Local integrators related to the divergence operator and its trace. More...

Functions
template<int dim>
void	cell_matrix (FullMatrix< double > &M, const FEValuesBase< dim > &fe, const FEValuesBase< dim > &fetest, double factor=1.)

template<int dim, typename number >
void	cell_residual (Vector< number > &result, const FEValuesBase< dim > &fetest, const ArrayView< const std::vector< Tensor< 1, dim >>> &input, const double factor=1.)

template<int dim, typename number >
void	cell_residual (Vector< number > &result, const FEValuesBase< dim > &fetest, const ArrayView< const std::vector< double >> &input, const double factor=1.)

template<int dim>
void	gradient_matrix (FullMatrix< double > &M, const FEValuesBase< dim > &fe, const FEValuesBase< dim > &fetest, double factor=1.)

template<int dim, typename number >
void	gradient_residual (Vector< number > &result, const FEValuesBase< dim > &fetest, const std::vector< Tensor< 1, dim >> &input, const double factor=1.)

template<int dim, typename number >
void	gradient_residual (Vector< number > &result, const FEValuesBase< dim > &fetest, const std::vector< double > &input, const double factor=1.)

template<int dim>
void	u_dot_n_matrix (FullMatrix< double > &M, const FEValuesBase< dim > &fe, const FEValuesBase< dim > &fetest, double factor=1.)

template<int dim, typename number >
void	u_dot_n_residual (Vector< number > &result, const FEValuesBase< dim > &fe, const FEValuesBase< dim > &fetest, const ArrayView< const std::vector< double >> &data, double factor=1.)

template<int dim, typename number >
void	u_times_n_residual (Vector< number > &result, const FEValuesBase< dim > &fetest, const std::vector< double > &data, double factor=1.)

template<int dim>
void	u_dot_n_matrix (FullMatrix< double > &M11, FullMatrix< double > &M12, FullMatrix< double > &M21, FullMatrix< double > &M22, const FEValuesBase< dim > &fe1, const FEValuesBase< dim > &fe2, const FEValuesBase< dim > &fetest1, const FEValuesBase< dim > &fetest2, double factor=1.)

template<int dim>
void	grad_div_matrix (FullMatrix< double > &M, const FEValuesBase< dim > &fe, const double factor=1.)

template<int dim, typename number >
void	grad_div_residual (Vector< number > &result, const FEValuesBase< dim > &fetest, const ArrayView< const std::vector< Tensor< 1, dim >>> &input, const double factor=1.)

template<int dim>
void	u_dot_n_jump_matrix (FullMatrix< double > &M11, FullMatrix< double > &M12, FullMatrix< double > &M21, FullMatrix< double > &M22, const FEValuesBase< dim > &fe1, const FEValuesBase< dim > &fe2, double factor=1.)

template<int dim>
double	norm (const FEValuesBase< dim > &fe, const ArrayView< const std::vector< Tensor< 1, dim >>> &Du)

Detailed Description

Local integrators related to the divergence operator and its trace.

Author: Guido Kanschat

Date: 2010

Function Documentation

◆ cell_matrix()

template<int dim>

void LocalIntegrators::Divergence::cell_matrix	(	FullMatrix< double > &	M,
		const FEValuesBase< dim > &	fe,
		const FEValuesBase< dim > &	fetest,
		double	factor = `1.`
	)

Cell matrix for divergence. The derivative is on the trial function.

\[ \int_Z v\nabla \cdot \mathbf u \,dx \]

This is the strong divergence operator and the trial space should be at least H^div. The test functions may be discontinuous.

Author: Guido Kanschat

Date: 2011

Definition at line 59 of file divergence.h.

◆ cell_residual() [1/2]

template<int dim, typename number >

void LocalIntegrators::Divergence::cell_residual	(	Vector< number > &	result,
		const FEValuesBase< dim > &	fetest,
		const ArrayView< const std::vector< Tensor< 1, dim >>> &	input,
		const double	factor = `1.`
	)

The residual of the divergence operator in strong form.

\[ \int_Z v\nabla \cdot \mathbf u \,dx \]

This is the strong divergence operator and the trial space should be at least H^div. The test functions may be discontinuous.

The function cell_matrix() is the Frechet derivative of this function with respect to the test functions.

Author: Guido Kanschat

Date: 2011

Definition at line 101 of file divergence.h.

◆ cell_residual() [2/2]

template<int dim, typename number >

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

The residual of the divergence operator in weak form.

\[ - \int_Z \nabla v \cdot \mathbf u \,dx \]

This is the weak divergence operator and the test space should be at least H¹. The trial functions may be discontinuous.

Todo:: Verify: The function cell_matrix() is the Frechet derivative of this function with respect to the test functions.

Author: Guido Kanschat

Date: 2013

Definition at line 137 of file divergence.h.

◆ gradient_matrix()

template<int dim>

void LocalIntegrators::Divergence::gradient_matrix	(	FullMatrix< double > &	M,
		const FEValuesBase< dim > &	fe,
		const FEValuesBase< dim > &	fetest,
		double	factor = `1.`
	)

Cell matrix for gradient. The derivative is on the trial function.

\[ \int_Z \nabla u \cdot \mathbf v\,dx \]

This is the strong gradient and the trial space should be at least in H¹. The test functions can be discontinuous.

Author: Guido Kanschat

Date: 2011

Definition at line 171 of file divergence.h.

◆ gradient_residual() [1/2]

template<int dim, typename number >

void LocalIntegrators::Divergence::gradient_residual	(	Vector< number > &	result,
		const FEValuesBase< dim > &	fetest,
		const std::vector< Tensor< 1, dim >> &	input,
		const double	factor = `1.`
	)

The residual of the gradient operator in strong form.

\[ \int_Z \mathbf v\cdot\nabla u \,dx \]

This is the strong gradient operator and the trial space should be at least H¹. The test functions may be discontinuous.

The function gradient_matrix() is the Frechet derivative of this function with respect to the test functions.

Author: Guido Kanschat

Date: 2011

Definition at line 214 of file divergence.h.

◆ gradient_residual() [2/2]

template<int dim, typename number >

void LocalIntegrators::Divergence::gradient_residual	(	Vector< number > &	result,
		const FEValuesBase< dim > &	fetest,
		const std::vector< double > &	input,
		const double	factor = `1.`
	)

The residual of the gradient operator in weak form.

\[ -\int_Z \nabla\cdot \mathbf v u \,dx \]

This is the weak gradient operator and the test space should be at least H^div. The trial functions may be discontinuous.

Todo:: Verify: The function gradient_matrix() is the Frechet derivative of this function with respect to the test functions.

Author: Guido Kanschat

Date: 2013

Definition at line 250 of file divergence.h.

◆ u_dot_n_matrix() [1/2]

template<int dim>

void LocalIntegrators::Divergence::u_dot_n_matrix	(	FullMatrix< double > &	M,
		const FEValuesBase< dim > &	fe,
		const FEValuesBase< dim > &	fetest,
		double	factor = `1.`
	)

The trace of the divergence operator, namely the product of the normal component of the vector valued trial space and the test space.

\[ \int_F (\mathbf u\cdot \mathbf n) v \,ds \]

Author: Guido Kanschat

Date: 2011

Definition at line 282 of file divergence.h.

◆ u_dot_n_residual()

template<int dim, typename number >

void LocalIntegrators::Divergence::u_dot_n_residual	(	Vector< number > &	result,
		const FEValuesBase< dim > &	fe,
		const FEValuesBase< dim > &	fetest,
		const ArrayView< const std::vector< double >> &	data,
		double	factor = `1.`
	)

The trace of the divergence operator, namely the product of the normal component of the vector valued trial space and the test space.

\[ \int_F (\mathbf u\cdot \mathbf n) v \,ds \]

Author: Guido Kanschat

Date: 2011

Definition at line 318 of file divergence.h.

◆ u_times_n_residual()

template<int dim, typename number >

void LocalIntegrators::Divergence::u_times_n_residual	(	Vector< number > &	result,
		const FEValuesBase< dim > &	fetest,
		const std::vector< double > &	data,
		double	factor = `1.`
	)

The trace of the gradient operator, namely the product of the normal component of the vector valued test space and the trial space.

\[ \int_F u (\mathbf v\cdot \mathbf n) \,ds \]

Author: Guido Kanschat

Date: 2013

Definition at line 353 of file divergence.h.

◆ u_dot_n_matrix() [2/2]

template<int dim>

void LocalIntegrators::Divergence::u_dot_n_matrix	(	FullMatrix< double > &	M11,
		FullMatrix< double > &	M12,
		FullMatrix< double > &	M21,
		FullMatrix< double > &	M22,
		const FEValuesBase< dim > &	fe1,
		const FEValuesBase< dim > &	fe2,
		const FEValuesBase< dim > &	fetest1,
		const FEValuesBase< dim > &	fetest2,
		double	factor = `1.`
	)

The trace of the divergence operator, namely the product of the jump of the normal component of the vector valued trial function and the mean value of the test function.

\[ \int_F (\mathbf u_1\cdot \mathbf n_1 + \mathbf u_2 \cdot \mathbf n_2) \frac{v_1+v_2}{2} \,ds \]

Author: Guido Kanschat

Date: 2011

Definition at line 390 of file divergence.h.

◆ grad_div_matrix()

template<int dim>

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

Deprecated:: Use LocalIntegrators::GradDiv::cell_matrix() instead.

Definition at line 449 of file divergence.h.

◆ grad_div_residual()

template<int dim, typename number >

void LocalIntegrators::Divergence::grad_div_residual	(	Vector< number > &	result,
		const FEValuesBase< dim > &	fetest,
		const ArrayView< const std::vector< Tensor< 1, dim >>> &	input,
		const double	factor = `1.`
	)

Deprecated:: Use LocalIntegrators::GradDiv::cell_residual() instead.

Definition at line 468 of file divergence.h.

◆ u_dot_n_jump_matrix()

template<int dim>

void LocalIntegrators::Divergence::u_dot_n_jump_matrix	(	FullMatrix< double > &	M11,
		FullMatrix< double > &	M12,
		FullMatrix< double > &	M21,
		FullMatrix< double > &	M22,
		const FEValuesBase< dim > &	fe1,
		const FEValuesBase< dim > &	fe2,
		double	factor = `1.`
	)

The jump of the normal component

\[ \int_F (\mathbf u_1\cdot \mathbf n_1 + \mathbf u_2 \cdot \mathbf n_2) (\mathbf v_1\cdot \mathbf n_1 + \mathbf v_2 \cdot \mathbf n_2) \,ds \]

Author: Guido Kanschat

Date: 2011

Definition at line 490 of file divergence.h.

◆ norm()

template<int dim>

double LocalIntegrators::Divergence::norm	(	const FEValuesBase< dim > &	fe,
		const ArrayView< const std::vector< Tensor< 1, dim >>> &	Du
	)

The L²-norm of the divergence over the quadrature set determined by the FEValuesBase object.

The vector is expected to consist of dim vectors of length equal to the number of quadrature points. The number of components of the finite element has to be equal to the space dimension.

Author: Guido Kanschat

Date: 2013

Definition at line 548 of file divergence.h.

Functions

Detailed Description

Function Documentation

◆ cell_matrix()

◆ cell_residual() [1/2]

◆ cell_residual() [2/2]

◆ gradient_matrix()

◆ gradient_residual() [1/2]

◆ gradient_residual() [2/2]

◆ u_dot_n_matrix() [1/2]

◆ u_dot_n_residual()

◆ u_times_n_residual()

◆ u_dot_n_matrix() [2/2]

◆ grad_div_matrix()

◆ grad_div_residual()

◆ u_dot_n_jump_matrix()

◆ norm()