def test_chained_full_resample_matrix(ctx_factory, ndim, visualize=False): from meshmode.discretization.connection.chained import \ make_full_resample_matrix ctx = ctx_factory() queue = cl.CommandQueue(ctx) actx = PyOpenCLArrayContext(queue) discr = create_discretization(actx, ndim) connections = [] conn = create_refined_connection(actx, discr) connections.append(conn) conn = create_refined_connection(actx, conn.to_discr) connections.append(conn) from meshmode.discretization.connection import \ ChainedDiscretizationConnection chained = ChainedDiscretizationConnection(connections) def f(x): from six.moves import reduce return 0.1 * reduce(lambda x, y: x * actx.np.sin(5 * y), x) resample_mat = actx.to_numpy(make_full_resample_matrix(actx, chained)) x = thaw(actx, connections[0].from_discr.nodes()) fx = f(x) f1 = resample_mat @ actx.to_numpy(flatten(fx)) f2 = actx.to_numpy(flatten(chained(fx))) f3 = actx.to_numpy(flatten(connections[1](connections[0](fx)))) assert np.allclose(f1, f2) assert np.allclose(f2, f3)
def test_vortex_init(ctx_factory): """ Simple test to check that Vortex2D initializer creates the expected solution field. """ cl_ctx = ctx_factory() queue = cl.CommandQueue(cl_ctx) actx = PyOpenCLArrayContext(queue) dim = 2 nel_1d = 4 from meshmode.mesh.generation import generate_regular_rect_mesh mesh = generate_regular_rect_mesh(a=[(0.0, ), (-5.0, )], b=[(10.0, ), (5.0, )], nelements_per_axis=(nel_1d, ) * dim) order = 3 logger.info(f"Number of elements: {mesh.nelements}") discr = EagerDGDiscretization(actx, mesh, order=order) nodes = thaw(actx, discr.nodes()) # Init soln with Vortex vortex = Vortex2D() cv = vortex(nodes) gamma = 1.4 p = 0.4 * (cv.energy - 0.5 * np.dot(cv.momentum, cv.momentum) / cv.mass) exp_p = cv.mass**gamma errmax = actx.to_numpy(discr.norm(p - exp_p, np.inf)) logger.info(f"vortex_soln = {cv}") logger.info(f"pressure = {p}") assert errmax < 1e-15
def test_external_call(ctx_factory): cl_ctx = ctx_factory() queue = cl.CommandQueue(cl_ctx) actx = PyOpenCLArrayContext(queue) def double(queue, x): return 2 * x from meshmode.mesh.generation import generate_regular_rect_mesh dims = 2 mesh = generate_regular_rect_mesh(a=(0, ) * dims, b=(1, ) * dims, n=(4, ) * dims) discr = DGDiscretizationWithBoundaries(actx, mesh, order=1) ones = sym.Ones(sym.DD_VOLUME) op = (ones * 3 + sym.FunctionSymbol("double")(ones)) from grudge.function_registry import (base_function_registry, register_external_function) freg = register_external_function(base_function_registry, "double", implementation=double, dd=sym.DD_VOLUME) bound_op = bind(discr, op, function_registry=freg) result = bound_op(actx, double=double) assert actx.to_numpy(flatten(result) == 5).all()
def test_unregularized_off_surface_fmm_vs_direct(ctx_factory): cl_ctx = ctx_factory() queue = cl.CommandQueue(cl_ctx) actx = PyOpenCLArrayContext(queue) nelements = 300 target_order = 8 fmm_order = 4 # {{{ geometry 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( actx, 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(actx) + 1 fplot = FieldPlotter(np.zeros(2), extent=5, npoints=100) from pytential.target import PointsTarget ptarget = PointsTarget(fplot.points) from pytential import GeometryCollection places = GeometryCollection({ "unregularized_direct": direct, "unregularized_fmm": fmm, "targets": ptarget}) # }}} # {{{ check from sumpy.kernel import LaplaceKernel op = sym.D(LaplaceKernel(2), sym.var("sigma"), qbx_forced_limit=None) direct_fld_in_vol = bind(places, op, auto_where=("unregularized_direct", "targets"))( actx, sigma=sigma) fmm_fld_in_vol = bind(places, op, auto_where=("unregularized_fmm", "targets"))(actx, sigma=sigma) err = actx.np.fabs(fmm_fld_in_vol - direct_fld_in_vol) linf_err = actx.to_numpy(err).max() print("l_inf error:", linf_err) assert linf_err < 5e-3
def test_unregularized_with_ones_kernel(ctx_factory): cl_ctx = ctx_factory() queue = cl.CommandQueue(cl_ctx) actx = PyOpenCLArrayContext(queue) 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(actx, mesh, InterpolatoryQuadratureSimplexGroupFactory(order)) from pytential.unregularized import UnregularizedLayerPotentialSource lpot_source = UnregularizedLayerPotentialSource(discr) from pytential.target import PointsTarget targets = PointsTarget(np.zeros((2, 1), dtype=float)) places = GeometryCollection({ sym.DEFAULT_SOURCE: lpot_source, sym.DEFAULT_TARGET: lpot_source, "target_non_self": targets}) from sumpy.kernel import one_kernel_2d sigma_sym = sym.var("sigma") op = sym.IntG(one_kernel_2d, sigma_sym, qbx_forced_limit=None) sigma = discr.zeros(actx) + 1 result_self = bind(places, op, auto_where=places.auto_where)( actx, sigma=sigma) result_nonself = bind(places, op, auto_where=(places.auto_source, "target_non_self"))( actx, sigma=sigma) from meshmode.dof_array import flatten assert np.allclose(actx.to_numpy(flatten(result_self)), 2 * np.pi) assert np.allclose(actx.to_numpy(result_nonself), 2 * np.pi)
def test_to_fd_idempotency(ctx_factory, mm_mesh, fspace_degree): """ Make sure mm->fd->mm and (mm->)->fd->mm->fd are identity """ cl_ctx = ctx_factory() queue = cl.CommandQueue(cl_ctx) actx = PyOpenCLArrayContext(queue) # make sure degree is higher order than mesh fspace_degree += mm_mesh.groups[0].order # Make a function space and a function with unique values at each node factory = InterpolatoryQuadratureSimplexGroupFactory(fspace_degree) discr = Discretization(actx, mm_mesh, factory) fdrake_connection = build_connection_to_firedrake(discr) fdrake_mesh = fdrake_connection.firedrake_fspace().mesh() dtype = fdrake_mesh.coordinates.dat.data.dtype mm_unique = discr.zeros(actx, dtype=dtype) unique_vals = np.arange(np.size(mm_unique[0]), dtype=dtype) mm_unique[0].set(unique_vals.reshape(mm_unique[0].shape)) mm_unique_copy = DOFArray(actx, (mm_unique[0].copy(), )) # Test for idempotency mm->fd->mm fdrake_unique = fdrake_connection.from_meshmode(mm_unique) fdrake_connection.from_firedrake(fdrake_unique, out=mm_unique_copy) np.testing.assert_allclose(actx.to_numpy(mm_unique_copy[0]), actx.to_numpy(mm_unique[0]), atol=CLOSE_ATOL) # Test for idempotency (mm->)fd->mm->fd fdrake_unique_copy = fdrake_connection.from_meshmode(mm_unique_copy) np.testing.assert_allclose(fdrake_unique_copy.dat.data, fdrake_unique.dat.data, atol=CLOSE_ATOL)
def main(): cl_ctx = cl.create_some_context() queue = cl.CommandQueue(cl_ctx) actx = PyOpenCLArrayContext(queue) nel_1d = 16 from meshmode.mesh.generation import generate_regular_rect_mesh mesh = generate_regular_rect_mesh(a=(-0.5, -0.5), b=(0.5, 0.5), n=(nel_1d, nel_1d)) order = 3 # no deep meaning here, just a fudge factor dt = 0.75 / (nel_1d * order**2) print("%d elements" % mesh.nelements) discr = DGDiscretization(actx, mesh, order=order) fields = flat_obj_array(bump(actx, discr), [discr.zeros(actx) for i in range(discr.dim)]) from meshmode.discretization.visualization import make_visualizer vis = make_visualizer(actx, discr.volume_discr, discr.order + 3) def rhs(t, w): return wave_operator(actx, discr, c=1, w=w) t = 0 t_final = 3 istep = 0 while t < t_final: fields = rk4_step(fields, t, dt, rhs) if istep % 10 == 0: # FIXME: Maybe an integral function to go with the # DOFArray would be nice? assert len(fields[0]) == 1 print(istep, t, la.norm(actx.to_numpy(fields[0][0]))) vis.write_vtk_file("fld-wave-min-%04d.vtu" % istep, [ ("u", fields[0]), ("v", fields[1:]), ]) t += dt istep += 1
def _visualize_refinement(actx: PyOpenCLArrayContext, discr, niter, stage_nr, stage_name, flags, visualize=False): if not visualize: return if stage_nr not in (1, 2): raise ValueError("unexpected stage number") flags = flags.get() logger.info("for stage %s: splitting %d/%d stage-%d elements", stage_name, np.sum(flags), discr.mesh.nelements, stage_nr) from meshmode.discretization.visualization import make_visualizer vis = make_visualizer(actx, discr, 3) assert len(flags) == discr.mesh.nelements flags = flags.astype(bool) nodes_flags_template = discr.zeros(actx) nodes_flags = [] for grp in discr.groups: meg = grp.mesh_el_group nodes_flags_grp = actx.to_numpy(nodes_flags_template[grp.index]) nodes_flags_grp[flags[meg.element_nr_base:meg.nelements + meg.element_nr_base]] = 1 nodes_flags.append(actx.from_numpy(nodes_flags_grp)) nodes_flags = DOFArray(actx, tuple(nodes_flags)) vis_data = [ ("refine_flags", nodes_flags), ] if 0: from pytential import sym, bind bdry_normals = bind(discr, sym.normal( discr.ambient_dim))(actx).as_vector(dtype=object) vis_data.append(("bdry_normals", bdry_normals), ) vis.write_vtk_file(f"refinement-{stage_name}-{niter:03d}.vtu", vis_data)
def test_lump_init(ctx_factory): """ Simple test to check that Lump initializer creates the expected solution field. """ cl_ctx = ctx_factory() queue = cl.CommandQueue(cl_ctx) actx = PyOpenCLArrayContext(queue) dim = 2 nel_1d = 4 from meshmode.mesh.generation import generate_regular_rect_mesh mesh = generate_regular_rect_mesh(a=[(0.0, ), (-5.0, )], b=[(10.0, ), (5.0, )], nelements_per_axis=(nel_1d, ) * dim) order = 3 logger.info(f"Number of elements: {mesh.nelements}") discr = EagerDGDiscretization(actx, mesh, order=order) nodes = thaw(actx, discr.nodes()) # Init soln with Vortex center = np.zeros(shape=(dim, )) velocity = np.zeros(shape=(dim, )) center[0] = 5 velocity[0] = 1 lump = Lump(dim=dim, center=center, velocity=velocity) cv = lump(nodes) p = 0.4 * (cv.energy - 0.5 * np.dot(cv.momentum, cv.momentum) / cv.mass) exp_p = 1.0 errmax = actx.to_numpy(discr.norm(p - exp_p, np.inf)) logger.info(f"lump_soln = {cv}") logger.info(f"pressure = {p}") assert errmax < 1e-15
def test_shock_init(ctx_factory): """ Simple test to check that Shock1D initializer creates the expected solution field. """ cl_ctx = ctx_factory() queue = cl.CommandQueue(cl_ctx) actx = PyOpenCLArrayContext(queue) nel_1d = 10 dim = 2 from meshmode.mesh.generation import generate_regular_rect_mesh mesh = generate_regular_rect_mesh(a=[(0.0, ), (1.0, )], b=[(-0.5, ), (0.5, )], nelements_per_axis=(nel_1d, ) * dim) order = 3 print(f"Number of elements: {mesh.nelements}") discr = EagerDGDiscretization(actx, mesh, order=order) nodes = thaw(actx, discr.nodes()) initr = SodShock1D() initsoln = initr(time=0.0, x_vec=nodes) print("Sod Soln:", initsoln) xpl = 1.0 xpr = 0.1 tol = 1e-15 nodes_x = nodes[0] eos = IdealSingleGas() p = eos.pressure(initsoln) assert actx.to_numpy( discr.norm(actx.np.where(nodes_x < 0.5, p - xpl, p - xpr), np.inf)) < tol
def test_mass_mat_trig(ctx_factory, ambient_dim, quad_tag): """Check the integral of some trig functions on an interval using the mass matrix. """ cl_ctx = ctx_factory() queue = cl.CommandQueue(cl_ctx) actx = PyOpenCLArrayContext(queue) nelements = 17 order = 4 a = -4.0 * np.pi b = +9.0 * np.pi true_integral = 13 * np.pi / 2 * (b - a)**(ambient_dim - 1) from meshmode.discretization.poly_element import QuadratureSimplexGroupFactory dd_quad = sym.DOFDesc(sym.DTAG_VOLUME_ALL, quad_tag) if quad_tag is sym.QTAG_NONE: quad_tag_to_group_factory = {} else: quad_tag_to_group_factory = { quad_tag: QuadratureSimplexGroupFactory(order=2 * order) } from meshmode.mesh.generation import generate_regular_rect_mesh mesh = generate_regular_rect_mesh(a=(a, ) * ambient_dim, b=(b, ) * ambient_dim, n=(nelements, ) * ambient_dim, order=1) discr = DGDiscretizationWithBoundaries( actx, mesh, order=order, quad_tag_to_group_factory=quad_tag_to_group_factory) def _get_variables_on(dd): sym_f = sym.var("f", dd=dd) sym_x = sym.nodes(ambient_dim, dd=dd) sym_ones = sym.Ones(dd) return sym_f, sym_x, sym_ones sym_f, sym_x, sym_ones = _get_variables_on(sym.DD_VOLUME) f_volm = actx.to_numpy(flatten(bind(discr, sym.cos(sym_x[0])**2)(actx))) ones_volm = actx.to_numpy(flatten(bind(discr, sym_ones)(actx))) sym_f, sym_x, sym_ones = _get_variables_on(dd_quad) f_quad = bind(discr, sym.cos(sym_x[0])**2)(actx) ones_quad = bind(discr, sym_ones)(actx) mass_op = bind(discr, sym.MassOperator(dd_quad, sym.DD_VOLUME)(sym_f)) num_integral_1 = np.dot(ones_volm, actx.to_numpy(flatten(mass_op(f=f_quad)))) err_1 = abs(num_integral_1 - true_integral) assert err_1 < 1e-9, err_1 num_integral_2 = np.dot(f_volm, actx.to_numpy(flatten(mass_op(f=ones_quad)))) err_2 = abs(num_integral_2 - true_integral) assert err_2 < 1.0e-9, err_2 if quad_tag is sym.QTAG_NONE: # NOTE: `integral` always makes a square mass matrix and # `QuadratureSimplexGroupFactory` does not have a `mass_matrix` method. num_integral_3 = bind(discr, sym.integral(sym_f, dd=dd_quad))(f=f_quad) err_3 = abs(num_integral_3 - true_integral) assert err_3 < 5.0e-10, err_3
def test_ellipse_eigenvalues(ctx_factory, ellipse_aspect, mode_nr, qbx_order, force_direct, visualize=False): logging.basicConfig(level=logging.INFO) print("ellipse_aspect: %s, mode_nr: %d, qbx_order: %d" % (ellipse_aspect, mode_nr, qbx_order)) cl_ctx = ctx_factory() queue = cl.CommandQueue(cl_ctx) actx = PyOpenCLArrayContext(queue) target_order = 8 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. # https://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 = 12 if force_direct: fmm_order = False pre_density_discr = Discretization( actx, mesh, InterpolatoryQuadratureSimplexGroupFactory(target_order)) qbx = QBXLayerPotentialSource( pre_density_discr, 4 * target_order, qbx_order, fmm_order=fmm_order, _expansions_in_tree_have_extent=True, ) places = GeometryCollection(qbx) density_discr = places.get_discretization(places.auto_source.geometry) from meshmode.dof_array import thaw, flatten nodes = thaw(actx, density_discr.nodes()) if visualize: # plot geometry, centers, normals centers = bind(places, sym.expansion_centers(qbx.ambient_dim, +1))(actx) normals = bind(places, sym.normal(qbx.ambient_dim))(actx).as_vector(object) nodes_h = np.array( [actx.to_numpy(axis) for axis in flatten(nodes)]) centers_h = np.array( [actx.to_numpy(axis) for axis in flatten(centers)]) normals_h = np.array( [actx.to_numpy(axis) for axis in flatten(normals)]) pt.plot(nodes_h[0], nodes_h[1], "x-") pt.plot(centers_h[0], centers_h[1], "o") pt.quiver(nodes_h[0], nodes_h[1], normals_h[0], normals_h[1]) pt.gca().set_aspect("equal") pt.show() angle = actx.np.arctan2(nodes[1] * ellipse_aspect, nodes[0]) ellipse_fraction = ((1 - ellipse_aspect) / (1 + ellipse_aspect))**mode_nr # (2.6) in [1] J = actx.np.sqrt( # noqa actx.np.sin(angle)**2 + (1 / ellipse_aspect)**2 * actx.np.cos(angle)**2) from sumpy.kernel import LaplaceKernel lap_knl = LaplaceKernel(2) # {{{ single layer sigma_sym = sym.var("sigma") s_sigma_op = sym.S(lap_knl, sigma_sym, qbx_forced_limit=+1) sigma = actx.np.cos(mode_nr * angle) / J s_sigma = bind(places, s_sigma_op)(actx, 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(actx.to_numpy(flatten(s_sigma_ref - s_sigma)), label="err") pt.legend() pt.show() h_max = bind(places, sym.h_max(qbx.ambient_dim))(actx) s_err = (norm(density_discr, s_sigma - s_sigma_ref) / norm(density_discr, s_sigma_ref)) s_eoc_rec.add_data_point(h_max, s_err) # }}} # {{{ double layer d_sigma_op = sym.D(lap_knl, sigma_sym, qbx_forced_limit="avg") sigma = actx.np.cos(mode_nr * angle) d_sigma = bind(places, d_sigma_op)(actx, sigma=sigma) # SIGN BINGO! :) d_eigval = -(-1)**mode_nr * 1 / 2 * ellipse_fraction d_sigma_ref = d_eigval * sigma if 0: pt.plot(actx.to_numpy(flatten(d_sigma)), label="result") pt.plot(actx.to_numpy(flatten(d_sigma_ref)), label="ref") pt.legend() pt.show() if ellipse_aspect == 1: d_ref_norm = norm(density_discr, sigma) else: d_ref_norm = norm(density_discr, d_sigma_ref) d_err = (norm(density_discr, d_sigma - d_sigma_ref) / d_ref_norm) d_eoc_rec.add_data_point(h_max, d_err) # }}} if ellipse_aspect == 1: # {{{ S' sp_sigma_op = sym.Sp(lap_knl, sym.var("sigma"), qbx_forced_limit="avg") sigma = actx.np.cos(mode_nr * angle) sp_sigma = bind(places, sp_sigma_op)(actx, sigma=sigma) sp_eigval = 0 sp_sigma_ref = sp_eigval * sigma sp_err = (norm(density_discr, sp_sigma - sp_sigma_ref) / norm(density_discr, sigma)) sp_eoc_rec.add_data_point(h_max, 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 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_target_association(ctx_factory, curve_name, curve_f, nelements, visualize=False): cl_ctx = ctx_factory() queue = cl.CommandQueue(cl_ctx) actx = PyOpenCLArrayContext(queue) # {{{ generate lpot source order = 16 # Make the curve mesh. mesh = make_curve_mesh(curve_f, np.linspace(0, 1, nelements + 1), order) from meshmode.discretization import Discretization from meshmode.discretization.poly_element import \ InterpolatoryQuadratureSimplexGroupFactory factory = InterpolatoryQuadratureSimplexGroupFactory(order) discr = Discretization(actx, mesh, factory) lpot_source = QBXLayerPotentialSource( discr, qbx_order=order, # not used in target association fine_order=order) places = GeometryCollection(lpot_source) # }}} # {{{ generate targets from pyopencl.clrandom import PhiloxGenerator rng = PhiloxGenerator(cl_ctx, seed=RNG_SEED) dd = places.auto_source.to_stage1() centers = dof_array_to_numpy( actx, bind( places, sym.interleaved_expansion_centers(lpot_source.ambient_dim, dofdesc=dd))(actx)) density_discr = places.get_discretization(dd.geometry) noise = actx.to_numpy( rng.uniform(queue, density_discr.ndofs, dtype=np.float, a=0.01, b=1.0)) tunnel_radius = dof_array_to_numpy( actx, bind( places, sym._close_target_tunnel_radii(lpot_source.ambient_dim, dofdesc=dd))(actx)) def targets_from_sources(sign, dist, dim=2): nodes = dof_array_to_numpy( actx, bind(places, sym.nodes(dim, dofdesc=dd))(actx).as_vector(np.object)) normals = dof_array_to_numpy( actx, bind(places, sym.normal(dim, dofdesc=dd))(actx).as_vector(np.object)) return actx.from_numpy(nodes + normals * sign * dist) from pytential.target import PointsTarget int_targets = PointsTarget(targets_from_sources(-1, noise * tunnel_radius)) ext_targets = PointsTarget(targets_from_sources(+1, noise * tunnel_radius)) far_targets = PointsTarget( targets_from_sources(+1, FAR_TARGET_DIST_FROM_SOURCE)) # Create target discretizations. target_discrs = ( # On-surface targets, interior (density_discr, -1), # On-surface targets, exterior (density_discr, +1), # Interior close targets (int_targets, -2), # Exterior close targets (ext_targets, +2), # Far targets, should not need centers (far_targets, 0), ) sizes = np.cumsum([discr.ndofs for discr, _ in target_discrs]) ( surf_int_slice, surf_ext_slice, vol_int_slice, vol_ext_slice, far_slice, ) = [slice(start, end) for start, end in zip(np.r_[0, sizes], sizes)] # }}} # {{{ run target associator and check from pytential.qbx.target_assoc import (TargetAssociationCodeContainer, associate_targets_to_qbx_centers) from pytential.qbx.utils import TreeCodeContainer code_container = TargetAssociationCodeContainer(actx, TreeCodeContainer(actx)) target_assoc = (associate_targets_to_qbx_centers( places, places.auto_source, code_container.get_wrangler(actx), target_discrs, target_association_tolerance=1e-10).get(queue=queue)) expansion_radii = dof_array_to_numpy( actx, bind( places, sym.expansion_radii(lpot_source.ambient_dim, granularity=sym.GRANULARITY_CENTER))(actx)) from meshmode.dof_array import thaw surf_targets = dof_array_to_numpy(actx, thaw(actx, density_discr.nodes())) int_targets = actx.to_numpy(int_targets.nodes()) ext_targets = actx.to_numpy(ext_targets.nodes()) def visualize_curve_and_assoc(): import matplotlib.pyplot as plt from meshmode.mesh.visualization import draw_curve draw_curve(density_discr.mesh) targets = int_targets tgt_slice = surf_int_slice plt.plot(centers[0], centers[1], "+", color="orange") ax = plt.gca() for tx, ty, tcenter in zip(targets[0, tgt_slice], targets[1, tgt_slice], target_assoc.target_to_center[tgt_slice]): if tcenter >= 0: ax.add_artist( plt.Line2D( (tx, centers[0, tcenter]), (ty, centers[1, tcenter]), )) ax.set_aspect("equal") plt.show() if visualize: visualize_curve_and_assoc() # Checks that the targets match with centers on the appropriate side and # within the allowable distance. def check_close_targets(centers, targets, true_side, target_to_center, target_to_side_result, tgt_slice): targets_have_centers = (target_to_center >= 0).all() assert targets_have_centers assert (target_to_side_result == true_side).all() TOL = 1e-3 dists = la.norm((targets.T - centers.T[target_to_center]), axis=1) assert (dists <= (1 + TOL) * expansion_radii[target_to_center]).all() # Center side order = -1, 1, -1, 1, ... target_to_center_side = 2 * (target_assoc.target_to_center % 2) - 1 # interior surface check_close_targets(centers, surf_targets, -1, target_assoc.target_to_center[surf_int_slice], target_to_center_side[surf_int_slice], surf_int_slice) # exterior surface check_close_targets(centers, surf_targets, +1, target_assoc.target_to_center[surf_ext_slice], target_to_center_side[surf_ext_slice], surf_ext_slice) # interior volume check_close_targets(centers, int_targets, -1, target_assoc.target_to_center[vol_int_slice], target_to_center_side[vol_int_slice], vol_int_slice) # exterior volume check_close_targets(centers, ext_targets, +1, target_assoc.target_to_center[vol_ext_slice], target_to_center_side[vol_ext_slice], vol_ext_slice) # Checks that far targets are not assigned a center. assert (target_assoc.target_to_center[far_slice] == -1).all()
def test_sphere_eigenvalues(ctx_factory, mode_m, mode_n, qbx_order, fmm_backend): logging.basicConfig(level=logging.INFO) special = pytest.importorskip("scipy.special") cl_ctx = ctx_factory() queue = cl.CommandQueue(cl_ctx) actx = PyOpenCLArrayContext(queue) target_order = 8 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() dp_eoc_rec = EOCRecorder() def rel_err(comp, ref): return (norm(density_discr, comp - ref) / norm(density_discr, ref)) for nrefinements in [0, 1]: from meshmode.mesh.generation import generate_icosphere mesh = generate_icosphere(1, target_order) from meshmode.mesh.refinement import Refiner refiner = Refiner(mesh) for i in range(nrefinements): flags = np.ones(mesh.nelements, dtype=bool) refiner.refine(flags) mesh = refiner.get_current_mesh() pre_density_discr = Discretization( actx, mesh, InterpolatoryQuadratureSimplexGroupFactory(target_order)) qbx = QBXLayerPotentialSource( pre_density_discr, 4 * target_order, qbx_order, fmm_order=6, fmm_backend=fmm_backend, ) places = GeometryCollection(qbx) from meshmode.dof_array import flatten, unflatten, thaw density_discr = places.get_discretization(places.auto_source.geometry) nodes = thaw(actx, density_discr.nodes()) r = actx.np.sqrt(nodes[0] * nodes[0] + nodes[1] * nodes[1] + nodes[2] * nodes[2]) phi = actx.np.arccos(nodes[2] / r) theta = actx.np.arctan2(nodes[0], nodes[1]) ymn = unflatten( actx, density_discr, actx.from_numpy( special.sph_harm(mode_m, mode_n, actx.to_numpy(flatten(theta)), actx.to_numpy(flatten(phi))))) from sumpy.kernel import LaplaceKernel lap_knl = LaplaceKernel(3) # {{{ single layer s_sigma_op = bind( places, sym.S(lap_knl, sym.var("sigma"), qbx_forced_limit=+1)) s_sigma = s_sigma_op(actx, sigma=ymn) s_eigval = 1 / (2 * mode_n + 1) h_max = bind(places, sym.h_max(qbx.ambient_dim))(actx) s_eoc_rec.add_data_point(h_max, rel_err(s_sigma, s_eigval * ymn)) # }}} # {{{ double layer d_sigma_op = bind( places, sym.D(lap_knl, sym.var("sigma"), qbx_forced_limit="avg")) d_sigma = d_sigma_op(actx, sigma=ymn) d_eigval = -1 / (2 * (2 * mode_n + 1)) d_eoc_rec.add_data_point(h_max, rel_err(d_sigma, d_eigval * ymn)) # }}} # {{{ S' sp_sigma_op = bind( places, sym.Sp(lap_knl, sym.var("sigma"), qbx_forced_limit="avg")) sp_sigma = sp_sigma_op(actx, sigma=ymn) sp_eigval = -1 / (2 * (2 * mode_n + 1)) sp_eoc_rec.add_data_point(h_max, rel_err(sp_sigma, sp_eigval * ymn)) # }}} # {{{ D' dp_sigma_op = bind( places, sym.Dp(lap_knl, sym.var("sigma"), qbx_forced_limit="avg")) dp_sigma = dp_sigma_op(actx, sigma=ymn) dp_eigval = -(mode_n * (mode_n + 1)) / (2 * mode_n + 1) dp_eoc_rec.add_data_point(h_max, rel_err(dp_sigma, dp_eigval * ymn)) # }}} 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 - 0.5 print("Errors for S':") print(sp_eoc_rec) required_order = qbx_order assert sp_eoc_rec.order_estimate() > required_order - 1.5 print("Errors for D':") print(dp_eoc_rec) required_order = qbx_order assert dp_eoc_rec.order_estimate() > required_order - 1.5
def main(curve_fn=starfish, visualize=True): import logging logging.basicConfig(level=logging.WARNING) # INFO for more progress info import pyopencl as cl cl_ctx = cl.create_some_context() queue = cl.CommandQueue(cl_ctx) actx = PyOpenCLArrayContext(queue, force_device_scalars=True) from meshmode.mesh.generation import make_curve_mesh mesh = make_curve_mesh( curve_fn, 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)) qbx = QBXLayerPotentialSource( pre_density_discr, 4*target_order, qbx_order, fmm_order=qbx_order+3, target_association_tolerance=0.005, #fmm_backend="fmmlib", ) from pytential.target import PointsTarget fplot = FieldPlotter(np.zeros(2), extent=5, npoints=1000) targets_dev = actx.from_numpy(fplot.points) from pytential import GeometryCollection places = GeometryCollection({ "qbx": qbx, "targets": PointsTarget(targets_dev), }, auto_where="qbx") density_discr = places.get_discretization("qbx") nodes = thaw(density_discr.nodes(), actx) angle = actx.np.arctan2(nodes[1], nodes[0]) if k: kernel = HelmholtzKernel(2) kernel_kwargs = {"k": sym.var("k")} else: kernel = LaplaceKernel(2) kernel_kwargs = {} 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) #op = sym.S(kernel, sym.var("sigma"), qbx_forced_limit=None, **kwargs) if 0: from random import randrange sigma = actx.zeros(density_discr.ndofs, angle.entry_dtype) for _ in range(5): sigma[randrange(len(sigma))] = 1 from arraycontext import unflatten sigma = unflatten(angle, sigma, actx) else: sigma = actx.np.cos(mode_nr*angle) if isinstance(kernel, HelmholtzKernel): for i, elem in np.ndenumerate(sigma): sigma[i] = elem.astype(np.complex128) bound_bdry_op = bind(places, op()) if visualize: fld_in_vol = actx.to_numpy( bind(places, op( source="qbx", target="targets", qbx_forced_limit=None))(actx, sigma=sigma, k=k)) if enable_mayavi: fplot.show_scalar_in_mayavi(fld_in_vol.real, max_val=5) else: fplot.write_vtk_file("layerpot-potential.vts", [ ("potential", fld_in_vol) ]) if 0: apply_op = bound_bdry_op.scipy_op(actx, "sigma", np.float64, k=k) from sumpy.tools import build_matrix mat = build_matrix(apply_op) import matplotlib.pyplot as pt pt.imshow(mat) pt.colorbar() pt.show() if enable_mayavi: # {{{ plot boundary field from arraycontext import flatten fld_on_bdry = actx.to_numpy( flatten(bound_bdry_op(actx, sigma=sigma, k=k), actx)) nodes_host = actx.to_numpy( flatten(density_discr.nodes(), actx) ).reshape(density_discr.ambient_dim, -1) mlab.points3d(nodes_host[0], nodes_host[1], fld_on_bdry.real, scale_factor=0.03) mlab.colorbar() mlab.show()
def test_from_fd_transfer(ctx_factory, fspace_degree, fdrake_mesh_name, fdrake_mesh_pars, dim, only_convert_bdy): """ Make sure creating a function which projects onto one dimension then transports it is the same (up to resampling error) as projecting to one dimension on the transported mesh """ # build estimate-of-convergence recorder from pytools.convergence import EOCRecorder # (fd -> mm ? True : False, dimension projecting onto) eoc_recorders = {(True, d): EOCRecorder() for d in range(dim)} if not only_convert_bdy: for d in range(dim): eoc_recorders[(False, d)] = EOCRecorder() # make a computing context cl_ctx = ctx_factory() queue = cl.CommandQueue(cl_ctx) actx = PyOpenCLArrayContext(queue) def get_fdrake_mesh_and_h_from_par(mesh_par): if fdrake_mesh_name == "UnitInterval": assert dim == 1 n = mesh_par fdrake_mesh = UnitIntervalMesh(n) h = 1 / n elif fdrake_mesh_name == "UnitSquare": assert dim == 2 n = mesh_par fdrake_mesh = UnitSquareMesh(n, n) h = 1 / n elif fdrake_mesh_name == "UnitCube": assert dim == 3 n = mesh_par fdrake_mesh = UnitCubeMesh(n, n, n) h = 1 / n elif fdrake_mesh_name in ("blob2d-order1", "blob2d-order4"): assert dim == 2 if fdrake_mesh_name == "blob2d-order1": from firedrake import Mesh fdrake_mesh = Mesh(f"{fdrake_mesh_name}-h{mesh_par}.msh", dim=dim) else: from meshmode.mesh.io import read_gmsh from meshmode.interop.firedrake import export_mesh_to_firedrake mm_mesh = read_gmsh(f"{fdrake_mesh_name}-h{mesh_par}.msh", force_ambient_dim=dim) fdrake_mesh, _, _ = export_mesh_to_firedrake(mm_mesh) h = float(mesh_par) elif fdrake_mesh_name == "warp": from meshmode.mesh.generation import generate_warped_rect_mesh from meshmode.interop.firedrake import export_mesh_to_firedrake mm_mesh = generate_warped_rect_mesh(dim, order=4, n=mesh_par) fdrake_mesh, _, _ = export_mesh_to_firedrake(mm_mesh) h = 1 / mesh_par else: raise ValueError("fdrake_mesh_name not recognized") return (fdrake_mesh, h) # Record error for each refinement of each mesh for mesh_par in fdrake_mesh_pars: fdrake_mesh, h = get_fdrake_mesh_and_h_from_par(mesh_par) # make function space and build connection fdrake_fspace = FunctionSpace(fdrake_mesh, "DG", fspace_degree) if only_convert_bdy: fdrake_connection = \ build_connection_from_firedrake(actx, fdrake_fspace, restrict_to_boundary="on_boundary") else: fdrake_connection = build_connection_from_firedrake( actx, fdrake_fspace) # get this for making functions in firedrake spatial_coord = SpatialCoordinate(fdrake_mesh) # get nodes in handier format for making meshmode functions discr = fdrake_connection.discr # nodes is np array (ambient_dim,) of DOFArray (ngroups,) # of arrays (nelements, nunit_dofs), we want a single np array # of shape (ambient_dim, nelements, nunit_dofs) nodes = discr.nodes() group_nodes = np.array( [actx.to_numpy(dof_arr[0]) for dof_arr in nodes]) # Now, for each coordinate d, test transferring the function # x -> sin(dth component of x) for d in range(dim): fdrake_f = Function(fdrake_fspace).interpolate( sin(spatial_coord[d])) # transport fdrake function and put in numpy fd2mm_f = fdrake_connection.from_firedrake(fdrake_f, actx=actx) fd2mm_f = actx.to_numpy(fd2mm_f[0]) meshmode_f = np.sin(group_nodes[d, :, :]) # record fd -> mm error err = np.max(np.abs(fd2mm_f - meshmode_f)) eoc_recorders[(True, d)].add_data_point(h, err) if not only_convert_bdy: # now transport mm -> fd meshmode_f_dofarr = discr.zeros(actx) meshmode_f_dofarr[0][:] = meshmode_f mm2fd_f = fdrake_connection.from_meshmode(meshmode_f_dofarr) # record mm -> fd error err = np.max(np.abs(fdrake_f.dat.data - mm2fd_f.dat.data)) eoc_recorders[(False, d)].add_data_point(h, err) # assert that order is correct or error is "low enough" for ((fd2mm, d), eoc_rec) in eoc_recorders.items(): print( "\nfiredrake -> meshmode: %s\nvector *x* -> *sin(x[%s])*\n" % (fd2mm, d), eoc_rec) assert (eoc_rec.order_estimate() >= fspace_degree or eoc_rec.max_error() < 2e-14)
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(f"unknown mesh name: {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), ])
_expansion_stick_out_factor=getattr( case, "_expansion_stick_out_factor", 0), ) places = GeometryCollection(qbx) from pytential.qbx.refinement import refine_geometry_collection kernel_length_scale = 5 / case.k if case.k else None places = refine_geometry_collection(places, kernel_length_scale=kernel_length_scale) # {{{ compute values of a solution to the PDE density_discr = places.get_discretization(places.auto_source.geometry) from meshmode.dof_array import thaw, flatten, unflatten nodes_host = [actx.to_numpy(axis) for axis in flatten(thaw(actx, density_discr.nodes()))] normal = bind(places, sym.normal(d))(actx).as_vector(object) normal_host = [actx.to_numpy(axis)for axis in flatten(normal)] if k != 0: if d == 2: 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 elif d == 3: center = np.array([3, 1, 2]) diff = nodes_host - center[:, np.newaxis] r = la.norm(diff, axis=0) u = np.exp(1j*k*r) / r
def main(): import logging logging.basicConfig(level=logging.WARNING) # INFO for more progress info import pyopencl as cl cl_ctx = cl.create_some_context() queue = cl.CommandQueue(cl_ctx) actx = PyOpenCLArrayContext(queue, force_device_scalars=True) 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(actx.freeze(actx.from_numpy(fplot.points))) }, auto_where=("qbx", "targets")) density_discr = places.get_discretization("unaccel_qbx") nodes = thaw(density_discr.nodes(), actx) 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 = actx.to_numpy( bind(places, op, auto_where=("unaccel_qbx", "targets"))(actx, sigma=sigma, k=k)) fmm_fld_in_vol = actx.to_numpy( bind(places, op, auto_where=("qbx", "targets"))(actx, sigma=sigma, k=k)) 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 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) actx = PyOpenCLArrayContext(queue) # 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( actx, mesh, InterpolatoryQuadratureSimplexGroupFactory(target_order)) direct_qbx = QBXLayerPotentialSource( pre_density_discr, 4*target_order, qbx_order, fmm_order=False, target_association_tolerance=0.05, ) 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, ) fplot = FieldPlotter(np.zeros(2), extent=5, npoints=500) from pytential.target import PointsTarget ptarget = PointsTarget(fplot.points) from sumpy.kernel import LaplaceKernel places = GeometryCollection({ "direct_qbx": direct_qbx, "fmm_qbx": fmm_qbx, "target": ptarget}) direct_density_discr = places.get_discretization("direct_qbx") fmm_density_discr = places.get_discretization("fmm_qbx") from pytential.qbx import QBXTargetAssociationFailedException op = sym.D(LaplaceKernel(2), sym.var("sigma"), qbx_forced_limit=None) try: direct_sigma = direct_density_discr.zeros(actx) + 1 direct_fld_in_vol = bind(places, op, auto_where=("direct_qbx", "target"))( actx, sigma=direct_sigma) except QBXTargetAssociationFailedException as e: fplot.show_scalar_in_matplotlib( actx.to_numpy(actx.thaw(e.failed_target_flags))) import matplotlib.pyplot as pt pt.show() raise fmm_sigma = fmm_density_discr.zeros(actx) + 1 fmm_fld_in_vol = bind(places, op, auto_where=("fmm_qbx", "target"))( actx, sigma=fmm_sigma) err = actx.np.fabs(fmm_fld_in_vol - direct_fld_in_vol) linf_err = actx.to_numpy(err).max() 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", actx.to_numpy(fmm_fld_in_vol)), ("direct_fld_in_vol", actx.to_numpy(direct_fld_in_vol)) ]) assert linf_err < 1e-3
def timing_run(nx, ny, visualize=False): import logging logging.basicConfig(level=logging.WARNING) # INFO for more progress info import pyopencl as cl cl_ctx = cl.create_some_context() queue = cl.CommandQueue(cl_ctx) actx = PyOpenCLArrayContext(queue, force_device_scalars=True) mesh = make_mesh(nx=nx, ny=ny, visualize=visualize) density_discr = Discretization( actx, 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) places = {"qbx": qbx} if visualize: from sumpy.visualization import FieldPlotter fplot = FieldPlotter(np.zeros(2), extent=5, npoints=1500) targets = PointsTarget(actx.from_numpy(fplot.points)) places.update({ "plot_targets": targets, "qbx_indicator": qbx.copy(target_association_tolerance=0.05, fmm_level_to_order=lambda knl, knl_args, tree, lev: 7, qbx_order=2), "qbx_target_assoc": qbx.copy(target_association_tolerance=0.1) }) from pytential import GeometryCollection places = GeometryCollection(places, auto_where="qbx") density_discr = places.get_discretization("qbx") # {{{ describe bvp from sumpy.kernel import 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") S_sym = sym.S(kernel, inv_sqrt_w_sigma, k=k_sym, qbx_forced_limit=+1) D_sym = sym.D(kernel, inv_sqrt_w_sigma, k=k_sym, qbx_forced_limit="avg") bdry_op_sym = -loc_sign * 0.5 * sigma_sym + sqrt_w * (alpha * S_sym + D_sym) # }}} bound_op = bind(places, bdry_op_sym) # {{{ fix rhs and solve mode_nr = 3 nodes = thaw(density_discr.nodes(), actx) angle = actx.np.arctan2(nodes[1], nodes[0]) sigma = actx.np.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(places, sym_op) print("FMM WARM-UP RUN 1: %5d elements" % mesh.nelements) bound_op(actx, sigma=sigma, k=k) queue.finish() print("FMM WARM-UP RUN 2: %5d elements" % mesh.nelements) bound_op(actx, sigma=sigma, k=k) queue.finish() from time import time t_start = time() bound_op(actx, sigma=sigma, k=k) actx.queue.finish() elapsed = time() - t_start print("FMM TIMING RUN: %5d elements -> %g s" % (mesh.nelements, elapsed)) if visualize: ones_density = 1 + density_discr.zeros(actx) sym_op = sym_op.copy(qbx_forced_limit=None) indicator = actx.to_numpy( bind(places, sym_op, auto_where=("qbx_indicator", "plot_targets"))(actx, sigma=ones_density, k=k)) try: fld_in_vol = actx.to_numpy( bind(places, sym_op, auto_where=("qbx_target_assoc", "plot_targets"))(actx, sigma=sigma, k=k)) except QBXTargetAssociationFailedException as e: fplot.write_vtk_file("scaling-study-failed-targets.vts", [ ("failed", actx.to_numpy(e.failed_target_flags)), ]) raise fplot.write_vtk_file(f"scaling-study-potential-{nx}-{ny}.vts", [ ("potential", fld_in_vol), ("indicator", indicator), ]) return (mesh.nelements, elapsed)
def test_from_fd_idempotency(ctx_factory, fdrake_mesh, fspace_degree, fspace_type, only_convert_bdy): """ Make sure fd->mm->fd and (fd->)->mm->fd->mm are identity """ # Make a function space and a function with unique values at each node if fspace_type == "scalar": fdrake_fspace = FunctionSpace(fdrake_mesh, "DG", fspace_degree) # Just use the node nr fdrake_unique = Function(fdrake_fspace) fdrake_unique.dat.data[:] = np.arange(fdrake_unique.dat.data.shape[0]) elif fspace_type == "vector": fdrake_fspace = VectorFunctionSpace(fdrake_mesh, "DG", fspace_degree) # use the coordinates xx = SpatialCoordinate(fdrake_fspace.mesh()) fdrake_unique = Function(fdrake_fspace).interpolate(xx) elif fspace_type == "tensor": fdrake_fspace = TensorFunctionSpace(fdrake_mesh, "DG", fspace_degree) # use the coordinates, duplicated into the right tensor shape xx = SpatialCoordinate(fdrake_fspace.mesh()) dim = fdrake_fspace.mesh().geometric_dimension() unique_expr = as_tensor([xx for _ in range(dim)]) fdrake_unique = Function(fdrake_fspace).interpolate(unique_expr) # Make connection cl_ctx = ctx_factory() queue = cl.CommandQueue(cl_ctx) actx = PyOpenCLArrayContext(queue) # If only converting boundary, first go ahead and do one round of # fd->mm->fd. This will zero out any degrees of freedom absent in # the meshmode mesh (because they are not associated to cells # with >= 1 node on the boundary) # # Otherwise, just continue as normal if only_convert_bdy: fdrake_connection = \ build_connection_from_firedrake(actx, fdrake_fspace, restrict_to_boundary="on_boundary") temp = fdrake_connection.from_firedrake(fdrake_unique, actx=actx) fdrake_unique = fdrake_connection.from_meshmode(temp) else: fdrake_connection = build_connection_from_firedrake( actx, fdrake_fspace) # Test for idempotency fd->mm->fd mm_field = fdrake_connection.from_firedrake(fdrake_unique, actx=actx) fdrake_unique_copy = Function(fdrake_fspace) fdrake_connection.from_meshmode(mm_field, out=fdrake_unique_copy) np.testing.assert_allclose(fdrake_unique_copy.dat.data, fdrake_unique.dat.data, atol=CLOSE_ATOL) # Test for idempotency (fd->)mm->fd->mm mm_field_copy = fdrake_connection.from_firedrake(fdrake_unique_copy, actx=actx) if fspace_type == "scalar": np.testing.assert_allclose(actx.to_numpy(mm_field_copy[0]), actx.to_numpy(mm_field[0]), atol=CLOSE_ATOL) else: for dof_arr_cp, dof_arr in zip(mm_field_copy.flatten(), mm_field.flatten()): np.testing.assert_allclose(actx.to_numpy(dof_arr_cp[0]), actx.to_numpy(dof_arr[0]), atol=CLOSE_ATOL)
def test_to_fd_transfer(ctx_factory, fspace_degree, mesh_name, mesh_pars, dim): """ Make sure creating a function which projects onto one dimension then transports it is the same (up to resampling error) as projecting to one dimension on the transported mesh """ # build estimate-of-convergence recorder from pytools.convergence import EOCRecorder # dimension projecting onto -> EOCRecorder eoc_recorders = {d: EOCRecorder() for d in range(dim)} # make a computing context cl_ctx = ctx_factory() queue = cl.CommandQueue(cl_ctx) actx = PyOpenCLArrayContext(queue) # Get each of the refinements of the meshmeshes and record # conversions errors for mesh_par in mesh_pars: if mesh_name in ("blob2d-order1", "blob2d-order4"): assert dim == 2 from meshmode.mesh.io import read_gmsh mm_mesh = read_gmsh(f"{mesh_name}-h{mesh_par}.msh", force_ambient_dim=dim) h = float(mesh_par) elif mesh_name == "warp": from meshmode.mesh.generation import generate_warped_rect_mesh mm_mesh = generate_warped_rect_mesh(dim, order=4, n=mesh_par) h = 1 / mesh_par else: raise ValueError("mesh_name not recognized") # Make discr and connect it to firedrake factory = InterpolatoryQuadratureSimplexGroupFactory(fspace_degree) discr = Discretization(actx, mm_mesh, factory) fdrake_connection = build_connection_to_firedrake(discr) fdrake_fspace = fdrake_connection.firedrake_fspace() spatial_coord = SpatialCoordinate(fdrake_fspace.mesh()) # get the group's nodes in a numpy array nodes = discr.nodes() group_nodes = np.array( [actx.to_numpy(dof_arr[0]) for dof_arr in nodes]) for d in range(dim): meshmode_f = discr.zeros(actx) meshmode_f[0][:] = group_nodes[d, :, :] # connect to firedrake and evaluate expr in firedrake fdrake_f = Function(fdrake_fspace).interpolate(spatial_coord[d]) # transport to firedrake and record error mm2fd_f = fdrake_connection.from_meshmode(meshmode_f) err = np.max(np.abs(fdrake_f.dat.data - mm2fd_f.dat.data)) eoc_recorders[d].add_data_point(h, err) # assert that order is correct or error is "low enough" for d, eoc_rec in eoc_recorders.items(): print("\nvector *x* -> *x[%s]*\n" % d, eoc_rec) assert (eoc_rec.order_estimate() >= fspace_degree or eoc_rec.max_error() < 2e-14)
def main(mesh_name="ellipse", visualize=False): import logging logging.basicConfig(level=logging.INFO) # 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(f"unknown mesh name: {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 test_off_surface_eval(ctx_factory, use_fmm, visualize=False): logging.basicConfig(level=logging.INFO) cl_ctx = ctx_factory() queue = cl.CommandQueue(cl_ctx) actx = PyOpenCLArrayContext(queue) # 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( actx, mesh, InterpolatoryQuadratureSimplexGroupFactory(target_order)) qbx = QBXLayerPotentialSource( pre_density_discr, 4*target_order, qbx_order, fmm_order=fmm_order, ) from pytential.target import PointsTarget fplot = FieldPlotter(np.zeros(2), extent=0.54, npoints=30) targets = PointsTarget(fplot.points) places = GeometryCollection((qbx, targets)) density_discr = places.get_discretization(places.auto_source.geometry) from sumpy.kernel import LaplaceKernel op = sym.D(LaplaceKernel(2), sym.var("sigma"), qbx_forced_limit=-2) sigma = density_discr.zeros(actx) + 1 fld_in_vol = bind(places, op)(actx, sigma=sigma) fld_in_vol_exact = -1 err = actx.np.fabs(fld_in_vol - fld_in_vol_exact) linf_err = actx.to_numpy(err).max() print("l_inf error:", linf_err) if visualize: fplot.show_scalar_in_matplotlib(actx.to_numpy(fld_in_vol)) import matplotlib.pyplot as pt pt.colorbar() pt.show() assert linf_err < 1e-3
("Einc", inc_field_scat.e), ("Hinc", inc_field_scat.h), ("bdry_normals", bdry_normals), ("e_bc_residual", eh_bc_values[:3]), ("h_bc_residual", eh_bc_values[3]), ]) from pytential.qbx import QBXTargetAssociationFailedException try: fplot_repr = eval_repr_at(places, target="plot_targets", source="qbx_target_tol") except QBXTargetAssociationFailedException as e: fplot.write_vtk_file("failed-targets.vts", [ ("failed_targets", actx.to_numpy(actx.thaw(e.failed_target_flags))), ]) raise fplot_repr = EHField(vector_from_device(actx.queue, fplot_repr)) fplot_inc = EHField( vector_from_device( actx.queue, eval_inc_field_at(places, target="plot_targets"))) fplot.write_vtk_file("potential-%s.vts" % resolution, [ ("E", fplot_repr.e), ("H", fplot_repr.h), ("Einc", fplot_inc.e), ("Hinc", fplot_inc.h), ])
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), ])
qbx = case.get_layer_potential(actx, case.resolutions[-1], case.target_order) places = GeometryCollection(qbx, auto_where=case.name) density_discr = places.get_discretization(case.name) srcindices = case.get_block_indices(actx, density_discr, matrix_indices=False) from pytential.linalg.proxy import ProxyGenerator generator = ProxyGenerator(places) proxies, pxyranges, pxycenters, pxyradii = \ generator(actx, places.auto_source, srcindices) proxies = np.vstack([actx.to_numpy(p) for p in proxies]) pxyranges = actx.to_numpy(pxyranges) pxycenters = np.vstack([actx.to_numpy(c) for c in pxycenters]) pxyradii = actx.to_numpy(pxyradii) for i in range(srcindices.nblocks): ipxy = np.s_[pxyranges[i]:pxyranges[i + 1]] r = la.norm(proxies[:, ipxy] - pxycenters[:, i].reshape(-1, 1), axis=0) assert np.allclose(r - pxyradii[i], 0.0, atol=1.0e-14) # }}} # {{{ visualization srcindices = srcindices.get(queue)
def test_interpolation(ctx_factory, name, source_discr_stage, target_granularity): ctx = ctx_factory() queue = cl.CommandQueue(ctx) actx = PyOpenCLArrayContext(queue) nelements = 32 target_order = 7 qbx_order = 4 where = sym.as_dofdesc("test_interpolation") from_dd = sym.DOFDescriptor(geometry=where.geometry, discr_stage=source_discr_stage, granularity=sym.GRANULARITY_NODE) to_dd = sym.DOFDescriptor(geometry=where.geometry, discr_stage=sym.QBX_SOURCE_QUAD_STAGE2, granularity=target_granularity) mesh = make_curve_mesh(starfish, np.linspace(0.0, 1.0, nelements + 1), target_order) discr = Discretization( actx, mesh, InterpolatoryQuadratureSimplexGroupFactory(target_order)) from pytential.qbx import QBXLayerPotentialSource qbx = QBXLayerPotentialSource(discr, fine_order=4 * target_order, qbx_order=qbx_order, fmm_order=False) from pytential import GeometryCollection places = GeometryCollection(qbx, auto_where=where) sigma_sym = sym.var("sigma") op_sym = sym.sin(sym.interp(from_dd, to_dd, sigma_sym)) bound_op = bind(places, op_sym, auto_where=where) from meshmode.dof_array import thaw, flatten, unflatten def discr_and_nodes(stage): density_discr = places.get_discretization(where.geometry, stage) return density_discr, np.array([ actx.to_numpy(flatten(axis)) for axis in thaw(actx, density_discr.nodes()) ]) _, target_nodes = discr_and_nodes(sym.QBX_SOURCE_QUAD_STAGE2) source_discr, source_nodes = discr_and_nodes(source_discr_stage) sigma_target = np.sin(la.norm(target_nodes, axis=0)) sigma_dev = unflatten(actx, source_discr, actx.from_numpy(la.norm(source_nodes, axis=0))) sigma_target_interp = actx.to_numpy( flatten(bound_op(actx, sigma=sigma_dev))) if name in ("default", "default_explicit", "stage2", "quad"): error = la.norm(sigma_target_interp - sigma_target) / la.norm(sigma_target) assert error < 1.0e-10 elif name in ("stage2_center", ): assert len(sigma_target_interp) == 2 * len(sigma_target) else: raise ValueError(f"unknown test case name: {name}")