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// Copyright (2007) Sandia Corporation
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// 2. Redistributions in binary form must reproduce the above copyright
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// 3. Neither the name of the Corporation nor the names of the
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// THIS SOFTWARE IS PROVIDED BY SANDIA CORPORATION "AS IS" AND ANY
// EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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// Denis Ridzal (dridzal@sandia.gov), or
// Kara Peterson (kjpeter@sandia.gov)
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/** \file Intrepid_HGRAD_WEDGE_C2_FEM.hpp
\brief Header file for the Intrepid::G_WEDGE_C2_FEM class.
\author Created by P. Bochev and D. Ridzal.
*/
#ifndef INTREPID_HGRAD_WEDGE_C2_FEM_HPP
#define INTREPID_HGRAD_WEDGE_C2_FEM_HPP
#include "Intrepid_Basis.hpp"
namespace Intrepid {
/** \class Intrepid::Basis_HGRAD_WEDGE_C2_FEM
\brief Implementation of the default H(grad)-compatible FEM basis of degree 2 on Wedge cell
Implements Lagrangian basis of degree 2 on the reference Wedge cell. The basis has
cardinality 18 and spans a COMPLETE 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( 0, 0,-1) |
|---------|--------------|--------------|--------------|-------------|---------------------------|
| 1 | 0 | 1 | 0 | 1 | L_1(u) = u( 1, 0,-1) |
|---------|--------------|--------------|--------------|-------------|---------------------------|
| 2 | 0 | 2 | 0 | 1 | L_2(u) = u( 0, 1,-1) |
|---------|--------------|--------------|--------------|-------------|---------------------------|
| 3 | 0 | 3 | 0 | 1 | L_3(u) = u( 0, 0, 1) |
|---------|--------------|--------------|--------------|-------------|---------------------------|
| 4 | 0 | 4 | 0 | 1 | L_4(u) = u( 1, 0, 1) |
|---------|--------------|--------------|--------------|-------------|---------------------------|
| 5 | 0 | 5 | 0 | 1 | L_5(u) = u( 0, 1, 1) |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|---------|--------------|--------------|--------------|-------------|---------------------------|
| 6 | 1 | 0 | 0 | 1 | L_6(u) = u(1/2, 0,-1) |
|---------|--------------|--------------|--------------|-------------|---------------------------|
| 7 | 1 | 1 | 0 | 1 | L_7(u) = u(1/2,1/2,-1) |
|---------|--------------|--------------|--------------|-------------|---------------------------|
| 8 | 1 | 2 | 0 | 1 | L_8(u) = u( 0,1/2,-1) |
|---------|--------------|--------------|--------------|-------------|---------------------------|
| 9 | 1 | 6 | 0 | 1 | L_9(u) = u( 0, 0, 0) |
|---------|--------------|--------------|--------------|-------------|---------------------------|
| 10 | 1 | 7 | 0 | 1 | L_10(u)= u( 1, 0, 0) |
|---------|--------------|--------------|--------------|-------------|---------------------------|
| 11 | 1 | 8 | 0 | 1 | L_11(u)= u( 0, 1, 0) |
|---------|--------------|--------------|--------------|-------------|---------------------------|
| 12 | 1 | 3 | 0 | 1 | L_12(u)= u(1/2, 0, 1) |
|---------|--------------|--------------|--------------|-------------|---------------------------|
| 13 | 1 | 4 | 0 | 1 | L_13(u)= u(1/2,1/2, 1) |
|---------|--------------|--------------|--------------|-------------|---------------------------|
| 14 | 1 | 5 | 0 | 1 | L_14(u)= u( 0,1/2, 1) |
|---------|--------------|--------------|--------------|-------------|---------------------------|
|---------|--------------|--------------|--------------|-------------|---------------------------|
| 15 | 2 | 0 | 0 | 1 | L_15(u)= u(1/2, 0, 0) |
|---------|--------------|--------------|--------------|-------------|---------------------------|
| 16 | 2 | 1 | 0 | 1 | L_16(u)= u(1/2,1/2, 0) |
|---------|--------------|--------------|--------------|-------------|---------------------------|
| 17 | 2 | 2 | 0 | 1 | L_17(u)= u( 0,1/2, 0) |
|=========|==============|==============|==============|=============|===========================|
| MAX | maxScDim=2 | maxScOrd=8 | maxDfOrd=0 | - | |
|=========|==============|==============|==============|=============|===========================|
\endverbatim
\remark Ordering of DoFs follows the node order in Wedge<18> topology. Note that node
order in this topology does not follow the natural oder of k-subcells where the nodes
are located, except for nodes 0 to 5 which coincide with the vertices of the base
Wedge<6> topology. As a result, L_0 to L_5 are associated with nodes 0 to 5, but
L_6 to L_14 are not associated with edges 0 to 9 in that order. The last three nodes
are located on 2-subcells (faces) and follow their order. Thus, L_15, L_16 and L17 are
associated with faces 0, 1 and 2 in that order.
*/
template<class Scalar, class ArrayScalar>
class Basis_HGRAD_WEDGE_C2_FEM : public Basis<Scalar, ArrayScalar> {
private:
/** \brief Initializes <var>tagToOrdinal_</var> and <var>ordinalToTag_</var> lookup arrays.
*/
void initializeTags();
public:
/** \brief Constructor.
*/
Basis_HGRAD_WEDGE_C2_FEM();
/** \brief FEM basis evaluation on a <strong>reference Wedge</strong> cell.
Returns values of <var>operatorType</var> acting on FEM basis functions for a set of
points in the <strong>reference Wedge</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_WEDGE_C2_FEMDef.hpp"
#endif
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