targets) bound_tgt_op = bind((qbx, points_target), op.representation(sym.var("u"))) test_via_bdry = bound_tgt_op(queue, u=weighted_u, k=case.k) err = test_via_bdry - test_direct err = err.get() test_direct = test_direct.get() test_via_bdry = test_via_bdry.get() # {{{ remove effect of net source charge if case.k == 0 and case.bc_type == "neumann" and loc_sign == -1: # remove constant offset in interior Laplace Neumann error tgt_ones = np.ones_like(test_direct) tgt_ones = tgt_ones/la.norm(tgt_ones) err = err - np.vdot(tgt_ones, err)*tgt_ones # }}} rel_err_2 = la.norm(err)/la.norm(test_direct) rel_err_inf = la.norm(err, np.inf)/la.norm(test_direct, np.inf) # }}} print("rel_err_2: %g rel_err_inf: %g" % (rel_err_2, rel_err_inf)) else: rel_err_2 = None rel_err_inf = None # {{{ test gradient if case.check_gradient and case.prob_side != "scat": bound_grad_op = bind((qbx, points_target), op.representation( sym.var("u"), map_potentials=lambda pot: sym.grad(mesh.ambient_dim, pot), qbx_forced_limit=None)) #print(bound_t_deriv_op.code) grad_from_src = bound_grad_op( queue, u=weighted_u, **concrete_knl_kwargs) grad_ref = (bind( (point_source, points_target), sym.grad(mesh.ambient_dim, pot_src) )(queue, charges=source_charges_dev, **concrete_knl_kwargs) ) grad_err = (grad_from_src - grad_ref) rel_grad_err_inf = ( la.norm(grad_err[0].get(), np.inf) / la.norm(grad_ref[0].get(), np.inf)) print("rel_grad_err_inf: %g" % rel_grad_err_inf) # }}} # {{{ test tangential derivative if case.check_tangential_deriv and case.prob_side != "scat": bound_t_deriv_op = bind(qbx, op.representation( sym.var("u"), map_potentials=lambda pot: sym.tangential_derivative(2, pot), qbx_forced_limit=loc_sign)) #print(bound_t_deriv_op.code) tang_deriv_from_src = bound_t_deriv_op( queue, u=weighted_u, **concrete_knl_kwargs).as_scalar().get() tang_deriv_ref = (bind( (point_source, density_discr), sym.tangential_derivative(2, pot_src) )(queue, charges=source_charges_dev, **concrete_knl_kwargs) .as_scalar().get()) if 0: pt.plot(tang_deriv_ref.real) pt.plot(tang_deriv_from_src.real) pt.show() td_err = (tang_deriv_from_src - tang_deriv_ref) rel_td_err_inf = la.norm(td_err, np.inf)/la.norm(tang_deriv_ref, np.inf) print("rel_td_err_inf: %g" % rel_td_err_inf) else: rel_td_err_inf = None # }}} # {{{ any-D file plotting if visualize: bdry_vis = make_visualizer(queue, density_discr, case.target_order+3) bdry_normals = bind(density_discr, sym.normal(qbx.ambient_dim))(queue)\ .as_vector(dtype=object) sym_sqrt_j = sym.sqrt_jac_q_weight(density_discr.ambient_dim) u = bind(density_discr, sym.var("u")/sym_sqrt_j)(queue, u=weighted_u) bdry_vis.write_vtk_file("source-%s.vtu" % resolution, [ ("u", u), ("bc", bc), #("bdry_normals", bdry_normals), ]) from sumpy.visualization import make_field_plotter_from_bbox # noqa from meshmode.mesh.processing import find_bounding_box vis_grid_spacing = (0.1, 0.1, 0.1)[:qbx.ambient_dim] if hasattr(case, "vis_grid_spacing"): vis_grid_spacing = case.vis_grid_spacing vis_extend_factor = 0.2 if hasattr(case, "vis_extend_factor"): vis_grid_spacing = case.vis_grid_spacing fplot = make_field_plotter_from_bbox( find_bounding_box(mesh), h=vis_grid_spacing, extend_factor=vis_extend_factor) qbx_tgt_tol = qbx.copy(target_association_tolerance=0.15) from pytential.target import PointsTarget try: solved_pot = bind( (qbx_tgt_tol, PointsTarget(fplot.points)), op.representation(sym.var("u")) )(queue, u=weighted_u, k=case.k) except QBXTargetAssociationFailedException as e: fplot.write_vtk_file( "failed-targets.vts", [ ("failed_targets", e.failed_target_flags.get(queue)) ]) raise from sumpy.kernel import LaplaceKernel ones_density = density_discr.zeros(queue) ones_density.fill(1) indicator = bind( (qbx_tgt_tol, PointsTarget(fplot.points)), -sym.D(LaplaceKernel(density_discr.ambient_dim), sym.var("sigma"), qbx_forced_limit=None))( queue, sigma=ones_density).get() solved_pot = solved_pot.get() true_pot = bind((point_source, PointsTarget(fplot.points)), pot_src)( queue, charges=source_charges_dev, **concrete_knl_kwargs).get() #fplot.show_scalar_in_mayavi(solved_pot.real, max_val=5) if case.prob_side == "scat": fplot.write_vtk_file( "potential-%s.vts" % resolution, [ ("pot_scattered", solved_pot), ("pot_incoming", -true_pot), ("indicator", indicator), ] ) else: fplot.write_vtk_file( "potential-%s.vts" % resolution, [ ("solved_pot", solved_pot), ("true_pot", true_pot), ("indicator", indicator), ] ) # }}} class Result(Record): pass return Result( h_max=qbx.h_max, rel_err_2=rel_err_2, rel_err_inf=rel_err_inf, rel_td_err_inf=rel_td_err_inf, gmres_result=gmres_result)
def main(): import logging logging.basicConfig(level=logging.WARNING) # INFO for more progress info cl_ctx = cl.create_some_context() queue = cl.CommandQueue(cl_ctx) from meshmode.mesh.generation import ellipse, make_curve_mesh from functools import partial if 0: mesh = make_curve_mesh(partial(ellipse, 1), np.linspace(0, 1, nelements + 1), mesh_order) else: base_mesh = make_curve_mesh(partial(ellipse, 1), np.linspace(0, 1, nelements + 1), mesh_order) from meshmode.mesh.processing import affine_map, merge_disjoint_meshes nx = 2 ny = 2 dx = 2 / nx meshes = [ affine_map(base_mesh, A=np.diag([dx * 0.25, dx * 0.25]), b=np.array([dx * (ix - nx / 2), dx * (iy - ny / 2)])) for ix in range(nx) for iy in range(ny) ] mesh = merge_disjoint_meshes(meshes, single_group=True) if 0: from meshmode.mesh.visualization import draw_curve draw_curve(mesh) import matplotlib.pyplot as plt plt.show() pre_density_discr = Discretization( cl_ctx, mesh, InterpolatoryQuadratureSimplexGroupFactory(bdry_quad_order)) from pytential.qbx import (QBXLayerPotentialSource, QBXTargetAssociationFailedException) qbx, _ = QBXLayerPotentialSource(pre_density_discr, fine_order=bdry_ovsmp_quad_order, qbx_order=qbx_order, fmm_order=fmm_order).with_refinement() density_discr = qbx.density_discr # {{{ describe bvp from sumpy.kernel import LaplaceKernel, HelmholtzKernel kernel = HelmholtzKernel(2) cse = sym.cse sigma_sym = sym.var("sigma") sqrt_w = sym.sqrt_jac_q_weight(2) inv_sqrt_w_sigma = cse(sigma_sym / sqrt_w) # Brakhage-Werner parameter alpha = 1j # -1 for interior Dirichlet # +1 for exterior Dirichlet loc_sign = +1 bdry_op_sym = (-loc_sign * 0.5 * sigma_sym + sqrt_w * (alpha * sym.S( kernel, inv_sqrt_w_sigma, k=sym.var("k"), qbx_forced_limit=+1) - sym.D( kernel, inv_sqrt_w_sigma, k=sym.var("k"), qbx_forced_limit="avg"))) # }}} bound_op = bind(qbx, bdry_op_sym) # {{{ fix rhs and solve nodes = density_discr.nodes().with_queue(queue) k_vec = np.array([2, 1]) k_vec = k * k_vec / la.norm(k_vec, 2) def u_incoming_func(x): return cl.clmath.exp(1j * (x[0] * k_vec[0] + x[1] * k_vec[1])) bc = -u_incoming_func(nodes) bvp_rhs = bind(qbx, sqrt_w * sym.var("bc"))(queue, bc=bc) from pytential.solve import gmres gmres_result = gmres(bound_op.scipy_op(queue, "sigma", dtype=np.complex128, k=k), bvp_rhs, tol=1e-8, progress=True, stall_iterations=0, hard_failure=True) # }}} # {{{ postprocess/visualize sigma = gmres_result.solution repr_kwargs = dict(k=sym.var("k"), qbx_forced_limit=None) representation_sym = ( alpha * sym.S(kernel, inv_sqrt_w_sigma, **repr_kwargs) - sym.D(kernel, inv_sqrt_w_sigma, **repr_kwargs)) from sumpy.visualization import FieldPlotter fplot = FieldPlotter(np.zeros(2), extent=5, npoints=500) targets = cl.array.to_device(queue, fplot.points) u_incoming = u_incoming_func(targets) qbx_stick_out = qbx.copy(target_association_tolerance=0.05) ones_density = density_discr.zeros(queue) ones_density.fill(1) indicator = bind((qbx_stick_out, PointsTarget(targets)), sym.D(LaplaceKernel(2), sym.var("sigma"), qbx_forced_limit=None))(queue, sigma=ones_density).get() try: fld_in_vol = bind((qbx_stick_out, PointsTarget(targets)), representation_sym)(queue, sigma=sigma, k=k).get() except QBXTargetAssociationFailedException as e: fplot.write_vtk_file("failed-targets.vts", [("failed", e.failed_target_flags.get(queue))]) raise #fplot.show_scalar_in_mayavi(fld_in_vol.real, max_val=5) fplot.write_vtk_file("potential-helm.vts", [ ("potential", fld_in_vol), ("indicator", indicator), ("u_incoming", u_incoming.get()), ])
def test_3d_jump_relations(ctx_factory, relation, visualize=False): # logging.basicConfig(level=logging.INFO) cl_ctx = ctx_factory() queue = cl.CommandQueue(cl_ctx) if relation == "div_s": target_order = 3 else: target_order = 4 qbx_order = target_order from pytools.convergence import EOCRecorder eoc_rec = EOCRecorder() for nel_factor in [6, 10, 14]: from meshmode.mesh.generation import generate_torus mesh = generate_torus( 5, 2, order=target_order, n_outer=2*nel_factor, n_inner=nel_factor) from meshmode.discretization import Discretization from meshmode.discretization.poly_element import \ InterpolatoryQuadratureSimplexGroupFactory pre_discr = Discretization( cl_ctx, mesh, InterpolatoryQuadratureSimplexGroupFactory(3)) from pytential.qbx import QBXLayerPotentialSource qbx, _ = QBXLayerPotentialSource( pre_discr, fine_order=4*target_order, qbx_order=qbx_order, fmm_order=qbx_order + 5, fmm_backend="fmmlib" ).with_refinement() from sumpy.kernel import LaplaceKernel knl = LaplaceKernel(3) def nxcurlS(qbx_forced_limit): return sym.n_cross(sym.curl(sym.S( knl, sym.cse(sym.tangential_to_xyz(density_sym), "jxyz"), qbx_forced_limit=qbx_forced_limit))) x, y, z = qbx.density_discr.nodes().with_queue(queue) m = cl.clmath if relation == "nxcurls": density_sym = sym.make_sym_vector("density", 2) jump_identity_sym = ( nxcurlS(+1) - (nxcurlS("avg") + 0.5*sym.tangential_to_xyz(density_sym))) # The tangential coordinate system is element-local, so we can't just # conjure up some globally smooth functions, interpret their values # in the tangential coordinate system, and be done. Instead, generate # an XYZ function and project it. density = bind( qbx, sym.xyz_to_tangential(sym.make_sym_vector("jxyz", 3)))( queue, jxyz=sym.make_obj_array([ m.cos(0.5*x) * m.cos(0.5*y) * m.cos(0.5*z), m.sin(0.5*x) * m.cos(0.5*y) * m.sin(0.5*z), m.sin(0.5*x) * m.cos(0.5*y) * m.cos(0.5*z), ])) elif relation == "sp": density = m.cos(2*x) * m.cos(2*y) * m.cos(z) density_sym = sym.var("density") jump_identity_sym = ( sym.Sp(knl, density_sym, qbx_forced_limit=+1) - (sym.Sp(knl, density_sym, qbx_forced_limit="avg") - 0.5*density_sym)) elif relation == "div_s": density = m.cos(2*x) * m.cos(2*y) * m.cos(z) density_sym = sym.var("density") jump_identity_sym = ( sym.div(sym.S(knl, sym.normal(3).as_vector()*density_sym, qbx_forced_limit="avg")) + sym.D(knl, density_sym, qbx_forced_limit="avg")) else: raise ValueError("unexpected value of 'relation': %s" % relation) bound_jump_identity = bind(qbx, jump_identity_sym) jump_identity = bound_jump_identity(queue, density=density) err = ( norm(qbx, queue, jump_identity, np.inf) / norm(qbx, queue, density, np.inf)) print("ERROR", qbx.h_max, err) eoc_rec.add_data_point(qbx.h_max, err) # {{{ visualization if visualize and relation == "nxcurls": nxcurlS_ext = bind(qbx, nxcurlS(+1))(queue, density=density) nxcurlS_avg = bind(qbx, nxcurlS("avg"))(queue, density=density) jtxyz = bind(qbx, sym.tangential_to_xyz(density_sym))( queue, density=density) from meshmode.discretization.visualization import make_visualizer bdry_vis = make_visualizer(queue, qbx.density_discr, target_order+3) bdry_normals = bind(qbx, sym.normal(3))(queue)\ .as_vector(dtype=object) bdry_vis.write_vtk_file("source-%s.vtu" % nel_factor, [ ("jt", jtxyz), ("nxcurlS_ext", nxcurlS_ext), ("nxcurlS_avg", nxcurlS_avg), ("bdry_normals", bdry_normals), ]) if visualize and relation == "sp": sp_ext = bind(qbx, sym.Sp(knl, density_sym, qbx_forced_limit=+1))( queue, density=density) sp_avg = bind(qbx, sym.Sp(knl, density_sym, qbx_forced_limit="avg"))( queue, density=density) from meshmode.discretization.visualization import make_visualizer bdry_vis = make_visualizer(queue, qbx.density_discr, target_order+3) bdry_normals = bind(qbx, sym.normal(3))(queue)\ .as_vector(dtype=object) bdry_vis.write_vtk_file("source-%s.vtu" % nel_factor, [ ("density", density), ("sp_ext", sp_ext), ("sp_avg", sp_avg), ("bdry_normals", bdry_normals), ]) # }}} print(eoc_rec) assert eoc_rec.order_estimate() >= qbx_order - 1.5
def find_mode(): import warnings warnings.simplefilter("error", np.ComplexWarning) cl_ctx = cl.create_some_context() queue = cl.CommandQueue(cl_ctx) k0 = 1.4447 k1 = k0 * 1.02 beta_sym = sym.var("beta") from pytential.symbolic.pde.scalar import ( # noqa DielectricSRep2DBoundaryOperator as SRep, DielectricSDRep2DBoundaryOperator as SDRep) pde_op = SDRep(mode="te", k_vacuum=1, interfaces=((0, 1, sym.DEFAULT_SOURCE), ), domain_k_exprs=(k0, k1), beta=beta_sym, use_l2_weighting=False) u_sym = pde_op.make_unknown("u") op = pde_op.operator(u_sym) # {{{ discretization setup from meshmode.mesh.generation import ellipse, make_curve_mesh curve_f = partial(ellipse, 1) target_order = 7 qbx_order = 4 nelements = 30 from meshmode.mesh.processing import affine_map mesh = make_curve_mesh(curve_f, np.linspace(0, 1, nelements + 1), target_order) lambda_ = 1.55 circle_radius = 3.4 * 2 * np.pi / lambda_ mesh = affine_map(mesh, A=circle_radius * np.eye(2)) from meshmode.discretization import Discretization from meshmode.discretization.poly_element import \ InterpolatoryQuadratureSimplexGroupFactory from pytential.qbx import QBXLayerPotentialSource density_discr = Discretization( cl_ctx, mesh, InterpolatoryQuadratureSimplexGroupFactory(target_order)) qbx = QBXLayerPotentialSource( density_discr, 4 * target_order, qbx_order, # Don't use FMM for now fmm_order=False) # }}} x_vec = np.random.randn(len(u_sym) * density_discr.nnodes) y_vec = np.random.randn(len(u_sym) * density_discr.nnodes) def muller_solve_func(beta): from pytential.symbolic.execution import build_matrix mat = build_matrix(queue, qbx, op, u_sym, context={"beta": beta}).get() return 1 / x_vec.dot(la.solve(mat, y_vec)) starting_guesses = (1 + 0j) * (k0 + (k1 - k0) * np.random.rand(3)) from pytential.muller import muller beta, niter = muller(muller_solve_func, z_start=starting_guesses) print("beta")
def main(): # cl.array.to_device(queue, numpy_array) from meshmode.mesh.io import generate_gmsh, FileSource mesh = generate_gmsh( FileSource("ellipsoid.step"), 2, order=2, other_options=["-string", "Mesh.CharacteristicLengthMax = %g;" % h]) from meshmode.mesh.processing import perform_flips # Flip elements--gmsh generates inside-out geometry. mesh = perform_flips(mesh, np.ones(mesh.nelements)) print("%d elements" % mesh.nelements) from meshmode.mesh.processing import find_bounding_box bbox_min, bbox_max = find_bounding_box(mesh) bbox_center = 0.5*(bbox_min+bbox_max) bbox_size = max(bbox_max-bbox_min) / 2 logger.info("%d elements" % mesh.nelements) from pytential.qbx import QBXLayerPotentialSource from meshmode.discretization import Discretization from meshmode.discretization.poly_element import \ InterpolatoryQuadratureSimplexGroupFactory density_discr = Discretization( cl_ctx, mesh, InterpolatoryQuadratureSimplexGroupFactory(target_order)) qbx = QBXLayerPotentialSource(density_discr, 4*target_order, qbx_order, fmm_order=qbx_order + 10, fmm_backend="fmmlib") from pytential.symbolic.pde.maxwell import MuellerAugmentedMFIEOperator pde_op = MuellerAugmentedMFIEOperator( omega=0.4, epss=[1.4, 1.0], mus=[1.2, 1.0], ) from pytential import bind, sym unk = pde_op.make_unknown("sigma") sym_operator = pde_op.operator(unk) sym_rhs = pde_op.rhs( sym.make_sym_vector("Einc", 3), sym.make_sym_vector("Hinc", 3)) sym_repr = pde_op.representation(0, unk) if 1: expr = sym_repr print(sym.pretty(expr)) print("#"*80) from pytential.target import PointsTarget tgt_points=np.zeros((3,1)) tgt_points[0,0] = 100 tgt_points[1,0] = -200 tgt_points[2,0] = 300 bound_op = bind((qbx, PointsTarget(tgt_points)), expr) print(bound_op.code) if 1: def green3e(x,y,z,source,strength,k): # electric field corresponding to dyadic green's function # due to monochromatic electric dipole located at "source". # "strength" is the the intensity of the dipole. # E = (I + Hess)(exp(ikr)/r) dot (strength) # dx = x - source[0] dy = y - source[1] dz = z - source[2] rr = np.sqrt(dx**2 + dy**2 + dz**2) fout = np.exp(1j*k*rr)/rr evec = fout*strength qmat = np.zeros((3,3),dtype=np.complex128) qmat[0,0]=(2*dx**2-dy**2-dz**2)*(1-1j*k*rr) qmat[1,1]=(2*dy**2-dz**2-dx**2)*(1-1j*k*rr) qmat[2,2]=(2*dz**2-dx**2-dy**2)*(1-1j*k*rr) qmat[0,0]=qmat[0,0]+(-k**2*dx**2*rr**2) qmat[1,1]=qmat[1,1]+(-k**2*dy**2*rr**2) qmat[2,2]=qmat[2,2]+(-k**2*dz**2*rr**2) qmat[0,1]=(3-k**2*rr**2-3*1j*k*rr)*(dx*dy) qmat[1,2]=(3-k**2*rr**2-3*1j*k*rr)*(dy*dz) qmat[2,0]=(3-k**2*rr**2-3*1j*k*rr)*(dz*dx) qmat[1,0]=qmat[0,1] qmat[2,1]=qmat[1,2] qmat[0,2]=qmat[2,0] fout=np.exp(1j*k*rr)/rr**5/k**2 fvec = fout*np.dot(qmat,strength) evec = evec + fvec return evec def green3m(x,y,z,source,strength,k): # magnetic field corresponding to dyadic green's function # due to monochromatic electric dipole located at "source". # "strength" is the the intensity of the dipole. # H = curl((I + Hess)(exp(ikr)/r) dot (strength)) = # strength \cross \grad (exp(ikr)/r) # dx = x - source[0] dy = y - source[1] dz = z - source[2] rr = np.sqrt(dx**2 + dy**2 + dz**2) fout=(1-1j*k*rr)*np.exp(1j*k*rr)/rr**3 fvec = np.zeros(3,dtype=np.complex128) fvec[0] = fout*dx fvec[1] = fout*dy fvec[2] = fout*dz hvec = np.cross(strength,fvec) return hvec def dipole3e(x,y,z,source,strength,k): # # evalaute electric and magnetic field due # to monochromatic electric dipole located at "source" # with intensity "strength" evec = green3e(x,y,z,source,strength,k) evec = evec*1j*k hvec = green3m(x,y,z,source,strength,k) return evec,hvec def dipole3m(x,y,z,source,strength,k): # # evalaute electric and magnetic field due # to monochromatic magnetic dipole located at "source" # with intensity "strength" evec = green3m(x,y,z,source,strength,k) hvec = green3e(x,y,z,source,strength,k) hvec = -hvec*1j*k return evec,hvec def dipole3eall(x,y,z,sources,strengths,k): ns = len(strengths) evec = np.zeros(3,dtype=np.complex128) hvec = np.zeros(3,dtype=np.complex128) for i in range(ns): evect,hvect = dipole3e(x,y,z,sources[i],strengths[i],k) evec = evec + evect hvec = hvec + hvect nodes = density_discr.nodes().with_queue(queue).get() source = [0.01,-0.03,0.02] # source = cl.array.to_device(queue,np.zeros(3)) # source[0] = 0.01 # source[1] =-0.03 # source[2] = 0.02 strength = np.ones(3) # evec = cl.array.to_device(queue,np.zeros((3,len(nodes[0])),dtype=np.complex128)) # hvec = cl.array.to_device(queue,np.zeros((3,len(nodes[0])),dtype=np.complex128)) evec = np.zeros((3,len(nodes[0])),dtype=np.complex128) hvec = np.zeros((3,len(nodes[0])),dtype=np.complex128) for i in range(len(nodes[0])): evec[:,i],hvec[:,i] = dipole3e(nodes[0][i],nodes[1][i],nodes[2][i],source,strength,k) print(np.shape(hvec)) print(type(evec)) print(type(hvec)) evec = cl.array.to_device(queue,evec) hvec = cl.array.to_device(queue,hvec) bvp_rhs = bind(qbx, sym_rhs)(queue,Einc=evec,Hinc=hvec) print(np.shape(bvp_rhs)) print(type(bvp_rhs)) # print(bvp_rhs) 1/-1 bound_op = bind(qbx, sym_operator) from pytential.solve import gmres if 0: gmres_result = gmres( bound_op.scipy_op(queue, "sigma", dtype=np.complex128, k=k), bvp_rhs, tol=1e-8, progress=True, stall_iterations=0, hard_failure=True) sigma = gmres_result.solution fld_at_tgt = bind((qbx, PointsTarget(tgt_points)), sym_repr)(queue, sigma=bvp_rhs,k=k) fld_at_tgt = np.array([ fi.get() for fi in fld_at_tgt ]) print(fld_at_tgt) 1/0 # }}} #mlab.figure(bgcolor=(1, 1, 1)) if 1: from meshmode.discretization.visualization import make_visualizer bdry_vis = make_visualizer(queue, density_discr, target_order) bdry_normals = bind(density_discr, sym.normal(3))(queue)\ .as_vector(dtype=object) bdry_vis.write_vtk_file("source.vtu", [ ("sigma", sigma), ("bdry_normals", bdry_normals), ]) fplot = FieldPlotter(bbox_center, extent=2*bbox_size, npoints=(150, 150, 1)) qbx_tgt_tol = qbx.copy(target_association_tolerance=0.1) from pytential.target import PointsTarget from pytential.qbx import QBXTargetAssociationFailedException rho_sym = sym.var("rho") try: fld_in_vol = bind( (qbx_tgt_tol, PointsTarget(fplot.points)), sym.make_obj_array([ sym.S(pde_op.kernel, rho_sym, k=sym.var("k"), qbx_forced_limit=None), sym.d_dx(3, sym.S(pde_op.kernel, rho_sym, k=sym.var("k"), qbx_forced_limit=None)), sym.d_dy(3, sym.S(pde_op.kernel, rho_sym, k=sym.var("k"), qbx_forced_limit=None)), sym.d_dz(3, sym.S(pde_op.kernel, rho_sym, k=sym.var("k"), qbx_forced_limit=None)), ]) )(queue, jt=jt, rho=rho, k=k) except QBXTargetAssociationFailedException as e: fplot.write_vtk_file( "failed-targets.vts", [ ("failed_targets", e.failed_target_flags.get(queue)) ]) raise fld_in_vol = sym.make_obj_array( [fiv.get() for fiv in fld_in_vol]) #fplot.show_scalar_in_mayavi(fld_in_vol.real, max_val=5) fplot.write_vtk_file( "potential.vts", [ ("potential", fld_in_vol[0]), ("grad", fld_in_vol[1:]), ] )
def main(mesh_name="ellipsoid"): import logging logger = logging.getLogger(__name__) logging.basicConfig(level=logging.WARNING) # INFO for more progress info cl_ctx = cl.create_some_context() queue = cl.CommandQueue(cl_ctx) actx = PyOpenCLArrayContext(queue) if mesh_name == "ellipsoid": cad_file_name = "geometries/ellipsoid.step" h = 0.6 elif mesh_name == "two-cylinders": cad_file_name = "geometries/two-cylinders-smooth.step" h = 0.4 else: raise ValueError("unknown mesh name: %s" % mesh_name) from meshmode.mesh.io import generate_gmsh, FileSource mesh = generate_gmsh( FileSource(cad_file_name), 2, order=2, other_options=["-string", "Mesh.CharacteristicLengthMax = %g;" % h], target_unit="MM") from meshmode.mesh.processing import perform_flips # Flip elements--gmsh generates inside-out geometry. mesh = perform_flips(mesh, np.ones(mesh.nelements)) from meshmode.mesh.processing import find_bounding_box bbox_min, bbox_max = find_bounding_box(mesh) bbox_center = 0.5 * (bbox_min + bbox_max) bbox_size = max(bbox_max - bbox_min) / 2 logger.info("%d elements" % mesh.nelements) from pytential.qbx import QBXLayerPotentialSource from meshmode.discretization import Discretization from meshmode.discretization.poly_element import \ InterpolatoryQuadratureSimplexGroupFactory density_discr = Discretization( actx, mesh, InterpolatoryQuadratureSimplexGroupFactory(target_order)) qbx = QBXLayerPotentialSource(density_discr, 4 * target_order, qbx_order, fmm_order=qbx_order + 3, target_association_tolerance=0.15) from pytential.target import PointsTarget fplot = FieldPlotter(bbox_center, extent=3.5 * bbox_size, npoints=150) from pytential import GeometryCollection places = GeometryCollection( { "qbx": qbx, "targets": PointsTarget(fplot.points) }, auto_where="qbx") density_discr = places.get_discretization("qbx") nodes = thaw(actx, density_discr.nodes()) angle = actx.np.arctan2(nodes[1], nodes[0]) if k: kernel = HelmholtzKernel(3) else: kernel = LaplaceKernel(3) #op = sym.d_dx(sym.S(kernel, sym.var("sigma"), qbx_forced_limit=None)) op = sym.D(kernel, sym.var("sigma"), qbx_forced_limit=None) #op = sym.S(kernel, sym.var("sigma"), qbx_forced_limit=None) sigma = actx.np.cos(mode_nr * angle) if 0: from meshmode.dof_array import flatten, unflatten sigma = flatten(0 * angle) from random import randrange for i in range(5): sigma[randrange(len(sigma))] = 1 sigma = unflatten(actx, density_discr, sigma) if isinstance(kernel, HelmholtzKernel): for i, elem in np.ndenumerate(sigma): sigma[i] = elem.astype(np.complex128) fld_in_vol = actx.to_numpy( bind(places, op, auto_where=("qbx", "targets"))(actx, sigma=sigma, k=k)) #fplot.show_scalar_in_mayavi(fld_in_vol.real, max_val=5) fplot.write_vtk_file("layerpot-3d-potential.vts", [("potential", fld_in_vol)]) bdry_normals = bind(places, sym.normal( density_discr.ambient_dim))(actx).as_vector(dtype=object) from meshmode.discretization.visualization import make_visualizer bdry_vis = make_visualizer(actx, density_discr, target_order) bdry_vis.write_vtk_file("layerpot-3d-density.vtu", [ ("sigma", sigma), ("bdry_normals", bdry_normals), ])
mesh = make_curve_mesh(starfish, np.linspace(0, 1, nelements+1), target_order) from pytential.discretization.qbx import make_upsampling_qbx_discr discr = make_upsampling_qbx_discr( cl_ctx, mesh, target_order, qbx_order) nodes = discr.nodes().with_queue(queue) angle = cl.clmath.atan2(nodes[1], nodes[0]) from pytential import bind, sym representation = sym.S(0, sym.var("sigma")) op = representation bc = cl.clmath.cos(mode_nr*angle) bound_op = bind(discr, op) from sumpy.tools import build_matrix mat = build_matrix(bound_op.scipy_op(queue, "sigma")) w, v = la.eig(mat) import matplotlib.pyplot as pt pt.plot(w.real, w.imag, "x") pt.rc("font", size=20) pt.grid()
def main(): import logging logging.basicConfig(level=logging.WARNING) # INFO for more progress info cl_ctx = cl.create_some_context() queue = cl.CommandQueue(cl_ctx) from meshmode.mesh.generation import ellipse, make_curve_mesh from functools import partial if 0: mesh = make_curve_mesh( partial(ellipse, 1), np.linspace(0, 1, nelements+1), mesh_order) else: base_mesh = make_curve_mesh( partial(ellipse, 1), np.linspace(0, 1, nelements+1), mesh_order) from meshmode.mesh.processing import affine_map, merge_disjoint_meshes nx = 2 ny = 2 dx = 2 / nx meshes = [ affine_map( base_mesh, A=np.diag([dx*0.25, dx*0.25]), b=np.array([dx*(ix-nx/2), dx*(iy-ny/2)])) for ix in range(nx) for iy in range(ny)] mesh = merge_disjoint_meshes(meshes, single_group=True) if 0: from meshmode.mesh.visualization import draw_curve draw_curve(mesh) import matplotlib.pyplot as plt plt.show() pre_density_discr = Discretization( cl_ctx, mesh, InterpolatoryQuadratureSimplexGroupFactory(bdry_quad_order)) from pytential.qbx import ( QBXLayerPotentialSource, QBXTargetAssociationFailedException) qbx, _ = QBXLayerPotentialSource( pre_density_discr, fine_order=bdry_ovsmp_quad_order, qbx_order=qbx_order, fmm_order=fmm_order ).with_refinement() density_discr = qbx.density_discr # {{{ describe bvp from sumpy.kernel import LaplaceKernel, HelmholtzKernel kernel = HelmholtzKernel(2) cse = sym.cse sigma_sym = sym.var("sigma") sqrt_w = sym.sqrt_jac_q_weight(2) inv_sqrt_w_sigma = cse(sigma_sym/sqrt_w) # Brakhage-Werner parameter alpha = 1j # -1 for interior Dirichlet # +1 for exterior Dirichlet loc_sign = +1 bdry_op_sym = (-loc_sign*0.5*sigma_sym + sqrt_w*( alpha*sym.S(kernel, inv_sqrt_w_sigma, k=sym.var("k"), qbx_forced_limit=+1) - sym.D(kernel, inv_sqrt_w_sigma, k=sym.var("k"), qbx_forced_limit="avg") )) # }}} bound_op = bind(qbx, bdry_op_sym) # {{{ fix rhs and solve nodes = density_discr.nodes().with_queue(queue) k_vec = np.array([2, 1]) k_vec = k * k_vec / la.norm(k_vec, 2) def u_incoming_func(x): return cl.clmath.exp( 1j * (x[0] * k_vec[0] + x[1] * k_vec[1])) bc = -u_incoming_func(nodes) bvp_rhs = bind(qbx, sqrt_w*sym.var("bc"))(queue, bc=bc) from pytential.solve import gmres gmres_result = gmres( bound_op.scipy_op(queue, "sigma", dtype=np.complex128, k=k), bvp_rhs, tol=1e-8, progress=True, stall_iterations=0, hard_failure=True) # }}} # {{{ postprocess/visualize sigma = gmres_result.solution repr_kwargs = dict(k=sym.var("k"), qbx_forced_limit=None) representation_sym = ( alpha*sym.S(kernel, inv_sqrt_w_sigma, **repr_kwargs) - sym.D(kernel, inv_sqrt_w_sigma, **repr_kwargs)) from sumpy.visualization import FieldPlotter fplot = FieldPlotter(np.zeros(2), extent=5, npoints=500) targets = cl.array.to_device(queue, fplot.points) u_incoming = u_incoming_func(targets) qbx_stick_out = qbx.copy(target_association_tolerance=0.05) ones_density = density_discr.zeros(queue) ones_density.fill(1) indicator = bind( (qbx_stick_out, PointsTarget(targets)), sym.D(LaplaceKernel(2), sym.var("sigma"), qbx_forced_limit=None))( queue, sigma=ones_density).get() try: fld_in_vol = bind( (qbx_stick_out, PointsTarget(targets)), representation_sym)(queue, sigma=sigma, k=k).get() except QBXTargetAssociationFailedException as e: fplot.write_vtk_file( "failed-targets.vts", [ ("failed", e.failed_target_flags.get(queue)) ] ) raise #fplot.show_scalar_in_mayavi(fld_in_vol.real, max_val=5) fplot.write_vtk_file( "potential-helm.vts", [ ("potential", fld_in_vol), ("indicator", indicator), ("u_incoming", u_incoming.get()), ] )
def main(): import logging logger = logging.getLogger(__name__) logging.basicConfig(level=logging.WARNING) # INFO for more progress info from meshmode.mesh.io import generate_gmsh, FileSource mesh = generate_gmsh( FileSource(cad_file_name), 2, order=2, other_options=["-string", "Mesh.CharacteristicLengthMax = %g;" % h]) from meshmode.mesh.processing import perform_flips # Flip elements--gmsh generates inside-out geometry. mesh = perform_flips(mesh, np.ones(mesh.nelements)) from meshmode.mesh.processing import find_bounding_box bbox_min, bbox_max = find_bounding_box(mesh) bbox_center = 0.5*(bbox_min+bbox_max) bbox_size = max(bbox_max-bbox_min) / 2 logger.info("%d elements" % mesh.nelements) from pytential.qbx import QBXLayerPotentialSource from meshmode.discretization import Discretization from meshmode.discretization.poly_element import \ InterpolatoryQuadratureSimplexGroupFactory density_discr = Discretization( cl_ctx, mesh, InterpolatoryQuadratureSimplexGroupFactory(target_order)) qbx, _ = QBXLayerPotentialSource(density_discr, 4*target_order, qbx_order, fmm_order=qbx_order + 3, target_association_tolerance=0.15).with_refinement() nodes = density_discr.nodes().with_queue(queue) angle = cl.clmath.atan2(nodes[1], nodes[0]) from pytential import bind, sym #op = sym.d_dx(sym.S(kernel, sym.var("sigma"), qbx_forced_limit=None)) op = sym.D(kernel, sym.var("sigma"), qbx_forced_limit=None) #op = sym.S(kernel, sym.var("sigma"), qbx_forced_limit=None) sigma = cl.clmath.cos(mode_nr*angle) if 0: sigma = 0*angle from random import randrange for i in range(5): sigma[randrange(len(sigma))] = 1 if isinstance(kernel, HelmholtzKernel): sigma = sigma.astype(np.complex128) fplot = FieldPlotter(bbox_center, extent=3.5*bbox_size, npoints=150) from pytential.target import PointsTarget fld_in_vol = bind( (qbx, PointsTarget(fplot.points)), op)(queue, sigma=sigma, k=k).get() #fplot.show_scalar_in_mayavi(fld_in_vol.real, max_val=5) fplot.write_vtk_file( "potential-3d.vts", [ ("potential", fld_in_vol) ] ) bdry_normals = bind( density_discr, sym.normal(density_discr.ambient_dim))(queue).as_vector(dtype=object) from meshmode.discretization.visualization import make_visualizer bdry_vis = make_visualizer(queue, density_discr, target_order) bdry_vis.write_vtk_file("source-3d.vtu", [ ("sigma", sigma), ("bdry_normals", bdry_normals), ])
def main(): import logging logging.basicConfig(level=logging.INFO) cl_ctx = cl.create_some_context() queue = cl.CommandQueue(cl_ctx) from meshmode.mesh.generation import ellipse, make_curve_mesh from functools import partial mesh = make_curve_mesh( partial(ellipse, 3), np.linspace(0, 1, nelements+1), mesh_order) density_discr = Discretization( cl_ctx, mesh, InterpolatoryQuadratureSimplexGroupFactory(bdry_quad_order)) from pytential.qbx import QBXLayerPotentialSource qbx = QBXLayerPotentialSource( density_discr, fine_order=bdry_ovsmp_quad_order, qbx_order=qbx_order, fmm_order=fmm_order ) # {{{ describe bvp from sumpy.kernel import HelmholtzKernel kernel = HelmholtzKernel(2) cse = sym.cse sigma_sym = sym.var("sigma") sqrt_w = sym.sqrt_jac_q_weight() inv_sqrt_w_sigma = cse(sigma_sym/sqrt_w) # Brakhage-Werner parameter alpha = 1j # -1 for interior Dirichlet # +1 for exterior Dirichlet loc_sign = -1 bdry_op_sym = (-loc_sign*0.5*sigma_sym + sqrt_w*( alpha*sym.S(kernel, inv_sqrt_w_sigma, k=sym.var("k")) - sym.D(kernel, inv_sqrt_w_sigma, k=sym.var("k")) )) # }}} bound_op = bind(qbx, bdry_op_sym) # {{{ fix rhs and solve mode_nr = 3 nodes = density_discr.nodes().with_queue(queue) angle = cl.clmath.atan2(nodes[1], nodes[0]) bc = cl.clmath.cos(mode_nr*angle) bvp_rhs = bind(qbx, sqrt_w*sym.var("bc"))(queue, bc=bc) from pytential.solve import gmres gmres_result = gmres( bound_op.scipy_op(queue, "sigma", k=k), bvp_rhs, tol=1e-14, progress=True, stall_iterations=0, hard_failure=True) # }}} # {{{ postprocess/visualize sigma = gmres_result.solution representation_sym = ( alpha*sym.S(kernel, inv_sqrt_w_sigma, k=sym.var("k")) - sym.D(kernel, inv_sqrt_w_sigma, k=sym.var("k"))) from sumpy.visualization import FieldPlotter fplot = FieldPlotter(np.zeros(2), extent=5, npoints=1500) from pytential.target import PointsTarget fld_in_vol = bind( (qbx, PointsTarget(fplot.points)), representation_sym)(queue, sigma=sigma, k=k).get() #fplot.show_scalar_in_mayavi(fld_in_vol.real, max_val=5) fplot.write_vtk_file( "potential.vts", [ ("potential", fld_in_vol) ] )