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// Intrepid Package
// Copyright (2007) Sandia Corporation
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// Denis Ridzal (dridzal@sandia.gov), or
// Kara Peterson (kjpeter@sandia.gov)
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/** \file Intrepid_HGRAD_PYR_I2_FEM.hpp
\brief Header file for the Intrepid::HGRAD_PYR_I2_FEM class.
\author Created by P. Bochev, D. Ridzal and K. Peterson.
*/
#ifndef INTREPID_HGRAD_PYR_I2_FEM_HPP
#define INTREPID_HGRAD_PYR_I2_FEM_HPP
#include "Intrepid_Basis.hpp"
namespace Intrepid {
/** \class Intrepid::Basis_HGRAD_PYR_I2_FEM
\brief Implementation of an H(grad)-compatible FEM basis of degree 2 on a Pyramid cell
Implements Lagrangian basis of degree 2 on the reference Pyramid cell. The basis has
cardinality 13 and spans an INCOMPLETE bi-quadratic polynomial space. Basis functions are dual
to a unisolvent set of degrees-of-freedom (DoF) defined and enumerated as follows:
\verbatim
=================================================================================================
| | degree-of-freedom-tag table | |
| DoF |----------------------------------------------------------| DoF definition |
| ordinal | subc dim | subc ordinal | subc DoF ord |subc num DoF | |
|=========|==============|==============|==============|=============|===========================|
| 0 | 0 | 0 | 0 | 1 | L_0(u) = u(-1,-1, 0) |
|---------|--------------|--------------|--------------|-------------|---------------------------|
| 1 | 0 | 1 | 0 | 1 | L_1(u) = u( 1,-1, 0) |
|---------|--------------|--------------|--------------|-------------|---------------------------|
| 2 | 0 | 2 | 0 | 1 | L_2(u) = u( 1, 1, 0) |
|---------|--------------|--------------|--------------|-------------|---------------------------|
| 3 | 0 | 3 | 0 | 1 | L_3(u) = u(-1, 1, 0) |
|---------|--------------|--------------|--------------|-------------|---------------------------|
| 4 | 0 | 4 | 0 | 1 | L_4(u) = u( 0, 0, 1) |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|---------|--------------|--------------|--------------|-------------|---------------------------|
| 5 | 1 | 0 | 0 | 1 | L_5(u) = u( 0,-1, 0) |
|---------|--------------|--------------|--------------|-------------|---------------------------|
| 6 | 1 | 1 | 0 | 1 | L_6(u) = u( 1, 0, 0) |
|---------|--------------|--------------|--------------|-------------|---------------------------|
| 7 | 1 | 2 | 0 | 1 | L_7(u) = u( 0, 1, 0) |
|---------|--------------|--------------|--------------|-------------|---------------------------|
| 8 | 1 | 3 | 0 | 1 | L_8(u) = u(-1, 0, 0) |
|---------|--------------|--------------|--------------|-------------|---------------------------|
| 9 | 1 | 4 | 0 | 1 | L_9(u) = u(-1/2,-1/2,1/2) |
|---------|--------------|--------------|--------------|-------------|---------------------------|
| 10 | 1 | 5 | 0 | 1 | L_10(u)= u( 1/2,-1/2,1/2) |
|---------|--------------|--------------|--------------|-------------|---------------------------|
| 11 | 1 | 6 | 0 | 1 | L_11(u)= u( 1/2, 1/2,1/2) |
|---------|--------------|--------------|--------------|-------------|---------------------------|
| 12 | 1 | 7 | 0 | 1 | L_12(u)= u(-1/2, 1/2,1/2) |
|=========|==============|==============|==============|=============|===========================|
| MAX | maxScDim=1 | maxScOrd=7 | maxDfOrd=0 | - | |
|=========|==============|==============|==============|=============|===========================|
\endverbatim
\remark Ordering of DoFs follows the node order in Pyramid<13> topology.
\remark WARNING: Does not satisfy a patch test for arbitrarily deformed pyramids, but only
for pyramids with bottom quadrilateral nodes forming a plane.
*/
template<class Scalar, class ArrayScalar>
class Basis_HGRAD_PYR_I2_FEM : public Basis<Scalar, ArrayScalar> {
private:
/** \brief Initializes <var>tagToOrdinal_</var> and <var>ordinalToTag_</var> lookup arrays.
*/
void initializeTags();
public:
/** \brief Constructor.
*/
Basis_HGRAD_PYR_I2_FEM();
/** \brief FEM basis evaluation on a <strong>reference Pyramid</strong> cell.
Returns values of <var>operatorType</var> acting on FEM basis functions for a set of
points in the <strong>reference Pyramid</strong> cell. For rank and dimensions of
I/O array arguments see Section \ref basis_md_array_sec .
\param outputValues [out] - rank-2 or 3 array with the computed basis values
\param inputPoints [in] - rank-2 array with dimensions (P,D) containing reference points
\param operatorType [in] - operator applied to basis functions
*/
void getValues(ArrayScalar & outputValues,
const ArrayScalar & inputPoints,
const EOperator operatorType) const;
/** \brief FVD basis evaluation: invocation of this method throws an exception.
*/
void getValues(ArrayScalar & outputValues,
const ArrayScalar & inputPoints,
const ArrayScalar & cellVertices,
const EOperator operatorType = OPERATOR_VALUE) const;
};
}// namespace Intrepid
#include "Intrepid_HGRAD_PYR_I2_FEMDef.hpp"
#endif
|