def main():
# Basic params
tt = time.time()
q_reg = 2
q_sing = q_reg + 2
basis = BasisFunction.Constant
eps_solve = 1.0E-10
maxiter = 500
# Geometry
mg = MacroSurface3d.new_sphere()
gr = Surface3d.from_macrosurface3d(mg, 8)
print(
f'Created geometry with {gr.vertices} vertices, {gr.edges} edges and {gr.triangles} triangles'
)
# bem objects
bem_slp = Bem3d.new_slp_laplace(gr, q_reg, q_sing, basis, basis)
bem_dlp = Bem3d.new_dlp_laplace(gr, q_reg, q_sing, basis, basis, 0.5)
# Assemble H-matrix SLP
print('Assemble dense matrix V:')
V = AMatrix.new(gr.triangles, gr.triangles)
start = time.time()
bem_slp.assemble_amatrix(V)
t = time.time() - start
size = V.memsize() / 1024 / 1024
print(f' {t:.2f} s')
print(f' {size:.3f} MB')
# hmatrix 0.5I + K
print('Assemble dense matrix 0.5M + K:')
KM = AMatrix.new(gr.triangles, gr.triangles)
start = time.time()
bem_dlp.assemble_amatrix(KM)
t = time.time() - start
size = KM.memsize() / 1024 / 1024
print(f' {t:.2f} s')
print(f' {size:.3f} MB')
# Dirichlet data
gd = AVector.new(gr.triangles)
print('Compute L2-projection of Dirichlet data:')
start = time.time()
bem_dlp.project_l2_c(eval_dirichlet_fundamental_laplacebem3d, gd, bem_dlp)
t = time.time() - start
size = gd.memsize() / 1024 / 1024
print(f' {t:.2f} s')
print(f' {size:.3f} MB')
# Compute right-hand-side b = (0.5M + K)*gd
b = AVector.new(gr.triangles, zeros=True)
print('Compute right-hand-side:')
start = time.time()
b.mvm(1.0, False, KM, gd)
t = time.time() - start
size = b.memsize() / 1024 / 1024
print(f' {t:.2f} s')
# Solve linear system V x = b using CG-method.
x = AVector.new(gr.triangles, zeros=True)
print('Solve linear system:')
start = time.time()
krylovsolvers.solve_cg(V, b, x, eps_solve, maxiter)
t = time.time() - start
size = x.memsize() / 1024 / 1024
print(f' {t:.2f} s')
print(f' {size:.3f} MB')
# Compute L2-error compared to analytical solution of the Neumann data.
print('Compute L2-error against analytical solution of the Neumann data:')
start = time.time()
norm = bem_slp.norm_l2_diff_c(x, eval_neumann_fundamental_laplacebem3d,
None)
t = time.time() - start
print('Abs. L2-error:')
print(f' {t:.2f} s')
print(f' {norm:.5e}')
print('Rel. L2-error:')
start = time.time()
norm /= bem_slp.norm_l2(eval_neumann_fundamental_laplacebem3d, None)
t = time.time() - start
print(f' {t:.2f} s')
print(f' {norm:.5e}')
# cleanup
x.delete()
b.delete()
gd.delete()
V.delete()
KM.delete()
bem_slp.delete()
bem_dlp.delete()
mg.delete()
gr.delete()
uninit()
print(f'TOTAL TIME: {time.time() - tt:.5f} s')
def main():
# Basic params
tt = time.time()
# Set up basic parameters
q_reg = 2
q_sing = q_reg + 2
basis = BasisFunction.Constant
m = 4
clf = 2 * m * m * m
eta = 1.4
eps_solve = 1.0e-10
maxiter = 500
# Create geometry
mg = MacroSurface3d.new_sphere()
gr = Surface3d.from_macrosurface3d(mg, 8)
print(f'Created geometry with {gr.vertices} vertices, {gr.edges} edges and'
f' {gr.triangles} triangles')
# Set up basis data structures for H-matrix approximations
bem_slp = Bem3d.new_slp_laplace(gr, q_reg, q_sing, basis, basis)
bem_dlp = Bem3d.new_dlp_laplace(gr, q_reg, q_sing, basis, basis, 0.5)
root = bem_slp.build_cluster(clf, basis)
broot = Block.build(root, root, get_address(eta),
admissible_2_cluster, strict=False, lower=False)
bem_slp.setup_hmatrix_aprx_inter(IntDir.Row, root, root, broot, m)
bem_dlp.setup_hmatrix_aprx_inter(IntDir.Row, root, root, broot, m)
# Assemble H-matrix SLP
print('Assemble H-matrix V:')
V = HMatrix.from_block(broot, m * m * m)
start = time.time()
bem_slp.assemble_hmatrix(broot, V)
t = time.time() - start
size = V.memsize() / 1024 / 1024
print(f' {t:.2f} s')
print(f' {size:.3f} MB')
# Assemble H-matrix 0.5I + K
print('Assemble H-matrix 0.5M + K:')
KM = HMatrix.from_block(broot, m * m * m)
start = time.time()
bem_dlp.assemble_hmatrix(broot, KM)
t = time.time() - start
size = KM.memsize() / 1024 / 1024
print(f' {t:.2f} s')
print(f' {size:.3f} MB')
# Create Dirichlet data
gd = AVector.new(gr.triangles)
print('Compute L2-projection of Dirichlet data:')
start = time.time()
bem_dlp.project_l2_c(eval_dirichlet_fundamental_laplacebem3d, gd, bem_dlp)
t = time.time() - start
size = gd.memsize() / 1024 / 1024
print(f' {t:.2f} s')
print(f' {size:.3f} MB')
# Compute right-hand-side b = (0.5M + K)*gd
b = AVector.new(gr.triangles)
print('Compute right-hand-side:')
start = time.time()
b.clear()
b.mvm(1.0, False, KM, gd)
t = time.time() - start
size = b.memsize() / 1024 / 1024
print(f' {t:.2f} s')
print(f' {size:.3f} MB')
# Solve linear system V x = b using CG-method.
x = AVector.new(gr.triangles, zeros=True)
print('Solve linear system:')
start = time.time()
krylovsolvers.solve_cg(V, b, x, eps_solve, maxiter)
t = time.time() - start
size = x.memsize() / 1024 / 1024
print(f' {t:.2f} s')
print(f' {size:.3f} MB')
# Compute L2-error compared to analytical solution of the Neumann data.
print('Compute L2-error against analytical solution of the Neumann data:')
start = time.time()
norm = bem_slp.norm_l2_diff_c(x, eval_neumann_fundamental_laplacebem3d,
None)
t = time.time() - start
print('Abs. L2-error:')
print(f' {t:.2f} s')
print(f' {norm:.5e}')
start = time.time()
norm /= bem_slp.norm_l2(eval_neumann_fundamental_laplacebem3d, None)
t = time.time() - start
print('Rel. L2-error:')
print(f' {t:.2f} s')
print(f' {norm:.5e}')
# cleanup
x.delete()
b.delete()
gd.delete()
V.delete()
KM.delete()
broot.delete()
root.delete()
bem_slp.delete()
bem_dlp.delete()
mg.delete()
gr.delete()
uninit()
print(f'TOTAL TIME: {time.time() - tt:.5f} s')
def main():
# Set up basic parameters
tt = time.time()
q_reg = 2
q_sing = q_reg + 2
basis = CEnumBasisFunctionBem3d.BASIS_CONSTANT_BEM3D
m = 4
clf = 2 * m * m * m
eta = 1.4
eps_solve = 1.0e-10
maxiter = 500
# Create geometry
mg = new_sphere_macrosurface3d()
gr = build_from_macrosurface3d_surface3d(mg, 8)
print(
f'Created geometry with {gr.contents.vertices} vertices, {gr.contents.vertices} edges and {gr.contents.vertices} triangles'
)
# Set up basis data structures for H2-matrix approximations
bem_slp = new_slp_laplace_bem3d(gr, q_reg, q_sing, basis, basis)
# Create a new BEM-object, that can compute entries of DLP operator and 0.5*I.
bem_dlp = new_dlp_laplace_bem3d(gr, q_reg, q_sing, basis, basis, 0.5)
root = build_bem3d_cluster(bem_slp, clf, basis)
broot = build_strict_block(root, root, get_address(eta),
CFuncAdmissible(admissible_2_cluster))
# Create structure for row clusterbases
rbV = build_from_cluster_clusterbasis(root)
cbV = build_from_cluster_clusterbasis(root)
rbKM = build_from_cluster_clusterbasis(root)
cbKM = build_from_cluster_clusterbasis(root)
# Init H2-matrix approximation scheme by interpolation
setup_h2matrix_aprx_inter_bem3d(bem_dlp, rbKM, cbKM, broot, m)
setup_h2matrix_aprx_inter_bem3d(bem_slp, rbV, cbV, broot, m)
# Assemble row clusterbasis for SLP
print('Assemble row basis for H2-matrix V:')
start = time.time()
assemble_bem3d_h2matrix_row_clusterbasis(bem_slp, rbV)
t = time.time() - start
size = getsize_clusterbasis(rbV) / 1024 / 1024
print(f' {t:.2f} s')
print(f' {size:.3f} MB')
# Assemble column clusterbasis for SLP
print('Assemble column basis for H2-matrix V:')
start = time.time()
assemble_bem3d_h2matrix_col_clusterbasis(bem_slp, cbV)
t = time.time() - start
size = getsize_clusterbasis(cbV) / 1024 / 1024
print(f' {t:.2f} s')
print(f' {size:.3f} MB')
# Assemble H-matrix SLP
print('Assemble H2-matrix V:')
V = build_from_block_h2matrix(broot, rbV, cbV)
start = time.time()
assemble_bem3d_h2matrix(bem_slp, V)
t = time.time() - start
size = getsize_h2matrix(V) / 1024 / 1024
print(f' {t:.2f} s')
print(f' {size:.3f} MB')
# Assemble row clusterbasis for DLP
print('Assemble row basis for H2-matrix 0.5M + K:')
start = time.time()
assemble_bem3d_h2matrix_row_clusterbasis(bem_dlp, rbKM)
t = time.time() - start
size = getsize_clusterbasis(rbKM) / 1024 / 1024
print(f' {t:.2f} s')
print(f' {size:.3f} MB')
# Assemble column clusterbasis for DLP
print('Assemble column basis for H2-matrix 0.5M + K:')
start = time.time()
assemble_bem3d_h2matrix_col_clusterbasis(bem_dlp, cbKM)
t = time.time() - start
size = getsize_clusterbasis(cbKM) / 1024 / 1024
print(f' {t:.2f} s')
print(f' {size:.3f} MB')
# Assemble H-matrix 0.5I + K
print('Assemble H2-matrix 0.5M + K:')
KM = build_from_block_h2matrix(broot, rbKM, cbKM)
start = time.time()
assemble_bem3d_h2matrix(bem_dlp, KM)
t = time.time() - start
size = getsize_h2matrix(KM) / 1024 / 1024
print(f' {t:.2f} s')
print(f' {size:.3f} MB')
# Create Dirichlet data
gd = new_avector(gr.contents.triangles)
print('Compute L2-projection of Dirichlet data:')
start = time.time()
# L2-projection onto the space of piecewise constant function on the boundary.
projectL2_bem3d_c_avector(
bem_dlp, CFuncBoundaryFunc3d(eval_dirichlet_fundamental_laplacebem3d),
gd, to_voidp(bem_dlp))
t = time.time() - start
size = getsize_avector(gd) / 1024 / 1024
print(f' {t:.2f} s')
print(f' {size:.3f} MB')
# Compute right-hand-side b = (0.5M + K)*gd
b = new_avector(gr.contents.triangles)
print('Compute right-hand-side:')
start = time.time()
clear_avector(b)
addeval_h2matrix_avector(1.0, KM, gd, b)
t = time.time() - start
size = getsize_avector(b) / 1024 / 1024
print(f' {t:.2f} s')
print(f' {size:.3f} MB')
# Solve linear system V x = b using CG-method.
x = new_avector(gr.contents.triangles)
print('Solve linear system:')
start = time.time()
solve_cg_h2matrix_avector(V, b, x, eps_solve, maxiter)
t = time.time() - start
size = getsize_avector(x) / 1024 / 1024
print(f' {t:.2f} s')
print(f' {size:.3f} MB')
# Compute L2-error compared to analytical solution of the Neumann data.
print('Compute L2-error against analytical solution of the Neumann data:')
start = time.time()
norm = normL2diff_c_bem3d(
bem_slp, x, CFuncBoundaryFunc3d(eval_neumann_fundamental_laplacebem3d),
None)
t = time.time() - start
print('Abs. L2-error:')
print(f' {t:.2f} s')
print(f' {norm:.5e}')
print('Rel. L2-error:')
start = time.time()
norm /= normL2_bem3d(
bem_slp, CFuncBoundaryFunc3d(eval_neumann_fundamental_laplacebem3d),
None)
t = time.time() - start
print(f' {t:.2f} s')
print(f' {norm:.5e}')
# cleanup
del_avector(x)
del_avector(b)
del_avector(gd)
del_h2matrix(V)
del_h2matrix(KM)
del_block(broot)
del_cluster(root)
del_bem3d(bem_slp)
del_bem3d(bem_dlp)
del_macrosurface3d(mg)
del_surface3d(gr)
uninit()
t = time.time() - tt
print(f'TOTAL TIME: {t:.5f} s')
def main():
# Basic params
tt = time.time()
q_reg = 2 # ctypes.c_uint(2)
q_sing = 4 # ctypes.c_uint(q_reg.value + 2)
basis = CEnumBasisFunctionBem3d.BASIS_CONSTANT_BEM3D
eps_solve = 1E-10 # ctypes.c_double(1.0E-10)
maxiter = 500 # ctypes.c_uint(500)
# Geometry
mg = new_sphere_macrosurface3d()
gr = build_from_macrosurface3d_surface3d(mg, ctypes.c_uint(8))
print(
f'Created geometry with {gr.contents.vertices} vertices, {gr.contents.edges} edges and {gr.contents.triangles} triangles'
)
# bem objects
bem_slp = new_slp_laplace_bem3d(gr, q_reg, q_sing, basis, basis)
bem_dlp = new_dlp_laplace_bem3d(gr, q_reg, q_sing, basis, basis,
ctypes.c_double(0.5))
# Assemble H-matrix SLP
print('Assemble dense matrix V:')
V = new_amatrix(gr.contents.triangles, gr.contents.triangles)
start = time.time()
assemble_bem3d_amatrix(bem_slp, V)
t = time.time() - start
size = getsize_amatrix(V) / 1024 / 1024
print(f' {t:.2f} s')
print(f' {size:.3f} MB')
# hmatrix 0.5I + K
print('Assemble dense matrix 0.5M + K:')
KM = new_amatrix(gr.contents.triangles, gr.contents.triangles)
start = time.time()
assemble_bem3d_amatrix(bem_dlp, KM)
t = time.time() - start
size = getsize_amatrix(KM) / 1024 / 1024
print(f' {t:.2f} s')
print(f' {size:.3f} MB')
# Dirichlet data
gd = new_avector(gr.contents.triangles)
print('Compute L2-projection of Dirichlet data:')
start = time.time()
projectL2_bem3d_c_avector(
bem_dlp, CFuncBoundaryFunc3d(eval_dirichlet_fundamental_laplacebem3d),
gd, ctypes.cast(bem_dlp, ctypes.c_void_p))
t = time.time() - start
size = getsize_avector(gd) / 1024 / 1024
print(f' {t:.2f} s')
print(f' {size:.3f} MB')
# Compute right-hand-side b = (0.5M + K)*gd
b = new_avector(gr.contents.triangles)
print('Compute right-hand-side:')
start = time.time()
clear_avector(b)
addeval_amatrix_avector(ctypes.c_double(1.0), KM, gd, b)
t = time.time() - start
size = getsize_avector(b) / 1024 / 1024
print(f' {t:.2f} s')
print(f' {size:.3f} MB')
# Solve linear system V x = b using CG-method.
x = new_avector(gr.contents.triangles)
print('Solve linear system:')
start = time.time()
solve_cg_amatrix_avector(V, b, x, eps_solve, maxiter)
t = time.time() - start
size = getsize_avector(x) / 1024 / 1024
print(f' {t:.2f} s')
print(f' {size:.3f} MB')
# Compute L2-error compared to analytical solution of the Neumann data.
print('Compute L2-error against analytical solution of the Neumann data:')
start = time.time()
norm = normL2diff_c_bem3d(
bem_slp, x, CFuncBoundaryFunc3d(eval_neumann_fundamental_laplacebem3d),
None)
t = time.time() - start
print('Abs. L2-error:')
print(f' {t:.2f} s')
print(f' {norm:.5e}')
print('Rel. L2-error:')
start = time.time()
norm /= normL2_bem3d(
bem_slp, CFuncBoundaryFunc3d(eval_neumann_fundamental_laplacebem3d),
None)
t = time.time() - start
print(f' {t:.2f} s')
print(f' {norm:.5e}')
# cleanup
del_avector(x)
del_avector(b)
del_avector(gd)
del_amatrix(V)
del_amatrix(KM)
del_bem3d(bem_slp)
del_bem3d(bem_dlp)
del_macrosurface3d(mg)
del_surface3d(gr)
uninit()
print(f'TOTAL TIME: {time.time() - tt:.5f} s')