MFEM  v4.4.0 Finite element discretization library

Structure representing the matrices/tensors needed to evaluate (in reference space) the values, gradients, divergences, or curls of a FiniteElement at a the quadrature points of a given IntegrationRule. More...

#include <fe_base.hpp>

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## Public Types

enum  Mode { FULL, TENSOR }
Type of data stored in the arrays B, Bt, G, and Gt. More...

## Public Attributes

class FiniteElementFE
The FiniteElement that created and owns this object. More...

const IntegrationRuleIntRule
IntegrationRule that defines the quadrature points at which the basis functions of the FE are evaluated. More...

Mode mode
Describes the contents of the B, Bt, G, and Gt arrays, see Mode. More...

int ndof
Number of degrees of freedom = number of basis functions. When mode is TENSOR, this is the 1D number. More...

int nqpt
Number of quadrature points. When mode is TENSOR, this is the 1D number. More...

Array< double > B
Basis functions evaluated at quadrature points. More...

Array< double > Bt
Transpose of B. More...

Array< double > G

Array< double > Gt
Transpose of G. More...

## Detailed Description

Structure representing the matrices/tensors needed to evaluate (in reference space) the values, gradients, divergences, or curls of a FiniteElement at a the quadrature points of a given IntegrationRule.

Object of this type are typically created and owned by the respective FiniteElement object.

Definition at line 136 of file fe_base.hpp.

## Member Enumeration Documentation

Type of data stored in the arrays B, Bt, G, and Gt.

Enumerator
FULL

Full multidimensional representation which does not use tensor product structure. The ordering of the degrees of freedom is as defined by FE.

TENSOR

Tensor product representation using 1D matrices/tensors with dimensions using 1D number of quadrature points and degrees of freedom.

When representing a vector-valued FiniteElement, two DofToQuad objects are used to describe the "closed" and "open" 1D basis functions (TODO).

Definition at line 149 of file fe_base.hpp.

## Member Data Documentation

Basis functions evaluated at quadrature points.

The storage layout is column-major with dimensions:

• nqpt x ndof, for scalar elements, or
• nqpt x dim x ndof, for vector elements, (TODO)

where

• dim = dimension of the finite element reference space when mode is FULL, and dim = 1 when mode is TENSOR.

Definition at line 185 of file fe_base.hpp.

Transpose of B.

The storage layout is column-major with dimensions:

• ndof x nqpt, for scalar elements, or
• ndof x nqpt x dim, for vector elements (TODO).

Definition at line 191 of file fe_base.hpp.

The FiniteElement that created and owns this object.

This pointer is not owned.

Definition at line 141 of file fe_base.hpp.

The storage layout is column-major with dimensions:

• nqpt x dim x ndof, for scalar elements, or
• nqpt x ndof, for H(div) vector elements (TODO), or
• nqpt x cdim x ndof, for H(curl) vector elements (TODO),

where

• dim = dimension of the finite element reference space when mode is FULL, and 1 when mode is TENSOR,
• cdim = 1/1/3 in 1D/2D/3D, respectively, when mode is FULL, and cdim = 1 when mode is TENSOR.

Definition at line 206 of file fe_base.hpp.

Transpose of G.

The storage layout is column-major with dimensions:

• ndof x nqpt x dim, for scalar elements, or
• ndof x nqpt, for H(div) vector elements (TODO), or
• ndof x nqpt x cdim, for H(curl) vector elements (TODO).

Definition at line 213 of file fe_base.hpp.

IntegrationRule that defines the quadrature points at which the basis functions of the FE are evaluated.

This pointer is not owned.

Definition at line 146 of file fe_base.hpp.

Describes the contents of the B, Bt, G, and Gt arrays, see Mode.

Definition at line 166 of file fe_base.hpp.