Classes
class	ImmersedSurfaceQuadrature

Functions
template<int dim0, int dim1, int spacedim, typename Sparsity , typename number = double>
void	create_coupling_sparsity_pattern (const DoFHandler< dim0, spacedim > &space_dh, const DoFHandler< dim1, spacedim > &immersed_dh, const Quadrature< dim1 > &quad, Sparsity &sparsity, const AffineConstraints< number > &constraints=AffineConstraints< number >(), const ComponentMask &space_comps=ComponentMask(), const ComponentMask &immersed_comps=ComponentMask(), const Mapping< dim0, spacedim > &space_mapping=StaticMappingQ1< dim0, spacedim >::mapping, const Mapping< dim1, spacedim > &immersed_mapping=StaticMappingQ1< dim1, spacedim >::mapping)

template<int dim0, int dim1, int spacedim, typename Sparsity , typename number = double>
void	create_coupling_sparsity_pattern (const GridTools::Cache< dim0, spacedim > &cache, const DoFHandler< dim0, spacedim > &space_dh, const DoFHandler< dim1, spacedim > &immersed_dh, const Quadrature< dim1 > &quad, Sparsity &sparsity, const AffineConstraints< number > &constraints=AffineConstraints< number >(), const ComponentMask &space_comps=ComponentMask(), const ComponentMask &immersed_comps=ComponentMask(), const Mapping< dim1, spacedim > &immersed_mapping=StaticMappingQ1< dim1, spacedim >::mapping)

template<int dim0, int dim1, int spacedim, typename Matrix >
void	create_coupling_mass_matrix (const DoFHandler< dim0, spacedim > &space_dh, const DoFHandler< dim1, spacedim > &immersed_dh, const Quadrature< dim1 > &quad, Matrix &matrix, const AffineConstraints< typename Matrix::value_type > &constraints=AffineConstraints< typename Matrix::value_type >(), const ComponentMask &space_comps=ComponentMask(), const ComponentMask &immersed_comps=ComponentMask(), const Mapping< dim0, spacedim > &space_mapping=StaticMappingQ1< dim0, spacedim >::mapping, const Mapping< dim1, spacedim > &immersed_mapping=StaticMappingQ1< dim1, spacedim >::mapping)

template<int dim0, int dim1, int spacedim, typename Matrix >
void	create_coupling_mass_matrix (const GridTools::Cache< dim0, spacedim > &cache, const DoFHandler< dim0, spacedim > &space_dh, const DoFHandler< dim1, spacedim > &immersed_dh, const Quadrature< dim1 > &quad, Matrix &matrix, const AffineConstraints< typename Matrix::value_type > &constraints=AffineConstraints< typename Matrix::value_type >(), const ComponentMask &space_comps=ComponentMask(), const ComponentMask &immersed_comps=ComponentMask(), const Mapping< dim1, spacedim > &immersed_mapping=StaticMappingQ1< dim1, spacedim >::mapping)

Detailed Description

A namespace for functions offering tools to handle two meshes with no alignment requirements, but where one of the meshes is embedded inside the other in the real-space.

Typically these functions allow for computations on the real-space intersection between the two meshes e.g. surface integrals and construction of mass matrices.

Function Documentation

◆ create_coupling_sparsity_pattern() [1/2]

template<int dim0, int dim1, int spacedim, typename Sparsity , typename number = double>

void NonMatching::create_coupling_sparsity_pattern	(	const DoFHandler< dim0, spacedim > &	space_dh,
		const DoFHandler< dim1, spacedim > &	immersed_dh,
		const Quadrature< dim1 > &	quad,
		Sparsity &	sparsity,
		const AffineConstraints< number > &	constraints = `AffineConstraints<number>()`,
		const ComponentMask &	space_comps = `ComponentMask()`,
		const ComponentMask &	immersed_comps = `ComponentMask()`,
		const Mapping< dim0, spacedim > &	space_mapping = `StaticMappingQ1<dim0, spacedim>::mapping`,
		const Mapping< dim1, spacedim > &	immersed_mapping = `StaticMappingQ1<dim1, spacedim>::mapping`
	)

Create a coupling sparsity pattern for non-matching, overlapping grids.

Given two non-matching triangulations, representing the domains $\Omega$ and $B$ , with $B \subseteq \Omega$ , and two finite element spaces $V(\Omega) = \text{span}\{v_i\}_{i=0}^n$ and $Q(B) = \text{span}\{w_j\}_{j=0}^m$ , compute the sparsity pattern that would be necessary to assemble the matrix

$M_{ij} \dealcoloneq \int_{B} v_i(x) w_j(x) dx, \quad i \in [0,n), j \in [0,m),$

where $V(\Omega)$ is the finite element space associated with the space_dh passed to this function (or part of it, if specified in space_comps), while $Q(B)$ is the finite element space associated with the immersed_dh passed to this function (or part of it, if specified in immersed_comps).

The sparsity is filled by locating the position of quadrature points (obtained by the reference quadrature quad) defined on elements of $B$ with respect to the embedding triangulation $\Omega$ . For each overlapping cell, the entries corresponding to space_comps in space_dh and immersed_comps in immersed_dh are added to the sparsity pattern.

The space_comps and immersed_comps masks are assumed to be ordered in the same way: the first component of space_comps will couple with the first component of immersed_comps, the second with the second, and so on. If one of the two masks has more non-zero than the other, then the excess components will be ignored.

If the domain $B$ does not fall within $\Omega$ , an exception will be thrown by the algorithm that computes the quadrature point locations. In particular, notice that this function only makes sens for dim1 lower or equal than dim0. A static assert guards that this is actually the case.

For both spaces, it is possible to specify a custom Mapping, which defaults to StaticMappingQ1 for both.

This function will also work in parallel, provided that the immersed triangulation is of type parallel::shared::Triangulation<dim1,spacedim>. An exception is thrown if you use an immersed parallel::distributed::Triangulation<dim1,spacedim>.

See the tutorial program step-60 for an example on how to use this function.

Author: Luca Heltai, 2018

Definition at line 135 of file coupling.cc.

◆ create_coupling_sparsity_pattern() [2/2]

template<int dim0, int dim1, int spacedim, typename Sparsity , typename number = double>

void NonMatching::create_coupling_sparsity_pattern	(	const GridTools::Cache< dim0, spacedim > &	cache,
		const DoFHandler< dim0, spacedim > &	space_dh,
		const DoFHandler< dim1, spacedim > &	immersed_dh,
		const Quadrature< dim1 > &	quad,
		Sparsity &	sparsity,
		const AffineConstraints< number > &	constraints = `AffineConstraints<number>()`,
		const ComponentMask &	space_comps = `ComponentMask()`,
		const ComponentMask &	immersed_comps = `ComponentMask()`,
		const Mapping< dim1, spacedim > &	immersed_mapping = `StaticMappingQ1<dim1, spacedim>::mapping`
	)

Same as above, but takes an additional GridTools::Cache object, instead of creating one internally. In this version of the function, the parameter space_mapping cannot be specified, since it is taken from the cache parameter.

Author: Luca Heltai, 2018

Definition at line 167 of file coupling.cc.

◆ create_coupling_mass_matrix() [1/2]

template<int dim0, int dim1, int spacedim, typename Matrix >

void NonMatching::create_coupling_mass_matrix	(	const DoFHandler< dim0, spacedim > &	space_dh,
		const DoFHandler< dim1, spacedim > &	immersed_dh,
		const Quadrature< dim1 > &	quad,
		Matrix &	matrix,
		const AffineConstraints< typename Matrix::value_type > &	constraints = `AffineConstraints<typename Matrix::value_type>()`,
		const ComponentMask &	space_comps = `ComponentMask()`,
		const ComponentMask &	immersed_comps = `ComponentMask()`,
		const Mapping< dim0, spacedim > &	space_mapping = `StaticMappingQ1<dim0, spacedim>::mapping`,
		const Mapping< dim1, spacedim > &	immersed_mapping = `StaticMappingQ1<dim1, spacedim>::mapping`
	)

Create a coupling mass matrix for non-matching, overlapping grids.

Given two non-matching triangulations, representing the domains $\Omega$ and $B$ , with $B \subseteq \Omega$ , and two finite element spaces $V(\Omega) = \text{span}\{v_i\}_{i=0}^n$ and $Q(B) = \text{span}\{w_j\}_{j=0}^m$ , compute the coupling matrix

$M_{ij} \dealcoloneq \int_{B} v_i(x) w_j(x) dx, \quad i \in [0,n), j \in [0,m),$

where $V(\Omega)$ is the finite element space associated with the space_dh passed to this function (or part of it, if specified in space_comps), while $Q(B)$ is the finite element space associated with the immersed_dh passed to this function (or part of it, if specified in immersed_comps).

The corresponding sparsity patterns can be computed by calling the make_coupling_sparsity_pattern function. The elements of the matrix are computed by locating the position of quadrature points defined on elements of $B$ with respect to the embedding triangulation $\Omega$ .

The space_comps and immersed_comps masks are assumed to be ordered in the same way: the first component of space_comps will couple with the first component of immersed_comps, the second with the second, and so on. If one of the two masks has more non-zero entries non-zero than the other, then the excess components will be ignored.

If the domain $B$ does not fall within $\Omega$ , an exception will be thrown by the algorithm that computes the quadrature point locations. In particular, notice that this function only makes sense for dim1 lower or equal than dim0. A static assert guards that this is actually the case.

For both spaces, it is possible to specify a custom Mapping, which defaults to StaticMappingQ1 for both.

This function will also work in parallel, provided that the immersed triangulation is of type parallel::shared::Triangulation<dim1,spacedim>. An exception is thrown if you use an immersed parallel::distributed::Triangulation<dim1,spacedim>.

See the tutorial program step-60 for an example on how to use this function.

Author: Luca Heltai, 2018

Definition at line 322 of file coupling.cc.

◆ create_coupling_mass_matrix() [2/2]

template<int dim0, int dim1, int spacedim, typename Matrix >

void NonMatching::create_coupling_mass_matrix	(	const GridTools::Cache< dim0, spacedim > &	cache,
		const DoFHandler< dim0, spacedim > &	space_dh,
		const DoFHandler< dim1, spacedim > &	immersed_dh,
		const Quadrature< dim1 > &	quad,
		Matrix &	matrix,
		const AffineConstraints< typename Matrix::value_type > &	constraints = `AffineConstraints<typename Matrix::value_type>()`,
		const ComponentMask &	space_comps = `ComponentMask()`,
		const ComponentMask &	immersed_comps = `ComponentMask()`,
		const Mapping< dim1, spacedim > &	immersed_mapping = `StaticMappingQ1<dim1, spacedim>::mapping`
	)

Same as above, but takes an additional GridTools::Cache object, instead of creating one internally. In this version of the function, the parameter space_mapping cannot specified, since it is taken from the cache parameter.

Author: Luca Heltai, 2018

Definition at line 350 of file coupling.cc.