def test_3d_jump_relations(ctx_factory, relation, visualize=False): # logging.basicConfig(level=logging.INFO) cl_ctx = ctx_factory() queue = cl.CommandQueue(cl_ctx) actx = PyOpenCLArrayContext(queue) 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( actx, 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" ) places = GeometryCollection(qbx) density_discr = places.get_discretization(places.auto_source.geometry) 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))) from meshmode.dof_array import thaw x, y, z = thaw(actx, density_discr.nodes()) m = actx.np 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(places, sym.xyz_to_tangential(sym.make_sym_vector("jxyz", 3)))( actx, 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(places, jump_identity_sym) jump_identity = bound_jump_identity(actx, density=density) h_max = bind(places, sym.h_max(qbx.ambient_dim))(actx) err = ( norm(density_discr, jump_identity, np.inf) / norm(density_discr, 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(places, nxcurlS(+1))(actx, density=density) nxcurlS_avg = bind(places, nxcurlS("avg"))(actx, density=density) jtxyz = bind(places, sym.tangential_to_xyz(density_sym))( actx, density=density) from meshmode.discretization.visualization import make_visualizer bdry_vis = make_visualizer(actx, qbx.density_discr, target_order+3) bdry_normals = bind(places, sym.normal(3))(actx)\ .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": op = sym.Sp(knl, density_sym, qbx_forced_limit=+1) sp_ext = bind(places, op)(actx, density=density) op = sym.Sp(knl, density_sym, qbx_forced_limit="avg") sp_avg = bind(places, op)(actx, density=density) from meshmode.discretization.visualization import make_visualizer bdry_vis = make_visualizer(actx, qbx.density_discr, target_order+3) bdry_normals = bind(places, sym.normal(3))(actx).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 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 test_3d_jump_relations(actx_factory, relation, visualize=False): # logging.basicConfig(level=logging.INFO) actx = actx_factory() if relation == "div_s": target_order = 3 else: target_order = 4 qbx_order = target_order if relation == "sp": resolutions = [10, 14, 18] else: resolutions = [6, 10, 14] from pytools.convergence import EOCRecorder eoc_rec = EOCRecorder() for nel_factor in resolutions: from meshmode.mesh.generation import generate_torus mesh = generate_torus( 5, 2, n_major=2 * nel_factor, n_minor=nel_factor, order=target_order, ) from meshmode.discretization import Discretization from meshmode.discretization.poly_element import \ InterpolatoryQuadratureSimplexGroupFactory pre_density_discr = Discretization( actx, mesh, InterpolatoryQuadratureSimplexGroupFactory(target_order)) from pytential.qbx import QBXLayerPotentialSource qbx = QBXLayerPotentialSource(pre_density_discr, fine_order=5 * target_order, qbx_order=qbx_order, fmm_order=qbx_order + 5, fmm_backend="fmmlib") places = GeometryCollection(qbx) density_discr = places.get_discretization(places.auto_source.geometry) from sumpy.kernel import LaplaceKernel knl = LaplaceKernel(places.ambient_dim) def nxcurlS(qbx_forced_limit): sigma_sym = sym.cse(sym.tangential_to_xyz(density_sym), "jxyz") return sym.n_cross( sym.curl( sym.S(knl, sigma_sym, qbx_forced_limit=qbx_forced_limit))) x, y, z = thaw(density_discr.nodes(), actx) 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. jxyz = sym.make_obj_array([ actx.np.cos(0.5 * x) * actx.np.cos(0.5 * y) * actx.np.cos(0.5 * z), actx.np.sin(0.5 * x) * actx.np.cos(0.5 * y) * actx.np.sin(0.5 * z), actx.np.sin(0.5 * x) * actx.np.cos(0.5 * y) * actx.np.cos(0.5 * z), ]) density = bind( places, sym.xyz_to_tangential(sym.make_sym_vector("jxyz", 3)))(actx, jxyz=jxyz) elif relation == "sp": density_sym = sym.var("density") jump_identity_sym = ( 0.5 * density_sym + sym.Sp(knl, density_sym, qbx_forced_limit=+1) - sym.Sp(knl, density_sym, qbx_forced_limit="avg")) density = actx.np.cos(2 * x) * actx.np.cos(2 * y) * actx.np.cos(z) elif relation == "div_s": density_sym = sym.var("density") sigma_sym = sym.normal( places.ambient_dim).as_vector() * density_sym jump_identity_sym = ( sym.div(sym.S(knl, sigma_sym, qbx_forced_limit="avg")) + sym.D(knl, density_sym, qbx_forced_limit="avg")) density = actx.np.cos(2 * x) * actx.np.cos(2 * y) * actx.np.cos(z) else: raise ValueError(f"unexpected value of 'relation': '{relation}'") bound_jump_identity = bind(places, jump_identity_sym) jump_identity = bound_jump_identity(actx, density=density) h_max = actx.to_numpy( bind(places, sym.h_max(places.ambient_dim))(actx)) err = actx.to_numpy( norm(density_discr, jump_identity, np.inf) / norm(density_discr, density, np.inf)) eoc_rec.add_data_point(h_max, err) logging.info("error: nel %d h_max %.5e %.5e", nel_factor, h_max, err) # {{{ visualization if not visualize: continue from meshmode.discretization.visualization import make_visualizer vis = make_visualizer(actx, density_discr, target_order) normals = bind(places, sym.normal(places.ambient_dim).as_vector())(actx) error = actx.np.log10(actx.np.abs(jump_identity) + 1.0e-15) if relation == "nxcurls": nxcurlS_ext = bind(places, nxcurlS(+1))(actx, density=density) nxcurlS_avg = bind(places, nxcurlS("avg"))(actx, density=density) jtxyz = bind(places, sym.tangential_to_xyz(density_sym))(actx, density=density) vis.write_vtk_file(f"source-nxcurls-{nel_factor:03d}.vtu", [ ("jt", jtxyz), ("nxcurlS_ext", nxcurlS_ext), ("nxcurlS_avg", nxcurlS_avg), ("bdry_normals", normals), ("error", error), ]) elif relation == "sp": op = sym.Sp(knl, density_sym, qbx_forced_limit=+1) sp_ext = bind(places, op)(actx, density=density) op = sym.Sp(knl, density_sym, qbx_forced_limit="avg") sp_avg = bind(places, op)(actx, density=density) vis.write_vtk_file(f"source-sp-{nel_factor:03d}.vtu", [ ("density", density), ("sp_ext", sp_ext), ("sp_avg", sp_avg), ("bdry_normals", normals), ("error", error), ]) elif relation == "div_s": vis.write_vtk_file(f"source-div-{nel_factor:03d}.vtu", [ ("density", density), ("bdry_normals", normals), ("error", error), ]) # }}} logger.info("\n%s", str(eoc_rec)) assert eoc_rec.order_estimate() >= qbx_order - 1.5