Reference documentation for deal.II version GIT 8e09676776 2023-03-27 21:15:01+00:00
NonMatching Namespace Reference

internal

## Classes

class  FEImmersedSurfaceValues

class  MappingInfo

struct  RegionUpdateFlags

class  FEValues

class  FEInterfaceValues

class  MeshClassifier

class  FaceQuadratureGenerator< 1 >

## Enumerations

enum class  LocationToLevelSet { inside , outside , intersected , unassigned }

## Functions

template<int dim0, int dim1, int spacedim, typename number = double>
void create_coupling_sparsity_pattern (const DoFHandler< dim0, spacedim > &space_dh, const DoFHandler< dim1, spacedim > &immersed_dh, const Quadrature< dim1 > &quad, SparsityPatternBase &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, const AffineConstraints< number > &immersed_constraints=AffineConstraints< number >())

template<int dim0, int dim1, int spacedim, 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, SparsityPatternBase &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, const AffineConstraints< number > &immersed_constraints=AffineConstraints< number >())

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, const AffineConstraints< typename Matrix::value_type > &immersed_constraints=AffineConstraints< typename Matrix::value_type >())

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, const AffineConstraints< typename Matrix::value_type > &immersed_constraints=AffineConstraints< typename Matrix::value_type >())

template<int dim0, int dim1, int spacedim, typename Number = double>
void create_coupling_sparsity_pattern (const double &epsilon, const GridTools::Cache< dim0, spacedim > &cache0, const GridTools::Cache< dim1, spacedim > &cache1, const DoFHandler< dim0, spacedim > &dh0, const DoFHandler< dim1, spacedim > &dh1, const Quadrature< dim1 > &quad, SparsityPatternBase &sparsity, const AffineConstraints< Number > &constraints0=AffineConstraints< Number >(), const ComponentMask &comps0=ComponentMask(), const ComponentMask &comps1=ComponentMask())

template<int dim0, int dim1, int spacedim, typename Matrix >
void create_coupling_mass_matrix (Functions::CutOffFunctionBase< spacedim > &kernel, const double &epsilon, const GridTools::Cache< dim0, spacedim > &cache0, const GridTools::Cache< dim1, spacedim > &cache1, const DoFHandler< dim0, spacedim > &dh0, const DoFHandler< dim1, spacedim > &dh1, const Quadrature< dim0 > &quadrature0, const Quadrature< dim1 > &quadrature1, Matrix &matrix, const AffineConstraints< typename Matrix::value_type > &constraints0=AffineConstraints< typename Matrix::value_type >(), const ComponentMask &comps0=ComponentMask(), const ComponentMask &comps1=ComponentMask())

## Detailed Description

A namespace for functions offering tools to handle two meshes with no alignment requirements.

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

## ◆ LocationToLevelSet

 strong

Type describing how a cell or a face is located relative to the zero contour of a level set function, $$\psi$$. The values of the type correspond to:

inside if $$\psi(x) < 0$$, outside if $$\psi(x) > 0$$, intersected if $$\psi(x)$$ varies in sign,

over the cell/face. The value "unassigned" is used to describe that the location of a cell/face has not yet been determined.

Enumerator
inside
outside
intersected
unassigned

Definition at line 55 of file mesh_classifier.h.

## ◆ create_coupling_sparsity_pattern() [1/3]

template<int dim0, int dim1, int spacedim, 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, SparsityPatternBase & sparsity, const AffineConstraints< number > & constraints = AffineConstraints(), const ComponentMask & space_comps = ComponentMask(), const ComponentMask & immersed_comps = ComponentMask(), const Mapping< dim0, spacedim > & space_mapping = StaticMappingQ1::mapping, const Mapping< dim1, spacedim > & immersed_mapping = StaticMappingQ1::mapping, const AffineConstraints< number > & immersed_constraints = AffineConstraints() )

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.

Definition at line 173 of file coupling.cc.

## ◆ create_coupling_sparsity_pattern() [2/3]

template<int dim0, int dim1, int spacedim, 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, SparsityPatternBase & sparsity, const AffineConstraints< number > & constraints = AffineConstraints(), const ComponentMask & space_comps = ComponentMask(), const ComponentMask & immersed_comps = ComponentMask(), const Mapping< dim1, spacedim > & immersed_mapping = StaticMappingQ1::mapping, const AffineConstraints< number > & immersed_constraints = AffineConstraints() )

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.

Definition at line 203 of file coupling.cc.

## ◆ create_coupling_mass_matrix() [1/3]

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(), const ComponentMask & space_comps = ComponentMask(), const ComponentMask & immersed_comps = ComponentMask(), const Mapping< dim0, spacedim > & space_mapping = StaticMappingQ1::mapping, const Mapping< dim1, spacedim > & immersed_mapping = StaticMappingQ1::mapping, const AffineConstraints< typename Matrix::value_type > & immersed_constraints = AffineConstraints() )

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.

Definition at line 363 of file coupling.cc.

## ◆ create_coupling_mass_matrix() [2/3]

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(), const ComponentMask & space_comps = ComponentMask(), const ComponentMask & immersed_comps = ComponentMask(), const Mapping< dim1, spacedim > & immersed_mapping = StaticMappingQ1::mapping, const AffineConstraints< typename Matrix::value_type > & immersed_constraints = AffineConstraints() )

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.

Definition at line 393 of file coupling.cc.

## ◆ create_coupling_sparsity_pattern() [3/3]

template<int dim0, int dim1, int spacedim, typename Number = double>
 void NonMatching::create_coupling_sparsity_pattern ( const double & epsilon, const GridTools::Cache< dim0, spacedim > & cache0, const GridTools::Cache< dim1, spacedim > & cache1, const DoFHandler< dim0, spacedim > & dh0, const DoFHandler< dim1, spacedim > & dh1, const Quadrature< dim1 > & quad, SparsityPatternBase & sparsity, const AffineConstraints< Number > & constraints0 = AffineConstraints(), const ComponentMask & comps0 = ComponentMask(), const ComponentMask & comps1 = ComponentMask() )

Create a coupling sparsity pattern for non-matching independent grids, using a convolution kernel with compact support of radius epsilon.

Given two non-matching triangulations, representing the domains $$\Omega^0$$ and $$\Omega^1$$, both embedded in $$\mathbb{R}^d$$, and two finite element spaces $$V^0(\Omega^0) = \text{span}\{v_i\}_{i=0}^n$$ and $$V^1(\Omega^1) = \text{span}\{w_\alpha\}_{\alpha=0}^m$$, compute the sparsity pattern that would be necessary to assemble the matrix

$M_{i\alpha} \dealcoloneq \int_{\Omega^0} \int_{\Omega^1} v_i(x) K^{\epsilon}(x-y) w_\alpha(y) dx \ dy, \quad i \in [0,n), \alpha \in [0,m),$

where $$V^0(\Omega^0)$$ is the finite element space associated with the dh0 passed to this function (or part of it, if specified in comps0), while $$V^1(\Omega^1)$$ is the finite element space associated with the dh1 passed to this function (or part of it, if specified in comps1), and $$K^\epsilon$$ is a function derived from CutOffFunctionBase with compact support included in a ball of radius $$\epsilon$$.

The comps0 and comps1 masks are assumed to be ordered in the same way: the first component of comps0 will couple with the first component of comps1, the second with the second, and so on. If one of the two masks has more active components than the other, then the excess components will be ignored.

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 at least one of the triangulations is of type parallel::shared::Triangulation<dim1,spacedim>. An exception is thrown if both triagnulations are of type parallel::distributed::Triangulation<dim1,spacedim>.

This function assumes that the convolution has support contained in a box of radius epsilon. If epsilon is set to zero, then we assume that the kernel is the Dirac delta distribution, and the call is forwarded to the method in this namespace with the same name, that does not take an epsilon as input (but a quadrature formula quad is required). In this case, more restrictive conditions are required on the two spaces. See the documentation of the other create_coupling_sparsity_pattern() function.

Definition at line 622 of file coupling.cc.

## ◆ create_coupling_mass_matrix() [3/3]

template<int dim0, int dim1, int spacedim, typename Matrix >
 void NonMatching::create_coupling_mass_matrix ( Functions::CutOffFunctionBase< spacedim > & kernel, const double & epsilon, const GridTools::Cache< dim0, spacedim > & cache0, const GridTools::Cache< dim1, spacedim > & cache1, const DoFHandler< dim0, spacedim > & dh0, const DoFHandler< dim1, spacedim > & dh1, const Quadrature< dim0 > & quadrature0, const Quadrature< dim1 > & quadrature1, Matrix & matrix, const AffineConstraints< typename Matrix::value_type > & constraints0 = AffineConstraints(), const ComponentMask & comps0 = ComponentMask(), const ComponentMask & comps1 = ComponentMask() )

Create a coupling mass matrix for non-matching independent grids, using a convolution kernel with compact support.

Given two non-matching triangulations, representing the domains $$\Omega^0$$ and $$\Omega^1$$, both embedded in $$\mathbb{R}^d$$, and two finite element spaces $$V^0(\Omega^0) = \text{span}\{v_i\}_{i=0}^n$$ and $$V^1(\Omega^1) = \text{span}\{w_\alpha\}_{\alpha=0}^m$$, compute the matrix

$M_{i\alpha} \dealcoloneq \int_{\Omega^0} \int_{\Omega^1} v_i(x) K^{\epsilon}(x-y) w_\alpha(y) dx \ dy, \quad i \in [0,n), \alpha \in [0,m),$

where $$V^0(\Omega^0)$$ is the finite element space associated with the dh0 passed to this function (or part of it, if specified in comps0), while $$V^1(\Omega^1)$$ is the finite element space associated with the dh1 passed to this function (or part of it, if specified in comps1), and $$K^\epsilon$$ is a function derived from CutOffFunctionBase with compact support included in a ball of radius $$\epsilon$$.

The corresponding sparsity patterns can be computed by calling the make_coupling_sparsity_pattern() function.

The comps0 and comps1 masks are assumed to be ordered in the same way: the first component of comps0 will couple with the first component of comps1, the second with the second, and so on. If one of the two masks has more active components than the other, then the excess components will be ignored.

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 one of the two triangulations is of type parallel::shared::Triangulation<dim1,spacedim>. An exception is thrown if both triangulations are of type parallel::distributed::Triangulation<dim1,spacedim>.

The parameter epsilon is used to set the size of the cut-off function used to compute the convolution. If epsilon is set to zero, then we assume that the kernel is the Dirac delta distribution, and the call is forwarded to the method in this namespace with the same name, that does not take an epsilon as input.

Definition at line 760 of file coupling.cc.