AppShop::Matrix::Cell Namespace Reference

Integration of cell matrices. More...

Functions
template<int dim>
void	mass (FullMatrix< double > &M, const FEValuesBase< dim > &fe, const double a=1.)
	The mass matrix.
template<int dim>
void	mass (FullMatrix< double > &M, const FEValuesBase< dim > &fe, const FEValuesBase< dim > &fetest, const unsigned int component, const double a=1.)
	The mass matrix between different elements.
template<int dim>
void	mass_scaled (FullMatrix< double > &M, const FEValuesBase< dim > &fe, const std::vector< double > &a, bool divide)
	Mass matrix with varying coefficient.
template<int dim>
void	mass_scaled (FullMatrix< double > &M, const FEValuesBase< dim > &fe, const FEValuesBase< dim > &fetest, const unsigned int select, const std::vector< double > &factor, bool divide=false)
	Mass matrix with varying coefficient for different elements.
template<int dim>
void	advection (FullMatrix< double > &M, const FEValuesBase< dim > &fe, const std::vector< Point< dim > > &velocity)
	Linear advection in divergence form.
template<int dim>
void	advection (FullMatrix< double > &M, const FEValuesBase< dim > &fe, const VectorSlice< const std::vector< std::vector< double > > > &velocity, double factor=1.)
	Linear advection in divergence form.
template<int dim>
void	div_primal (std::vector< MatrixBlock< FullMatrix< double > > > &M, const std::vector< unsigned int > &indices, const FEValuesBase< dim > &fe, const FEValuesBase< dim > &fetest, double factor=1.)
	Cell matrix for divergence.
template<int dim>
void	div (std::vector< MatrixBlock< FullMatrix< double > > > &M, const std::vector< unsigned int > &indices, const FEValuesBase< dim > &fe, const FEValuesBase< dim > &fetest, double factor=1.)
	Cell matrix for divergence.
template<int dim>
void	div_scaled (FullMatrix< double > &M, const FEValuesBase< dim > &fe, const FEValuesBase< dim > &fetest, const std::vector< double > &factor)
	Same as div_cell(), but with a possibly varying coefficient.
template<int dim>
void	di (FullMatrix< double > &M, const FEValuesBase< dim > &fe, const FEValuesBase< dim > &fetest, unsigned int i)
	Directional derivative in direction i.
template<int dim>
void	di_scaled (FullMatrix< double > &M, const FEValuesBase< dim > &fe, const FEValuesBase< dim > &fetest, unsigned int d, std::vector< double > &factor)
	Same as di_cell(), but with varying coefficient.
template<int dim>
void	eps_div (FullMatrix< double > &M, const FEValuesBase< dim > &fe, const FEValuesBase< dim > &fetest)
	Discretization for the transpose of the symmetric gradient.
template<int dim>
void	laplacian (FullMatrix< double > &M, const FEValuesBase< dim > &fe, double nu=1.)
	Laplacian in weak form.
template<int dim>
void	laplacian (FullMatrix< double > &M, const FEValuesBase< dim > &fe, Tensor< 2, dim > nu)
	Laplacian in weak form with a Tensor coefficient to allow anisotropic media \[ (K \nabla u, \nabla v) \] .
template<int dim>
void	laplacian_scaled (FullMatrix< double > &M, const FEValuesBase< dim > &fe, const std::vector< double > &nu, bool divide=false)
	Laplacian with varying coefficient.
template<int dim>
void	laplacian_scaled (FullMatrix< double > &M, const FEValuesBase< dim > &fe, const double nu, bool divide=false)
	Laplacian with constant coefficient.
template<int dim>
void	div_div (FullMatrix< double > &M, const FEValuesBase< dim > &fe, const double factor=1.)
	Second order divergence form for vector valued elements.

Detailed Description

Integration of cell matrices.

Function Documentation

template<int dim>

void AppShop::Matrix::Cell::advection	(	FullMatrix< double > &	M,
		const FEValuesBase< dim > &	fe,
		const std::vector< Point< dim > > &	velocity
	)

Linear advection in divergence form.

The derivative is on the test function.

\[ -(u \mathbf w, \nabla v) \]

template<int dim>

void AppShop::Matrix::Cell::advection	(	FullMatrix< double > &	M,
		const FEValuesBase< dim > &	fe,
		const VectorSlice< const std::vector< std::vector< double > > > &	velocity,
		double	factor = 1.
	)

Linear advection in divergence form.

The derivative is on the test function.

\[ -(u \mathbf w, \nabla v) \]

template<int dim>

void AppShop::Matrix::Cell::di	(	FullMatrix< double > &	M,
		const FEValuesBase< dim > &	fe,
		const FEValuesBase< dim > &	fetest,
		unsigned int	i
	)

Directional derivative in direction i.

\[ -(u, \partial_i v) \]

template<int dim>

void AppShop::Matrix::Cell::di_scaled	(	FullMatrix< double > &	M,
		const FEValuesBase< dim > &	fe,
		const FEValuesBase< dim > &	fetest,
		unsigned int	d,
		std::vector< double > &	factor
	)

Same as di_cell(), but with varying coefficient.

\[ -(\alpha u, \partial_i v) \]

template<int dim>

void AppShop::Matrix::Cell::div	(	std::vector< MatrixBlock< FullMatrix< double > > > &	M,
		const std::vector< unsigned int > &	indices,
		const FEValuesBase< dim > &	fe,
		const FEValuesBase< dim > &	fetest,
		double	factor = 1.
	)

Cell matrix for divergence.

The derivative is on the test function.

\[ -(u , \nabla v) \]

• M Result matrix vector

• indices: the indices in the vector where we find the matrices.

• fe: finite element space for trial functions.

• fetest: finite element space for trial functions.

template<int dim>

void AppShop::Matrix::Cell::div_div	(	FullMatrix< double > &	M,
		const FEValuesBase< dim > &	fe,
		const double	factor = 1.
	)

Second order divergence form for vector valued elements.

\[ (\nabla \cdot u, \nabla \cdot v) \]

template<int dim>

void AppShop::Matrix::Cell::div_primal	(	std::vector< MatrixBlock< FullMatrix< double > > > &	M,
		const std::vector< unsigned int > &	indices,
		const FEValuesBase< dim > &	fe,
		const FEValuesBase< dim > &	fetest,
		double	factor = 1.
	)

Cell matrix for divergence.

The derivative is on the trial function.

\[ (\nabla \cdot u , v) \]

• M Result matrix vector

• indices: the indices in the vector where we find the matrices.

• fe: finite element space for trial functions.

• fetest: finite element space for trial functions.

template<int dim>

void AppShop::Matrix::Cell::div_scaled	(	FullMatrix< double > &	M,
		const FEValuesBase< dim > &	fe,
		const FEValuesBase< dim > &	fetest,
		const std::vector< double > &	factor
	)

Same as div_cell(), but with a possibly varying coefficient.

\[ -( \alpha u, \nabla v) \]

template<int dim>

void AppShop::Matrix::Cell::eps_div	(	FullMatrix< double > &	M,
		const FEValuesBase< dim > &	fe,
		const FEValuesBase< dim > &	fetest
	)

Discretization for the transpose of the symmetric gradient.

\[ -(u, \varepsilon(v)) \]

template<int dim>

void AppShop::Matrix::Cell::laplacian	(	FullMatrix< double > &	M,
		const FEValuesBase< dim > &	fe,
		double	nu = 1.
	)

Laplacian in weak form.

\[ (\nu \nabla u, \nabla v) \]

template<int dim>

void AppShop::Matrix::Cell::laplacian	(	FullMatrix< double > &	M,
		const FEValuesBase< dim > &	fe,
		Tensor< 2, dim >	nu
	)

Laplacian in weak form with a Tensor coefficient to allow anisotropic media

\[ (K \nabla u, \nabla v) \]

.

template<int dim>

void AppShop::Matrix::Cell::laplacian_scaled	(	FullMatrix< double > &	M,
		const FEValuesBase< dim > &	fe,
		const std::vector< double > &	nu,
		bool	divide = false
	)

Laplacian with varying coefficient.

If divide is true, divide gradient u times gradient v by factor.

\[ (\nu \nabla u, \nabla v) \]

template<int dim>

void AppShop::Matrix::Cell::laplacian_scaled	(	FullMatrix< double > &	M,
		const FEValuesBase< dim > &	fe,
		const double	nu,
		bool	divide = false
	)

Laplacian with constant coefficient.

If divide is true, divide gradient u times gradient v by factor.

\[ (\nu \nabla u, \nabla v) \]

template<int dim>

void AppShop::Matrix::Cell::mass	(	FullMatrix< double > &	M,
		const FEValuesBase< dim > &	fe,
		const double	a = 1.
	)

The mass matrix.

\[ (a u,v) \]

template<int dim>

void AppShop::Matrix::Cell::mass	(	FullMatrix< double > &	M,
		const FEValuesBase< dim > &	fe,
		const FEValuesBase< dim > &	fetest,
		const unsigned int	component,
		const double	a = 1.
	)

The mass matrix between different elements.

\[ (a u,v) \]

If component has a nonnegative value and the element is vector-valued, then only the component corresponding to this number is assembled.

template<int dim>

void AppShop::Matrix::Cell::mass_scaled	(	FullMatrix< double > &	M,
		const FEValuesBase< dim > &	fe,
		const std::vector< double > &	a,
		bool	divide
	)

Mass matrix with varying coefficient.

\[ (a u,v) \]

If divide is true, then divide by a instead of multiplying.

template<int dim>

void AppShop::Matrix::Cell::mass_scaled	(	FullMatrix< double > &	M,
		const FEValuesBase< dim > &	fe,
		const FEValuesBase< dim > &	fetest,
		const unsigned int	select,
		const std::vector< double > &	factor,
		bool	divide = false
	)

Mass matrix with varying coefficient for different elements.

\[ (a u,v) \]

If divide is true, then divide by a instead of multiplying.