def get_mesh(self, resolution, target_order): from meshmode.mesh.io import generate_gmsh, FileSource base_mesh = generate_gmsh( FileSource("ellipsoid.step"), 2, order=2, other_options=[ "-string", "Mesh.CharacteristicLengthMax = %g;" % resolution]) from meshmode.mesh.processing import perform_flips # Flip elements--gmsh generates inside-out geometry. base_mesh = perform_flips(base_mesh, np.ones(base_mesh.nelements)) from meshmode.mesh.processing import affine_map, merge_disjoint_meshes from meshmode.mesh.tools import rand_rotation_matrix pitch = 10 meshes = [ affine_map( base_mesh, A=rand_rotation_matrix(3), b=pitch*np.array([ (ix-self.nx//2), (iy-self.ny//2), (iz-self.ny//2)])) for ix in range(self.nx) for iy in range(self.ny) for iz in range(self.nz) ] mesh = merge_disjoint_meshes(meshes, single_group=True) return mesh
def test_element_orientation(): from meshmode.mesh.io import generate_gmsh, FileSource mesh_order = 3 mesh = generate_gmsh( FileSource("blob-2d.step"), 2, order=mesh_order, force_ambient_dim=2, other_options=["-string", "Mesh.CharacteristicLengthMax = 0.02;"]) from meshmode.mesh.processing import (perform_flips, find_volume_mesh_element_orientations ) mesh_orient = find_volume_mesh_element_orientations(mesh) assert (mesh_orient > 0).all() from random import randrange flippy = np.zeros(mesh.nelements, np.int8) for i in range(int(0.3 * mesh.nelements)): flippy[randrange(0, mesh.nelements)] = 1 mesh = perform_flips(mesh, flippy, skip_tests=True) mesh_orient = find_volume_mesh_element_orientations(mesh) assert ((mesh_orient < 0) == (flippy > 0)).all()
def test_element_orientation(): from meshmode.mesh.io import generate_gmsh, FileSource mesh_order = 3 mesh = generate_gmsh( FileSource("blob-2d.step"), 2, order=mesh_order, force_ambient_dim=2, other_options=["-string", "Mesh.CharacteristicLengthMax = 0.02;"] ) from meshmode.mesh.processing import (perform_flips, find_volume_mesh_element_orientations) mesh_orient = find_volume_mesh_element_orientations(mesh) assert (mesh_orient > 0).all() from random import randrange flippy = np.zeros(mesh.nelements, np.int8) for i in range(int(0.3*mesh.nelements)): flippy[randrange(0, mesh.nelements)] = 1 mesh = perform_flips(mesh, flippy, skip_tests=True) mesh_orient = find_volume_mesh_element_orientations(mesh) assert ((mesh_orient < 0) == (flippy > 0)).all()
def get_mesh(self, resolution, target_order): from meshmode.mesh.io import generate_gmsh, FileSource base_mesh = generate_gmsh(FileSource("ellipsoid.step"), 2, order=2, other_options=[ "-string", "Mesh.CharacteristicLengthMax = %g;" % resolution ]) from meshmode.mesh.processing import perform_flips # Flip elements--gmsh generates inside-out geometry. base_mesh = perform_flips(base_mesh, np.ones(base_mesh.nelements)) from meshmode.mesh.processing import affine_map, merge_disjoint_meshes from meshmode.mesh.tools import rand_rotation_matrix pitch = 10 meshes = [ affine_map(base_mesh, A=rand_rotation_matrix(3), b=pitch * np.array([(ix - self.nx // 2), (iy - self.ny // 2), (iz - self.ny // 2)])) for ix in range(self.nx) for iy in range(self.ny) for iz in range(self.nz) ] mesh = merge_disjoint_meshes(meshes, single_group=True) return mesh
def get_mesh(self, resolution, target_order): from meshmode.mesh.io import generate_gmsh, FileSource mesh = generate_gmsh( FileSource("ellipsoid.step"), 2, order=2, other_options=[ "-string", "Mesh.CharacteristicLengthMax = %g;" % resolution]) from meshmode.mesh.processing import perform_flips # Flip elements--gmsh generates inside-out geometry. return perform_flips(mesh, np.ones(mesh.nelements))
def get_mesh(self, resolution, target_order): from meshmode.mesh.io import generate_gmsh, FileSource mesh = generate_gmsh(FileSource("ellipsoid.step"), 2, order=2, other_options=[ "-string", "Mesh.CharacteristicLengthMax = %g;" % resolution ]) from meshmode.mesh.processing import perform_flips # Flip elements--gmsh generates inside-out geometry. return perform_flips(mesh, np.ones(mesh.nelements))
def get_mesh(self, resolution, target_order): from meshmode.mesh.io import generate_gmsh, FileSource mesh = generate_gmsh( FileSource("rounded-cube.step"), 2, order=3, other_options=[ "-string", "Mesh.CharacteristicLengthMax = %g;" % resolution]) from meshmode.mesh.processing import perform_flips, affine_map mesh = affine_map(mesh, b=np.array([-0.5, -0.5, -0.5])) mesh = affine_map(mesh, A=np.eye(3)*2) # now centered at origin and extends to -1,1 # Flip elements--gmsh generates inside-out geometry. return perform_flips(mesh, np.ones(mesh.nelements))
def get_mesh(self, resolution, target_order): from meshmode.mesh.io import generate_gmsh, FileSource mesh = generate_gmsh( FileSource("rounded-cube.step"), 2, order=3, other_options=[ "-string", "Mesh.CharacteristicLengthMax = %g;" % resolution]) from meshmode.mesh.processing import perform_flips, affine_map mesh = affine_map(mesh, b=np.array([-0.5, -0.5, -0.5])) mesh = affine_map(mesh, A=np.eye(3)*2) # now centered at origin and extends to -1,1 # Flip elements--gmsh generates inside-out geometry. return perform_flips(mesh, np.ones(mesh.nelements))
def get_mesh(self, resolution, target_order): from pytools import download_from_web_if_not_present download_from_web_if_not_present( "https://raw.githubusercontent.com/inducer/geometries/master/" "surface-3d/elliptiplane.brep") from meshmode.mesh.io import generate_gmsh, FileSource mesh = generate_gmsh( FileSource("elliptiplane.brep"), 2, order=2, other_options=[ "-string", "Mesh.CharacteristicLengthMax = %g;" % resolution]) # now centered at origin and extends to -1,1 # Flip elements--gmsh generates inside-out geometry. from meshmode.mesh.processing import perform_flips return perform_flips(mesh, np.ones(mesh.nelements))
def get_mesh(self, resolution, target_order): from pytools import download_from_web_if_not_present download_from_web_if_not_present( "https://raw.githubusercontent.com/inducer/geometries/master/" "surface-3d/elliptiplane.brep") from meshmode.mesh.io import generate_gmsh, FileSource mesh = generate_gmsh( FileSource("elliptiplane.brep"), 2, order=2, other_options=[ "-string", "Mesh.CharacteristicLengthMax = %g;" % resolution]) # now centered at origin and extends to -1,1 # Flip elements--gmsh generates inside-out geometry. from meshmode.mesh.processing import perform_flips return perform_flips(mesh, np.ones(mesh.nelements))
def get_mesh(self, resolution, mesh_order): from meshmode.mesh.io import ScriptSource source = ScriptSource( """ SetFactory("OpenCASCADE"); Sphere(1) = {{0, 0, 0, {r}}}; Dilate {{ {{0, 0, 0}}, {{ {r}, {r}, {rr} }} }} {{ Volume{{1}}; }} """.format(r=self.diameter, rr=self.aspect_ratio * self.diameter), "geo") from meshmode.mesh.io import generate_gmsh mesh = generate_gmsh(source, 2, order=mesh_order, other_options=[ "-optimize_ho", "-string", "Mesh.CharacteristicLengthMax = %g;" % resolution ], target_unit="MM") from meshmode.mesh.processing import perform_flips return perform_flips(mesh, np.ones(mesh.nelements))
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 get_mesh(self, resolution, target_order): from pytools import download_from_web_if_not_present download_from_web_if_not_present( "https://raw.githubusercontent.com/inducer/geometries/a869fc3/" "surface-3d/betterplane.brep") from meshmode.mesh.io import generate_gmsh, ScriptWithFilesSource mesh = generate_gmsh( ScriptWithFilesSource(""" Merge "betterplane.brep"; Mesh.CharacteristicLengthMax = %(lcmax)f; Mesh.ElementOrder = 2; Mesh.CharacteristicLengthExtendFromBoundary = 0; // 2D mesh optimization // Mesh.Lloyd = 1; l_superfine() = Unique(Abs(Boundary{ Surface{ 27, 25, 17, 13, 18 }; })); l_fine() = Unique(Abs(Boundary{ Surface{ 2, 6, 7}; })); l_coarse() = Unique(Abs(Boundary{ Surface{ 14, 16 }; })); // p() = Unique(Abs(Boundary{ Line{l_fine()}; })); // Characteristic Length{p()} = 0.05; Field[1] = Attractor; Field[1].NNodesByEdge = 100; Field[1].EdgesList = {l_superfine()}; Field[2] = Threshold; Field[2].IField = 1; Field[2].LcMin = 0.075; Field[2].LcMax = %(lcmax)f; Field[2].DistMin = 0.1; Field[2].DistMax = 0.4; Field[3] = Attractor; Field[3].NNodesByEdge = 100; Field[3].EdgesList = {l_fine()}; Field[4] = Threshold; Field[4].IField = 3; Field[4].LcMin = 0.1; Field[4].LcMax = %(lcmax)f; Field[4].DistMin = 0.15; Field[4].DistMax = 0.4; Field[5] = Attractor; Field[5].NNodesByEdge = 100; Field[5].EdgesList = {l_coarse()}; Field[6] = Threshold; Field[6].IField = 5; Field[6].LcMin = 0.15; Field[6].LcMax = %(lcmax)f; Field[6].DistMin = 0.2; Field[6].DistMax = 0.4; Field[7] = Min; Field[7].FieldsList = {2, 4, 6}; Background Field = 7; """ % { "lcmax": resolution, }, ["betterplane.brep"]), 2) # Flip elements--gmsh generates inside-out geometry. from meshmode.mesh.processing import perform_flips return perform_flips(mesh, np.ones(mesh.nelements))
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(): # 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), ])
def get_mesh(self, resolution, target_order): from pytools import download_from_web_if_not_present download_from_web_if_not_present( "https://raw.githubusercontent.com/inducer/geometries/a869fc3/" "surface-3d/betterplane.brep") from meshmode.mesh.io import generate_gmsh, ScriptWithFilesSource mesh = generate_gmsh( ScriptWithFilesSource( """ Merge "betterplane.brep"; Mesh.CharacteristicLengthMax = %(lcmax)f; Mesh.ElementOrder = 2; Mesh.CharacteristicLengthExtendFromBoundary = 0; // 2D mesh optimization // Mesh.Lloyd = 1; l_superfine() = Unique(Abs(Boundary{ Surface{ 27, 25, 17, 13, 18 }; })); l_fine() = Unique(Abs(Boundary{ Surface{ 2, 6, 7}; })); l_coarse() = Unique(Abs(Boundary{ Surface{ 14, 16 }; })); // p() = Unique(Abs(Boundary{ Line{l_fine()}; })); // Characteristic Length{p()} = 0.05; Field[1] = Attractor; Field[1].NNodesByEdge = 100; Field[1].EdgesList = {l_superfine()}; Field[2] = Threshold; Field[2].IField = 1; Field[2].LcMin = 0.075; Field[2].LcMax = %(lcmax)f; Field[2].DistMin = 0.1; Field[2].DistMax = 0.4; Field[3] = Attractor; Field[3].NNodesByEdge = 100; Field[3].EdgesList = {l_fine()}; Field[4] = Threshold; Field[4].IField = 3; Field[4].LcMin = 0.1; Field[4].LcMax = %(lcmax)f; Field[4].DistMin = 0.15; Field[4].DistMax = 0.4; Field[5] = Attractor; Field[5].NNodesByEdge = 100; Field[5].EdgesList = {l_coarse()}; Field[6] = Threshold; Field[6].IField = 5; Field[6].LcMin = 0.15; Field[6].LcMax = %(lcmax)f; Field[6].DistMin = 0.2; Field[6].DistMax = 0.4; Field[7] = Min; Field[7].FieldsList = {2, 4, 6}; Background Field = 7; """ % { "lcmax": resolution, }, ["betterplane.brep"]), 2) # Flip elements--gmsh generates inside-out geometry. from meshmode.mesh.processing import perform_flips return perform_flips(mesh, np.ones(mesh.nelements))