Reference documentation for deal.II version GIT 0980a66d4b 2023-03-23 20:20:03+00:00
MatrixFreeOperators::CellwiseInverseMassMatrix< dim, fe_degree, n_components, Number, VectorizedArrayType > Class Template Reference

#include <deal.II/matrix_free/operators.h>

## Public Member Functions

CellwiseInverseMassMatrix (const FEEvaluationBase< dim, n_components, Number, false, VectorizedArrayType > &fe_eval)

void apply (const AlignedVector< VectorizedArrayType > &inverse_coefficient, const unsigned int n_actual_components, const VectorizedArrayType *in_array, VectorizedArrayType *out_array) const

void apply (const VectorizedArrayType *in_array, VectorizedArrayType *out_array) const

void apply (const AlignedVector< Tensor< 2, n_components, VectorizedArrayType >> &inverse_dyadic_coefficients, const VectorizedArrayType *in_array, VectorizedArrayType *out_array) const

void transform_from_q_points_to_basis (const unsigned int n_actual_components, const VectorizedArrayType *in_array, VectorizedArrayType *out_array) const

void fill_inverse_JxW_values (AlignedVector< VectorizedArrayType > &inverse_jxw) const

## Private Attributes

const FEEvaluationBase< dim, n_components, Number, false, VectorizedArrayType > & fe_eval

## Detailed Description

### template<int dim, int fe_degree, int n_components = 1, typename Number = double, typename VectorizedArrayType = VectorizedArray<Number>> class MatrixFreeOperators::CellwiseInverseMassMatrix< dim, fe_degree, n_components, Number, VectorizedArrayType >

This class implements the operation of the action of the inverse of a mass matrix on an element for the special case of an evaluation object with as many quadrature points as there are cell degrees of freedom. It uses algorithms from FEEvaluation and produces the exact mass matrix for DGQ elements. This algorithm uses tensor products of inverse 1d shape matrices over quadrature points, so the inverse operation is exactly as expensive as applying the forward operator on each cell. Of course, for continuous finite elements this operation does not produce the inverse of a mass operation as the coupling between the elements cannot be considered by this operation.

The equation may contain variable coefficients, so the user is required to provide an array for the inverse of the local coefficient (this class provide a helper method 'fill_inverse_JxW_values' to get the inverse of a constant-coefficient operator). The local coefficient can either be scalar in each component, or dyadic, i.e. couple between components.

Definition at line 622 of file operators.h.

## ◆ CellwiseInverseMassMatrix()

template<int dim, int fe_degree, int n_components, typename Number , typename VectorizedArrayType >
 MatrixFreeOperators::CellwiseInverseMassMatrix< dim, fe_degree, n_components, Number, VectorizedArrayType >::CellwiseInverseMassMatrix ( const FEEvaluationBase< dim, n_components, Number, false, VectorizedArrayType > & fe_eval )
inline

Constructor. Initializes the shape information from the ShapeInfo field in the class FEEval.

Definition at line 1030 of file operators.h.

## ◆ apply() [1/3]

template<int dim, int fe_degree, int n_components, typename Number , typename VectorizedArrayType >
 void MatrixFreeOperators::CellwiseInverseMassMatrix< dim, fe_degree, n_components, Number, VectorizedArrayType >::apply ( const AlignedVector< VectorizedArrayType > & inverse_coefficient, const unsigned int n_actual_components, const VectorizedArrayType * in_array, VectorizedArrayType * out_array ) const
inline

Applies the inverse mass matrix operation on an input array. It is assumed that the passed input and output arrays are of correct size, namely FEEvaluation::dofs_per_cell long. The inverse of the local coefficient (also containing the inverse JxW values) must be passed as first argument. Passing more than one component in the coefficient is allowed. The coefficients are interpreted as scalar in each component.

Definition at line 1112 of file operators.h.

## ◆ apply() [2/3]

template<int dim, int fe_degree, int n_components, typename Number , typename VectorizedArrayType >
 void MatrixFreeOperators::CellwiseInverseMassMatrix< dim, fe_degree, n_components, Number, VectorizedArrayType >::apply ( const VectorizedArrayType * in_array, VectorizedArrayType * out_array ) const
inline

Applies the inverse mass matrix operation on an input array, using the inverse of the JxW values provided by the fe_eval argument passed to the constructor of this class. Note that the user code must call FEEvaluation::reinit() on the underlying evaluator to make the FEEvaluationBase::JxW() method return the information of the correct cell. It is assumed that the pointers of the input and output arrays are valid over the length FEEvaluation::dofs_per_cell, which is the number of entries processed by this function. The in_array and out_array arguments may point to the same memory position.

Definition at line 1089 of file operators.h.

## ◆ apply() [3/3]

template<int dim, int fe_degree, int n_components, typename Number , typename VectorizedArrayType >
 void MatrixFreeOperators::CellwiseInverseMassMatrix< dim, fe_degree, n_components, Number, VectorizedArrayType >::apply ( const AlignedVector< Tensor< 2, n_components, VectorizedArrayType >> & inverse_dyadic_coefficients, const VectorizedArrayType * in_array, VectorizedArrayType * out_array ) const
inline

This operation applies the inverse mass matrix operation on an input array with local dyadic-valued coefficients. The second-rank tensor at each quadrature point defines a linear operator on a vector holding the dof components. It is assumed that the passed input and output arrays are of correct size, namely FEEvaluation::dofs_per_cell long. The in_array and out_array arguments may point to the same memory position. inverse_dyadic_coefficients must be dofs_per_component long, and every element must be a second-rank tensor of dimension n_components. All entries should be multiplied with the inverse JxW values.

Definition at line 1148 of file operators.h.

## ◆ transform_from_q_points_to_basis()

template<int dim, int fe_degree, int n_components, typename Number , typename VectorizedArrayType >
 void MatrixFreeOperators::CellwiseInverseMassMatrix< dim, fe_degree, n_components, Number, VectorizedArrayType >::transform_from_q_points_to_basis ( const unsigned int n_actual_components, const VectorizedArrayType * in_array, VectorizedArrayType * out_array ) const
inline

This operation performs a projection from the data given in quadrature points to the actual basis underlying this object. This projection can also be interpreted as a change of the basis from the Lagrange interpolation polynomials in the quadrature points to the basis underlying the current fe_eval object.

Calling this function on an array as

inverse_mass.transform_from_q_points_to_basis(1, array,
phi.begin_dof_values());

is equivalent to

for (unsigned int q=0; q<phi.n_q_points; ++q)
phi.submit_value(array[q], q);
phi.integrate(EvaluationFlags::values);
inverse_mass.apply(coefficients, 1, phi.begin_dof_values(),
phi.begin_dof_values());

provided that coefficients holds the inverse of the quadrature weights and no additional coefficients. This setup highlights the underlying projection, testing a right hand side and applying an inverse mass matrix. This function works both for the scalar case as described in the example or for multiple components that are laid out component by component.

Compared to the more verbose alternative, the given procedure is considerably faster because it can bypass the integrate() step and the first half of the transformation to the quadrature points, reducing the number of tensor product calls from 3*dim*n_components to dim*n_components.

Definition at line 1191 of file operators.h.

## ◆ fill_inverse_JxW_values()

template<int dim, int fe_degree, int n_components, typename Number , typename VectorizedArrayType >
 void MatrixFreeOperators::CellwiseInverseMassMatrix< dim, fe_degree, n_components, Number, VectorizedArrayType >::fill_inverse_JxW_values ( AlignedVector< VectorizedArrayType > & inverse_jxw ) const
inline

Fills the given array with the inverse of the JxW values, i.e., a mass matrix with coefficient 1. Non-unit coefficients must be multiplied (in inverse form) to this array.

Definition at line 1052 of file operators.h.

## ◆ fe_eval

template<int dim, int fe_degree, int n_components = 1, typename Number = double, typename VectorizedArrayType = VectorizedArray<Number>>
 const FEEvaluationBase& MatrixFreeOperators::CellwiseInverseMassMatrix< dim, fe_degree, n_components, Number, VectorizedArrayType >::fe_eval
private

A reference to the FEEvaluation object for getting the JxW_values.

Definition at line 743 of file operators.h.

The documentation for this class was generated from the following file: