def _rebuild_operators(self):
if self.mesh.x.lbc.type == 'pml' and self.compact:
# build intermediates for the compact operator
raise ValidationFunctionError(
" This solver is in construction and is not yet complete. For variable density and compact PML."
)
dof = self.mesh.dof(include_bc=True)
oc = self.operator_components
built = oc.get('_numpy_components_built', False)
oc.M = make_diag_mtx(self.model_parameters.C.squeeze()**-2)
# build the static components
if not built:
# build Dxx
oc.Dxx = build_derivative_matrix(
self.mesh,
2,
self.spatial_accuracy_order,
dimension='x',
use_shifted_differences=self.spatial_shifted_differences)
# build Dzz
oc.Dzz = build_derivative_matrix(
self.mesh,
2,
self.spatial_accuracy_order,
dimension='z',
use_shifted_differences=self.spatial_shifted_differences)
# build Dx
oc.Dx = build_derivative_matrix(
self.mesh,
1,
self.spatial_accuracy_order,
dimension='x',
use_shifted_differences=self.spatial_shifted_differences)
# build Dz
oc.Dz = build_derivative_matrix(
self.mesh,
1,
self.spatial_accuracy_order,
dimension='z',
use_shifted_differences=self.spatial_shifted_differences)
# build sigma
oc.sx, oc.sz, oc.sxp, oc.szp = self._sigma_PML(self.mesh)
oc._numpy_components_built = True
else:
# build intermediates for operator with auxiliary fields
dof = self.mesh.dof(include_bc=True)
oc = self.operator_components
built = oc.get('_numpy_components_built', False)
# build the static components
if not built:
# build sigmax
sx = build_sigma(self.mesh, self.mesh.x)
oc.sigmax = make_diag_mtx(sx)
# build sigmaz
sz = build_sigma(self.mesh, self.mesh.z)
oc.sigmaz = make_diag_mtx(sz)
# build Dx
oc.minus_Dx = build_derivative_matrix(
self.mesh,
1,
self.spatial_accuracy_order,
dimension='x',
use_shifted_differences=self.spatial_shifted_differences)
oc.minus_Dx.data *= -1
# build Dz
oc.minus_Dz = build_derivative_matrix(
self.mesh,
1,
self.spatial_accuracy_order,
dimension='z',
use_shifted_differences=self.spatial_shifted_differences)
oc.minus_Dz.data *= -1
# build other useful things
oc.I = spsp.eye(dof, dof)
oc.empty = spsp.csr_matrix((dof, dof))
# useful intermediates
oc.sigma_xz = make_diag_mtx(sx * sz)
oc.sigma_xPz = oc.sigmax + oc.sigmaz
oc.minus_sigma_zMx_Dx = make_diag_mtx((sz - sx)) * oc.minus_Dx
oc.minus_sigma_xMz_Dz = make_diag_mtx((sx - sz)) * oc.minus_Dz
oc._numpy_components_built = True
kappa = self.model_parameters.kappa
rho = self.model_parameters.rho
oc.m1 = make_diag_mtx((kappa**-1).reshape(-1, ))
oc.m2 = make_diag_mtx((rho**-1).reshape(-1, ))
# build heterogenous laplacian
sh = self.mesh.shape(include_bc=True, as_grid=True)
deltas = [self.mesh.x.delta, self.mesh.z.delta]
oc.L = build_derivative_matrix_VDA(self.mesh,
2,
self.spatial_accuracy_order,
alpha=rho**-1)
# oc.L is a heterogenous laplacian operator. It computes div(m2 grad), where m2 = 1/rho.
# Currently the creation of oc.L is slow. This is because we have implemented a cenetered heterogenous laplacian.
# To speed up computation, we could compute a div(m2 grad) operator that is not centered by simply multiplying
# a divergence operator by oc.m2 by a gradient operator.
self.K = spsp.bmat([[
oc.m1 * oc.sigma_xz - oc.L, oc.minus_Dx * oc.m2,
oc.minus_Dz * oc.m2
], [oc.minus_sigma_zMx_Dx, oc.sigmax, oc.empty],
[oc.minus_sigma_xMz_Dz, oc.empty, oc.sigmaz]])
self.C = spsp.bmat([[oc.m1 * oc.sigma_xPz, oc.empty, oc.empty],
[oc.empty, oc.I, oc.empty],
[oc.empty, oc.empty, oc.I]])
self.M = spsp.bmat([[oc.m1, oc.empty, oc.empty],
[oc.empty, oc.empty, oc.empty],
[oc.empty, oc.empty, oc.empty]])
def _rebuild_operators(self):
VariableDensityAcousticTimeScalar_2D._rebuild_operators(self)
dof = self.mesh.dof(include_bc=True)
oc = self.operator_components
built = oc.get('_numpy_components_built', False)
# build the static components
if not built:
# build sigmax
sx = build_sigma(self.mesh, self.mesh.x)
oc.sigmax = make_diag_mtx(sx)
# build sigmaz
sz = build_sigma(self.mesh, self.mesh.z)
oc.sigmaz = make_diag_mtx(sz)
# build Dx
oc.Dx = build_derivative_matrix(self.mesh,
1,
self.spatial_accuracy_order,
dimension='x')
oc.minus_Dx = copy.deepcopy(
oc.Dx) #more storage, but less computations
oc.minus_Dx.data *= -1
# build Dz
oc.Dz = build_derivative_matrix(self.mesh,
1,
self.spatial_accuracy_order,
dimension='z')
oc.minus_Dz = copy.deepcopy(
oc.Dz) #more storage, but less computations
oc.minus_Dz.data *= -1
# build other useful things
oc.I = spsp.eye(dof, dof)
oc.empty = spsp.csr_matrix((dof, dof))
# useful intermediates
oc.sigma_xz = make_diag_mtx(sx * sz)
oc.sigma_xPz = oc.sigmax + oc.sigmaz
oc.minus_sigma_zMx_Dx = make_diag_mtx((sz - sx)) * oc.minus_Dx
oc.minus_sigma_xMz_Dz = make_diag_mtx((sx - sz)) * oc.minus_Dz
oc._numpy_components_built = True
kappa = self.model_parameters.kappa
rho = self.model_parameters.rho
oc.m1 = make_diag_mtx((kappa**-1).reshape(-1, ))
oc.m2 = make_diag_mtx((rho**-1).reshape(-1, ))
oc.L = build_derivative_matrix_VDA(self.mesh,
2,
self.spatial_accuracy_order,
alpha=rho**-1)
# oc.L is a heterogenous laplacian operator. It computes div(m2 grad), where m2 = 1/rho.
# Ian's implementation used the regular Dx operators in the PML even though the heterogeneous Laplacian with staggered derivative operators is used in the physical domain.
# I (Bram) did not change this or investigate if this causes some problems but am noting it here for completeness.
K = spsp.bmat([[
oc.m1 * oc.sigma_xz - oc.L, oc.minus_Dx * oc.m2,
oc.minus_Dz * oc.m2
], [oc.minus_sigma_zMx_Dx, oc.sigmax, oc.empty],
[oc.minus_sigma_xMz_Dz, oc.empty, oc.sigmaz]])
C = spsp.bmat([[oc.m1 * oc.sigma_xPz, oc.empty, oc.empty],
[oc.empty, oc.I, oc.empty], [oc.empty, oc.empty, oc.I]
]) / self.dt
M = spsp.bmat([[oc.m1, oc.empty, oc.empty],
[oc.empty, oc.empty, oc.empty],
[oc.empty, oc.empty, oc.empty]]) / self.dt**2
Stilde_inv = M + C
Stilde_inv.data = 1. / Stilde_inv.data
self.A_k = Stilde_inv * (2 * M - K + C)
self.A_km1 = -1 * Stilde_inv * (M)
self.A_f = Stilde_inv
def _rebuild_operators(self):
if self.mesh.x.lbc.type == 'pml' and self.compact:
# build intermediates for the compact operator
raise ValidationFunctionError(" This solver is in construction and is not yet complete. For variable density and compact PML.")
dof = self.mesh.dof(include_bc=True)
oc = self.operator_components
built = oc.get('_numpy_components_built', False)
oc.M = make_diag_mtx(self.model_parameters.C.squeeze()**-2)
# build the static components
if not built:
# build Dxx
oc.Dxx = build_derivative_matrix(self.mesh,
2,
self.spatial_accuracy_order,
dimension='x',
use_shifted_differences=self.spatial_shifted_differences)
# build Dzz
oc.Dzz = build_derivative_matrix(self.mesh,
2,
self.spatial_accuracy_order,
dimension='z',
use_shifted_differences=self.spatial_shifted_differences)
# build Dx
oc.Dx = build_derivative_matrix(self.mesh,
1,
self.spatial_accuracy_order,
dimension='x',
use_shifted_differences=self.spatial_shifted_differences)
# build Dz
oc.Dz = build_derivative_matrix(self.mesh,
1,
self.spatial_accuracy_order,
dimension='z',
use_shifted_differences=self.spatial_shifted_differences)
# build sigma
oc.sx, oc.sz, oc.sxp, oc.szp = self._sigma_PML(self.mesh)
oc._numpy_components_built = True
else:
# build intermediates for operator with auxiliary fields
dof = self.mesh.dof(include_bc=True)
oc = self.operator_components
built = oc.get('_numpy_components_built', False)
# build the static components
if not built:
# build sigmax
sx = build_sigma(self.mesh, self.mesh.x)
oc.sigmax = make_diag_mtx(sx)
# build sigmaz
sz = build_sigma(self.mesh, self.mesh.z)
oc.sigmaz = make_diag_mtx(sz)
# build Dx
oc.minus_Dx = build_derivative_matrix(self.mesh,
1,
self.spatial_accuracy_order,
dimension='x',
use_shifted_differences=self.spatial_shifted_differences)
oc.minus_Dx.data *= -1
# build Dz
oc.minus_Dz = build_derivative_matrix(self.mesh,
1,
self.spatial_accuracy_order,
dimension='z',
use_shifted_differences=self.spatial_shifted_differences)
oc.minus_Dz.data *= -1
# build other useful things
oc.I = spsp.eye(dof, dof)
oc.empty = spsp.csr_matrix((dof, dof))
# useful intermediates
oc.sigma_xz = make_diag_mtx(sx*sz)
oc.sigma_xPz = oc.sigmax + oc.sigmaz
oc.minus_sigma_zMx_Dx = make_diag_mtx((sz-sx))*oc.minus_Dx
oc.minus_sigma_xMz_Dz = make_diag_mtx((sx-sz))*oc.minus_Dz
oc._numpy_components_built = True
kappa = self.model_parameters.kappa
rho = self.model_parameters.rho
oc.m1 = make_diag_mtx((kappa**-1).reshape(-1,))
oc.m2 = make_diag_mtx((rho**-1).reshape(-1,))
# build heterogenous laplacian
sh = self.mesh.shape(include_bc=True,as_grid=True)
deltas = [self.mesh.x.delta,self.mesh.z.delta]
oc.L = build_derivative_matrix_VDA(self.mesh,
2,
self.spatial_accuracy_order,
alpha = rho**-1
)
# oc.L is a heterogenous laplacian operator. It computes div(m2 grad), where m2 = 1/rho.
# Currently the creation of oc.L is slow. This is because we have implemented a cenetered heterogenous laplacian.
# To speed up computation, we could compute a div(m2 grad) operator that is not centered by simply multiplying
# a divergence operator by oc.m2 by a gradient operator.
self.K = spsp.bmat([[oc.m1*oc.sigma_xz-oc.L, oc.minus_Dx*oc.m2, oc.minus_Dz*oc.m2 ],
[oc.minus_sigma_zMx_Dx, oc.sigmax, oc.empty ],
[oc.minus_sigma_xMz_Dz, oc.empty, oc.sigmaz ]])
self.C = spsp.bmat([[oc.m1*oc.sigma_xPz, oc.empty, oc.empty],
[oc.empty, oc.I, oc.empty],
[oc.empty, oc.empty, oc.I ]])
self.M = spsp.bmat([[ oc.m1, oc.empty, oc.empty],
[oc.empty, oc.empty, oc.empty],
[oc.empty, oc.empty, oc.empty]])
def _rebuild_operators(self):
VariableDensityAcousticTimeScalar_2D._rebuild_operators(self)
dof = self.mesh.dof(include_bc=True)
oc = self.operator_components
built = oc.get('_numpy_components_built', False)
# build the static components
if not built:
# build sigmax
sx = build_sigma(self.mesh, self.mesh.x)
oc.sigmax = make_diag_mtx(sx)
# build sigmaz
sz = build_sigma(self.mesh, self.mesh.z)
oc.sigmaz = make_diag_mtx(sz)
# build Dx
oc.Dx = build_derivative_matrix(self.mesh,
1,
self.spatial_accuracy_order,
dimension='x')
oc.minus_Dx = copy.deepcopy(oc.Dx) #more storage, but less computations
oc.minus_Dx.data *= -1
# build Dz
oc.Dz = build_derivative_matrix(self.mesh,
1,
self.spatial_accuracy_order,
dimension='z')
oc.minus_Dz = copy.deepcopy(oc.Dz) #more storage, but less computations
oc.minus_Dz.data *= -1
# build other useful things
oc.I = spsp.eye(dof, dof)
oc.empty = spsp.csr_matrix((dof, dof))
# useful intermediates
oc.sigma_xz = make_diag_mtx(sx*sz)
oc.sigma_xPz = oc.sigmax + oc.sigmaz
oc.minus_sigma_zMx_Dx = make_diag_mtx((sz-sx))*oc.minus_Dx
oc.minus_sigma_xMz_Dz = make_diag_mtx((sx-sz))*oc.minus_Dz
oc._numpy_components_built = True
kappa = self.model_parameters.kappa
rho = self.model_parameters.rho
oc.m1 = make_diag_mtx((kappa**-1).reshape(-1,))
oc.m2 = make_diag_mtx((rho**-1).reshape(-1,))
oc.L = build_derivative_matrix_VDA(self.mesh,
2,
self.spatial_accuracy_order,
alpha = rho**-1
)
# oc.L is a heterogenous laplacian operator. It computes div(m2 grad), where m2 = 1/rho.
# Ian's implementation used the regular Dx operators in the PML even though the heterogeneous Laplacian with staggered derivative operators is used in the physical domain.
# I (Bram) did not change this or investigate if this causes some problems but am noting it here for completeness.
K = spsp.bmat([[oc.m1*oc.sigma_xz-oc.L, oc.minus_Dx*oc.m2, oc.minus_Dz*oc.m2 ],
[oc.minus_sigma_zMx_Dx, oc.sigmax, oc.empty ],
[oc.minus_sigma_xMz_Dz, oc.empty, oc.sigmaz ]])
C = spsp.bmat([[oc.m1*oc.sigma_xPz, oc.empty, oc.empty],
[oc.empty, oc.I, oc.empty],
[oc.empty, oc.empty, oc.I ]]) / self.dt
M = spsp.bmat([[ oc.m1, oc.empty, oc.empty],
[oc.empty, oc.empty, oc.empty],
[oc.empty, oc.empty, oc.empty]]) / self.dt**2
Stilde_inv = M+C
Stilde_inv.data = 1./Stilde_inv.data
self.A_k = Stilde_inv*(2*M - K + C)
self.A_km1 = -1*Stilde_inv*(M)
self.A_f = Stilde_inv
