Reference documentation for deal.II version 9.5.0
\(\newcommand{\dealvcentcolon}{\mathrel{\mathop{:}}}\) \(\newcommand{\dealcoloneq}{\dealvcentcolon\mathrel{\mkern-1.2mu}=}\) \(\newcommand{\jump}[1]{\left[\!\left[ #1 \right]\!\right]}\) \(\newcommand{\average}[1]{\left\{\!\left\{ #1 \right\}\!\right\}}\)
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Functions
LocalIntegrators::Divergence Namespace Reference
Integrators

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 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.

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 Hdiv. The test functions may be discontinuous.

Definition at line 54 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 Hdiv. The test functions may be discontinuous.

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

Definition at line 93 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.

Definition at line 126 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.

Definition at line 157 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.

Definition at line 197 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 Hdiv. 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.

Definition at line 230 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.

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

Definition at line 259 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.

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

Definition at line 292 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.

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

Definition at line 324 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.

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

Definition at line 358 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

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

Definition at line 417 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.

Definition at line 472 of file divergence.h.

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