LocalIntegrators::L2 Namespace Reference

Local integrators related to L²-inner products. More...

Functions
template<int dim>
void	mass_matrix (FullMatrix< double > &M, const FEValuesBase< dim > &fe, const double factor=1.)
template<int dim>
void	weighted_mass_matrix (FullMatrix< double > &M, const FEValuesBase< dim > &fe, const std::vector< double > &weights)
template<int dim, typename number >
void	L2 (Vector< number > &result, const FEValuesBase< dim > &fe, const std::vector< double > &input, const double factor=1.)
template<int dim, typename number >
void	L2 (Vector< number > &result, const FEValuesBase< dim > &fe, const ArrayView< const std::vector< double >> &input, const double factor=1.)
template<int dim>
void	jump_matrix (FullMatrix< double > &M11, FullMatrix< double > &M12, FullMatrix< double > &M21, FullMatrix< double > &M22, const FEValuesBase< dim > &fe1, const FEValuesBase< dim > &fe2, const double factor1=1., const double factor2=1.)

Detailed Description

Local integrators related to L²-inner products.

Author

Guido Kanschat

Date

2010

Function Documentation

mass_matrix()

template<int dim>

void LocalIntegrators::L2::mass_matrix	(	FullMatrix< double > &	M,
		const FEValuesBase< dim > &	fe,
		const double	factor = 1.
	)

The mass matrix for scalar or vector values finite elements.

\[ \int_Z uv\,dx \quad \text{or} \quad \int_Z \mathbf u\cdot \mathbf v\,dx \]

Likewise, this term can be used on faces, where it computes the integrals

\[ \int_F uv\,ds \quad \text{or} \quad \int_F \mathbf u\cdot \mathbf v\,ds \]

Parameters

M	The mass matrix obtained as result.
fe	The FEValues object describing the local trial function space. update_values and update_JxW_values must be set.
factor	A constant that multiplies the mass matrix.

Author

Guido Kanschat

Date

2008, 2009, 2010

Definition at line 63 of file l2.h.

weighted_mass_matrix()

template<int dim>

void LocalIntegrators::L2::weighted_mass_matrix	(	FullMatrix< double > &	M,
		const FEValuesBase< dim > &	fe,
		const std::vector< double > &	weights
	)

The weighted mass matrix for scalar or vector values finite elements.

\[ \int_Z \omega(x) uv\,dx \quad \text{or} \quad \int_Z \omega(x) \mathbf u\cdot \mathbf v\,dx \]

Likewise, this term can be used on faces, where it computes the integrals

\[ \int_F \omega(x) uv\,ds \quad \text{or} \quad \int_F \omega(x) \mathbf u\cdot \mathbf v\,ds \]

Parameters

M	The weighted mass matrix obtained as result.
fe	The FEValues object describing the local trial function space. update_values and update_JxW_values must be set.
weights	The weights, \(\omega(x)\), evaluated at the quadrature points in the finite element (size must be equal to the number of quadrature points in the element).

Author

Guido Kanschat

Date

2014

Definition at line 117 of file l2.h.

L2() [1/2]

template<int dim, typename number >

void LocalIntegrators::L2::L2	(	Vector< number > &	result,
		const FEValuesBase< dim > &	fe,
		const std::vector< double > &	input,
		const double	factor = 1.
	)

L²-inner product for scalar functions.

\[ \int_Z fv\,dx \quad \text{or} \quad \int_F fv\,ds \]

Parameters

result	The vector obtained as result.
fe	The FEValues object describing the local trial function space. update_values and update_JxW_values must be set.
input	The representation of \(f\) evaluated at the quadrature points in the finite element (size must be equal to the number of quadrature points in the element).
factor	A constant that multiplies the result.

Author

Guido Kanschat

Date

2008, 2009, 2010

Definition at line 171 of file l2.h.

L2() [2/2]

template<int dim, typename number >

void LocalIntegrators::L2::L2	(	Vector< number > &	result,
		const FEValuesBase< dim > &	fe,
		const ArrayView< const std::vector< double >> &	input,
		const double	factor = 1.
	)

L²-inner product for a slice of a vector valued right hand side.

\[ \int_Z \mathbf f\cdot \mathbf v\,dx \quad \text{or} \quad \int_F \mathbf f\cdot \mathbf v\,ds \]

Parameters

result	The vector obtained as result.
fe	The FEValues object describing the local trial function space. update_values and update_JxW_values must be set.
input	The vector valued representation of \(\mathbf f\) evaluated at the quadrature points in the finite element (size of each component must be equal to the number of quadrature points in the element).
factor	A constant that multiplies the result.

Author

Guido Kanschat

Date

2008, 2009, 2010

Definition at line 204 of file l2.h.

jump_matrix()

template<int dim>

void LocalIntegrators::L2::jump_matrix	(	FullMatrix< double > &	M11,
		FullMatrix< double > &	M12,
		FullMatrix< double > &	M21,
		FullMatrix< double > &	M22,
		const FEValuesBase< dim > &	fe1,
		const FEValuesBase< dim > &	fe2,
		const double	factor1 = 1.,
		const double	factor2 = 1.
	)

The jump matrix between two cells for scalar or vector values finite elements. Note that the factor \(\gamma\) can be used to implement weighted jumps.

\[ \int_F [\gamma u][\gamma v]\,ds \quad \text{or} \int_F [\gamma \mathbf u]\cdot [\gamma \mathbf v]\,ds \]

Using appropriate weights, this term can be used to penalize violation of conformity in H¹.

Note that for the parameters that follow, the external matrix refers to the flux between cells, while the internal matrix refers to entries coupling inside the cell.

Parameters

M11	The internal matrix for the first cell obtained as result.
M12	The external matrix for the first cell obtained as result.
M21	The external matrix for the second cell obtained as result.
M22	The internal matrix for the second cell obtained as result.
fe1	The FEValues object describing the local trial function space for the first cell. update_values and update_JxW_values must be set.
fe2	The FEValues object describing the local trial function space for the second cell. update_values and update_JxW_values must be set.
factor1	A constant that multiplies the shape functions for the first cell.
factor2	A constant that multiplies the shape functions for the second cell.

Author

Guido Kanschat

Date

2008, 2009, 2010

Definition at line 255 of file l2.h.