feec.multipatch.non_matching_operators#

This module provides utilities for constructing the conforming projections for a H1-Hcurl-L2 broken FEEC de Rham sequence.

Functions#

`calculate_mass_matrix`(space_1d)	Calculate the mass-matrix of a 1d spline-space.
`calculate_mixed_mass_matrix`(domain_space, ...)	Calculate the mixed mass-matrix of two 1d spline-spaces on the same domain.
`calculate_poly_basis_integral`(space_1d[, ...])	Calculate the "mixed mass-matrix" of a 1d spline-space with polynomials.
`construct_extension_operator_1D`(domain, codomain)	Compute the matrix of the extension operator on the interface.
`construct_h1_conforming_projection`(Vh[, ...])	Construct the conforming projection for a scalar space for a given regularity (0 continuous, -1 discontinuous).
`construct_hcurl_conforming_projection`(Vh[, ...])	Construct the conforming projection for a vector Hcurl space for a given regularity (0 continuous, -1 discontinuous).
`construct_restriction_operator_1D`(...[, ...])	Compute the matrix of the (moment preserving) restriction operator on the interface.
`get_1d_moment_correction`(space_1d[, p_moments])	Calculate the coefficients for the one-dimensional moment correction.
`get_corners`(domain, boundary_only)	Given the domain, extract the vertices on their respective domains with local coordinates.
`get_extension_restriction`(coarse_space_1d, ...)	Calculate the extension and restriction matrices for refining along an interface.
`get_patch_index_from_face`(domain, face)	Return the patch index of subdomain/boundary
`knots_to_insert`(coarse_grid, fine_grid[, tol])	knot insertion for refinement of a 1d spline space.

Classes#

Inheritance diagram of psydac.feec.multipatch.non_matching_operators

Local2GlobalIndexMap(ndim, n_patches, ...)

Details#

This module provides utilities for constructing the conforming projections for a H1-Hcurl-L2 broken FEEC de Rham sequence.

get_patch_index_from_face(domain, face)[source]#

Return the patch index of subdomain/boundary

Parameters:

domain<Sympde.topology.Domain>: The Symbolic domain
face<Sympde.topology.BasicDomain>: A patch or a boundary of a patch

Returns:

i<int>: The index of a subdomain/boundary in the multipatch domain

class Local2GlobalIndexMap(ndim, n_patches, n_components)[source]#

Bases: object

set_patch_shapes(patch_index, *shapes)[source]#

get_index(k, d, cartesian_index)[source]#

Return a global scalar index.

Parameters:

kint: The patch index.
dint: The component of a scalar field in the system of equations.
cartesian_index: tuple[int]: Multi index [i1, i2, i3 …]

Returns:

Iint: The global scalar index.

knots_to_insert(coarse_grid, fine_grid, tol=1e-14)[source]#: knot insertion for refinement of a 1d spline space.

get_corners(domain, boundary_only)[source]#

Given the domain, extract the vertices on their respective domains with local coordinates.

Parameters:

domain: <Geometry>: The discrete domain of the projector
boundary_only<bool>: Only return vertices that lie on a boundary

construct_extension_operator_1D(domain, codomain)[source]#

Compute the matrix of the extension operator on the interface.

Parameters:

domain1d spline space on the interface (coarse grid)
codomain1d spline space on the interface (fine grid)

construct_restriction_operator_1D(coarse_space_1d, fine_space_1d, E, p_moments=-1)[source]#

Compute the matrix of the (moment preserving) restriction operator on the interface.

Parameters:

coarse_space_1d1d spline space on the interface (coarse grid)
fine_space_1d1d spline space on the interface (fine grid)
EExtension matrix
p_momentsAmount of moments to be preserved

get_extension_restriction(coarse_space_1d, fine_space_1d, p_moments=-1)[source]#

Calculate the extension and restriction matrices for refining along an interface.

Parameters:

coarse_space_1dSplineSpace: Spline space of the coarse space.
fine_space_1dSplineSpace: Spline space of the fine space.
p_moments{int}: Amount of moments to be preserved.

Returns:

E_1Dnumpy array: Extension matrix.
R_1Dnumpy array: Restriction matrix.
ER_1Dnumpy array: Extension-restriction matrix.

calculate_mass_matrix(space_1d)[source]#

Calculate the mass-matrix of a 1d spline-space.

Parameters:

space_1dSplineSpace: Spline space of the fine space.

Returns:

Mass_matnumpy array: Mass matrix.

calculate_mixed_mass_matrix(domain_space, codomain_space)[source]#

Calculate the mixed mass-matrix of two 1d spline-spaces on the same domain.

Parameters:

domain_spaceSplineSpace: Spline space of the domain space.
codomain_spaceSplineSpace: Spline space of the codomain space.

Returns:

Mass_matnumpy array: Mass matrix.

calculate_poly_basis_integral(space_1d, p_moments=-1)[source]#

Calculate the “mixed mass-matrix” of a 1d spline-space with polynomials.

Parameters:

space_1dSplineSpace: Spline space of the fine space.
p_momentsInt: Amount of moments to be preserved.

Returns:

Mass_matnumpy array: Mass matrix.

get_1d_moment_correction(space_1d, p_moments=-1)[source]#

Calculate the coefficients for the one-dimensional moment correction.

Parameters:

patch_spaceSplineSpace: 1d spline space.
p_momentsint: Number of moments to be preserved.

Returns:

gammaarray: Moment correction coefficients without the conformity factor.

construct_h1_conforming_projection(Vh, reg_orders=0, p_moments=-1, hom_bc=False)[source]#

Construct the conforming projection for a scalar space for a given regularity (0 continuous, -1 discontinuous).

Parameters:

VhTensorFemSpace: Finite Element Space coming from the discrete de Rham sequence.
reg_orders(int): Regularity in each space direction -1 or 0.
p_moments(int): Number of moments to be preserved.
hom_bc(bool): Homogeneous boundary conditions.

Returns:

cPscipy.sparse.csr_array: Conforming projection as a sparse matrix.

construct_hcurl_conforming_projection(Vh, reg_orders=0, p_moments=-1, hom_bc=False)[source]#

Construct the conforming projection for a vector Hcurl space for a given regularity (0 continuous, -1 discontinuous).

Parameters:

VhTensorFemSpace: Finite Element Space coming from the discrete de Rham sequence.
reg_orders(int): Regularity in each space direction -1 or 0.
p_moments(int): Number of polynomial moments to be preserved.
hom_bc(bool): Tangential homogeneous boundary conditions.

Returns:

cPscipy.sparse.csr_array: Conforming projection as a sparse matrix.