Functions

LocalIntegrators::Divergence Namespace Reference

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

Functions

template<int dim>
Tensor< 1, dim > grad_div (const Tensor< 2, dim > &h0, const Tensor< 2, dim > &h1, const Tensor< 2, dim > &h2)
template<int dim>
void cell_matrix (FullMatrix< double > &M, const FEValuesBase< dim > &fe, const FEValuesBase< dim > &fetest, 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>
void u_dot_n_matrix (FullMatrix< double > &M, const FEValuesBase< dim > &fe, const FEValuesBase< dim > &fetest, double factor=1.)
template<int dim>
void u_dot_n_residual (Vector< double > &result, const FEValuesBase< dim > &fe, const FEValuesBase< dim > &fetest, const VectorSlice< const std::vector< 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, 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.)

Detailed Description

Local integrators related to the divergence operator and its trace.

Author:
Guido Kanschat
Date:
2010

Function Documentation

template<int dim>
Tensor<1,dim> LocalIntegrators::Divergence::grad_div ( const Tensor< 2, dim > &  h0,
const Tensor< 2, dim > &  h1,
const Tensor< 2, dim > &  h2 
)

Auxiliary function. Computes the grad-div-operator from a set of Hessians.

Note:
The third tensor argument is not used in two dimensions and can for instance duplicate one of the previous.
Author:
Guido Kanschat
Date:
2011

Definition at line 49 of file divergence.h.

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 76 of file divergence.h.

References AssertDimension, FEValuesBase< dim, spacedim >::dofs_per_cell, FEValuesBase< dim, spacedim >::get_fe(), FEValuesBase< dim, spacedim >::JxW(), FullMatrix< number >::m(), FullMatrix< number >::n(), FEValuesBase< dim, spacedim >::n_quadrature_points, FEValuesBase< dim, spacedim >::shape_grad_component(), and FEValuesBase< dim, spacedim >::shape_value().

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 116 of file divergence.h.

References AssertDimension, FEValuesBase< dim, spacedim >::dofs_per_cell, FEValuesBase< dim, spacedim >::get_fe(), FEValuesBase< dim, spacedim >::JxW(), FullMatrix< number >::m(), FullMatrix< number >::n(), FEValuesBase< dim, spacedim >::n_quadrature_points, FEValuesBase< dim, spacedim >::shape_grad(), and FEValuesBase< dim, spacedim >::shape_value_component().

template<int dim>
void LocalIntegrators::Divergence::u_dot_n_matrix ( FullMatrix< double > &  M,
const FEValuesBase< dim > &  fe,
const FEValuesBase< dim > &  fetest,
double  factor = 1. 
)
template<int dim>
void LocalIntegrators::Divergence::u_dot_n_residual ( Vector< double > &  result,
const FEValuesBase< dim > &  fe,
const FEValuesBase< dim > &  fetest,
const VectorSlice< const std::vector< std::vector< double > > > &  data,
double  factor = 1. 
)
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. 
)
template<int dim>
void LocalIntegrators::Divergence::grad_div_matrix ( FullMatrix< double > &  M,
const FEValuesBase< dim > &  fe,
double  factor = 1. 
)
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. 
)
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