Intrepid2
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Implementation of the default HVOL-compatible Lagrange basis of arbitrary degree on Tetrahedron cell. More...
#include <Intrepid2_HVOL_TET_Cn_FEM.hpp>
Public Types | |
using | OrdinalTypeArray1DHost = typename Basis< DeviceType, outputValueType, pointValueType >::OrdinalTypeArray1DHost |
using | OrdinalTypeArray2DHost = typename Basis< DeviceType, outputValueType, pointValueType >::OrdinalTypeArray2DHost |
using | OrdinalTypeArray3DHost = typename Basis< DeviceType, outputValueType, pointValueType >::OrdinalTypeArray3DHost |
using | OutputViewType = typename Basis< DeviceType, outputValueType, pointValueType >::OutputViewType |
using | PointViewType = typename Basis< DeviceType, outputValueType, pointValueType >::PointViewType |
using | ScalarViewType = typename Basis< DeviceType, outputValueType, pointValueType >::ScalarViewType |
typedef Basis< DeviceType, outputValueType, pointValueType >::scalarType | scalarType |
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using | DeviceType = Device |
(Kokkos) Device type on which Basis is templated. Does not necessarily return true for Kokkos::is_device (may be Kokkos::Serial, for example). | |
using | ExecutionSpace = typename DeviceType::execution_space |
(Kokkos) Execution space for basis. | |
using | OutputValueType = outputValueType |
Output value type for basis; default is double. | |
using | PointValueType = pointValueType |
Point value type for basis; default is double. | |
using | OrdinalViewType = Kokkos::View< ordinal_type, DeviceType > |
View type for ordinal. | |
using | EBasisViewType = Kokkos::View< EBasis, DeviceType > |
View for basis type. | |
using | ECoordinatesViewType = Kokkos::View< ECoordinates, DeviceType > |
View for coordinate system type. | |
using | OrdinalTypeArray1DHost = Kokkos::View< ordinal_type *, typename ExecutionSpace::array_layout, Kokkos::HostSpace > |
View type for 1d host array. | |
using | OrdinalTypeArray2DHost = Kokkos::View< ordinal_type **, typename ExecutionSpace::array_layout, Kokkos::HostSpace > |
View type for 2d host array. | |
using | OrdinalTypeArray3DHost = Kokkos::View< ordinal_type ***, typename ExecutionSpace::array_layout, Kokkos::HostSpace > |
View type for 3d host array. | |
using | OrdinalTypeArrayStride1DHost = Kokkos::View< ordinal_type *, Kokkos::LayoutStride, Kokkos::HostSpace > |
View type for 1d host array. | |
using | OrdinalTypeArray1D = Kokkos::View< ordinal_type *, DeviceType > |
View type for 1d device array. | |
using | OrdinalTypeArray2D = Kokkos::View< ordinal_type **, DeviceType > |
View type for 2d device array. | |
using | OrdinalTypeArray3D = Kokkos::View< ordinal_type ***, DeviceType > |
View type for 3d device array. | |
using | OrdinalTypeArrayStride1D = Kokkos::View< ordinal_type *, Kokkos::LayoutStride, DeviceType > |
View type for 1d device array. | |
typedef ScalarTraits< pointValueType >::scalar_type | scalarType |
Scalar type for point values. | |
using | OutputViewType = Kokkos::DynRankView< OutputValueType, Kokkos::LayoutStride, DeviceType > |
View type for basis value output. | |
using | PointViewType = Kokkos::DynRankView< PointValueType, Kokkos::LayoutStride, DeviceType > |
View type for input points. | |
using | ScalarViewType = Kokkos::DynRankView< scalarType, Kokkos::LayoutStride, DeviceType > |
View type for scalars. | |
Public Member Functions | |
Basis_HVOL_TET_Cn_FEM (const ordinal_type order, const EPointType pointType=POINTTYPE_EQUISPACED) | |
Constructor. | |
virtual void | getValues (OutputViewType outputValues, const PointViewType inputPoints, const EOperator operatorType=OPERATOR_VALUE) const override |
Evaluation of a FEM basis on a reference cell. | |
virtual void | getDofCoords (ScalarViewType dofCoords) const override |
Returns spatial locations (coordinates) of degrees of freedom on the reference cell. | |
virtual void | getDofCoeffs (ScalarViewType dofCoeffs) const override |
Coefficients for computing degrees of freedom for Lagrangian basis If P is an element of the space spanned by the basis, \alpha_i := P(dofCoords(i)) \cdot dofCoeffs(i) are the nodal coefficients associated to basis function i. | |
void | getVandermondeInverse (ScalarViewType vinv) const |
virtual const char * | getName () const override |
Returns basis name. | |
virtual bool | requireOrientation () const override |
True if orientation is required. | |
virtual HostBasisPtr< outputValueType, pointValueType > | getHostBasis () const override |
Creates and returns a Basis object whose DeviceType template argument is Kokkos::HostSpace::device_type, but is otherwise identical to this. | |
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OutputValueType | getDummyOutputValue () |
Dummy array to receive input arguments. | |
PointValueType | getDummyPointValue () |
Dummy array to receive input arguments. | |
Kokkos::DynRankView< OutputValueType, DeviceType > | allocateOutputView (const int numPoints, const EOperator operatorType=OPERATOR_VALUE) const |
Allocate a View container suitable for passing to the getValues() variant that accepts Kokkos DynRankViews as arguments (as opposed to the Intrepid2 BasisValues and PointValues containers). | |
virtual BasisValues< OutputValueType, DeviceType > | allocateBasisValues (TensorPoints< PointValueType, DeviceType > points, const EOperator operatorType=OPERATOR_VALUE) const |
Allocate BasisValues container suitable for passing to the getValues() variant that takes a TensorPoints container as argument. | |
virtual void | getValues (OutputViewType, const PointViewType, const EOperator=OPERATOR_VALUE) const |
Evaluation of a FEM basis on a reference cell. | |
virtual void | getValues (BasisValues< OutputValueType, DeviceType > outputValues, const TensorPoints< PointValueType, DeviceType > inputPoints, const EOperator operatorType=OPERATOR_VALUE) const |
Evaluation of a FEM basis on a reference cell, using point and output value containers that allow preservation of tensor-product structure. | |
virtual void | getValues (OutputViewType, const PointViewType, const PointViewType, const EOperator=OPERATOR_VALUE) const |
Evaluation of an FVD basis evaluation on a physical cell. | |
virtual void | getDofCoords (ScalarViewType) const |
Returns spatial locations (coordinates) of degrees of freedom on the reference cell. | |
virtual void | getDofCoeffs (ScalarViewType) const |
Coefficients for computing degrees of freedom for Lagrangian basis If P is an element of the space spanned by the basis, \alpha_i := P(dofCoords(i)) \cdot dofCoeffs(i) are the nodal coefficients associated to basis function i. | |
OrdinalTypeArray1DHost | getFieldOrdinalsForDegree (OrdinalTypeArray1DHost °rees) const |
For hierarchical bases, returns the field ordinals that have at most the specified degree in each dimension. Assuming that these are less than or equal to the polynomial orders provided at Basis construction, the corresponding polynomials will form a superset of the Basis of the same type constructed with polynomial orders corresponding to the specified degrees. | |
OrdinalTypeArray1DHost | getFieldOrdinalsForH1Degree (OrdinalTypeArray1DHost °rees) const |
For hierarchical bases, returns the field ordinals that have at most the specified H^1 degree in each dimension. Assuming that these are less than or equal to the polynomial orders provided at Basis construction, the corresponding polynomials will form a superset of the Basis of the same type constructed with polynomial orders corresponding to the specified degrees. | |
std::vector< int > | getFieldOrdinalsForDegree (std::vector< int > °rees) const |
For hierarchical bases, returns the field ordinals that have at most the specified degree in each dimension. Assuming that these are less than or equal to the polynomial orders provided at Basis construction, the corresponding polynomials will form a superset of the Basis of the same type constructed with polynomial orders corresponding to the specified degrees. | |
std::vector< int > | getFieldOrdinalsForH1Degree (std::vector< int > °rees) const |
For hierarchical bases, returns the field ordinals that have at most the specified H^1 degree in each dimension. Assuming that these are less than or equal to the polynomial orders provided at Basis construction, the corresponding polynomials will form a superset of the Basis of the same type constructed with polynomial orders corresponding to the specified degrees. | |
OrdinalTypeArray1DHost | getPolynomialDegreeOfField (int fieldOrdinal) const |
For hierarchical bases, returns the polynomial degree (which may have multiple values in higher spatial dimensions) for the specified basis ordinal as a host array. | |
OrdinalTypeArray1DHost | getH1PolynomialDegreeOfField (int fieldOrdinal) const |
For hierarchical bases, returns the polynomial degree (which may have multiple values in higher spatial dimensions) for the specified basis ordinal as a host array. | |
std::vector< int > | getPolynomialDegreeOfFieldAsVector (int fieldOrdinal) const |
For hierarchical bases, returns the polynomial degree (which may have multiple values in higher spatial dimensions) for the specified basis ordinal as a host array. | |
std::vector< int > | getH1PolynomialDegreeOfFieldAsVector (int fieldOrdinal) const |
For hierarchical bases, returns the polynomial degree (which may have multiple values in higher spatial dimensions) for the specified basis ordinal as a host array. | |
int | getPolynomialDegreeLength () const |
For hierarchical bases, returns the number of entries required to specify the polynomial degree of a basis function. | |
virtual const char * | getName () const |
Returns basis name. | |
virtual bool | requireOrientation () const |
True if orientation is required. | |
ordinal_type | getCardinality () const |
Returns cardinality of the basis. | |
ordinal_type | getDegree () const |
Returns the degree of the basis. | |
EFunctionSpace | getFunctionSpace () const |
Returns the function space for the basis. | |
shards::CellTopology | getBaseCellTopology () const |
Returns the base cell topology for which the basis is defined. See Shards documentation https://trilinos.org/packages/shards for definition of base cell topology. | |
EBasis | getBasisType () const |
Returns the basis type. | |
ECoordinates | getCoordinateSystem () const |
Returns the type of coordinate system for which the basis is defined. | |
ordinal_type | getDofCount (const ordinal_type subcDim, const ordinal_type subcOrd) const |
DoF count for specified subcell. | |
ordinal_type | getDofOrdinal (const ordinal_type subcDim, const ordinal_type subcOrd, const ordinal_type subcDofOrd) const |
DoF tag to ordinal lookup. | |
virtual int | getNumTensorialExtrusions () const |
returns the number of tensorial extrusions relative to the cell topology returned by getBaseCellTopology(). Base class returns 0; overridden by TensorBasis. | |
const OrdinalTypeArray3DHost | getAllDofOrdinal () const |
DoF tag to ordinal data structure. | |
const OrdinalTypeArrayStride1DHost | getDofTag (const ordinal_type dofOrd) const |
DoF ordinal to DoF tag lookup. | |
const OrdinalTypeArray2DHost | getAllDofTags () const |
Retrieves all DoF tags. | |
virtual BasisPtr< DeviceType, OutputValueType, PointValueType > | getSubCellRefBasis (const ordinal_type subCellDim, const ordinal_type subCellOrd) const |
returns the basis associated to a subCell. | |
ordinal_type | getDomainDimension () const |
Returns the spatial dimension of the domain of the basis; this is equal to getBaseCellTopology().getDimension() + getNumTensorialExtrusions(). | |
virtual HostBasisPtr< OutputValueType, PointValueType > | getHostBasis () const |
Creates and returns a Basis object whose DeviceType template argument is Kokkos::HostSpace::device_type, but is otherwise identical to this. | |
Private Attributes | |
Kokkos::DynRankView< scalarType, DeviceType > | vinv_ |
inverse of Generalized Vandermonde matrix, whose columns store the expansion coefficients of the nodal basis in terms of phis_ | |
EPointType | pointType_ |
Additional Inherited Members | |
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template<typename OrdinalTypeView3D , typename OrdinalTypeView2D , typename OrdinalTypeView1D > | |
void | setOrdinalTagData (OrdinalTypeView3D &tagToOrdinal, OrdinalTypeView2D &ordinalToTag, const OrdinalTypeView1D tags, const ordinal_type basisCard, const ordinal_type tagSize, const ordinal_type posScDim, const ordinal_type posScOrd, const ordinal_type posDfOrd) |
Fills ordinalToTag_ and tagToOrdinal_ by basis-specific tag data. | |
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ordinal_type | basisCardinality_ |
Cardinality of the basis, i.e., the number of basis functions/degrees-of-freedom. | |
ordinal_type | basisDegree_ |
Degree of the largest complete polynomial space that can be represented by the basis. | |
shards::CellTopology | basisCellTopology_ |
Base topology of the cells for which the basis is defined. See the Shards package for definition of base cell topology. For TensorBasis subclasses, by default this the cell topology that is extruded (i.e., it is a lower-dimensional CellTopology than the space on which the tensor basis is defined). This allows tensor bases to be defined in higher dimensions than shards::CellTopology supports. TensorBasis subclasses can opt to use an equivalent shards CellTopology for basisCellTopology_, as well as using Intrepid2's tagging for tensor bases in dimensions up to 3, by calling TensorBasis::setShardsTopologyAndTags(). | |
EBasis | basisType_ |
Type of the basis. | |
ECoordinates | basisCoordinates_ |
The coordinate system for which the basis is defined. | |
EFunctionSpace | functionSpace_ = FUNCTION_SPACE_MAX |
The function space in which the basis is defined. | |
OrdinalTypeArray2DHost | ordinalToTag_ |
"true" if tagToOrdinal_ and ordinalToTag_ have been initialized | |
OrdinalTypeArray3DHost | tagToOrdinal_ |
DoF tag to ordinal lookup table. | |
Kokkos::DynRankView< scalarType, DeviceType > | dofCoords_ |
Coordinates of degrees-of-freedom for basis functions defined in physical space. | |
Kokkos::DynRankView< scalarType, DeviceType > | dofCoeffs_ |
Coefficients for computing degrees of freedom for Lagrangian basis If P is an element of the space spanned by the basis, \alpha_i := P(dofCoords_(i)) \cdot dofCoeffs_(i) are the nodal coefficients associated to basis functions i. | |
OrdinalTypeArray2DHost | fieldOrdinalPolynomialDegree_ |
Polynomial degree for each degree of freedom. Only defined for hierarchical bases right now. The number of entries per degree of freedom in this table depends on the basis type. For hypercubes, this will be the spatial dimension. We have not yet determined what this will be for simplices beyond 1D; there are not yet hierarchical simplicial bases beyond 1D in Intrepid2. | |
OrdinalTypeArray2DHost | fieldOrdinalH1PolynomialDegree_ |
H^1 polynomial degree for each degree of freedom. Only defined for hierarchical bases right now. The number of entries per degree of freedom in this table depends on the basis type. For hypercubes, this will be the spatial dimension. We have not yet determined what this will be for simplices beyond 1D; there are not yet hierarchical simplicial bases beyond 1D in Intrepid2. | |
Implementation of the default HVOL-compatible Lagrange basis of arbitrary degree on Tetrahedron cell.
Implements Lagrangian basis of degree n on the reference Tetrahedron cell. The basis has cardinality (n+1)(n+2)(n+3)/6 and spans a COMPLETE polynomial space of degree n. Nodal basis functions are dual to a unisolvent set of degrees-of-freedom (DoF) defined at a lattice of order n (see \ref PointTools). In particular, the degrees of freedom are point evaluation at points in the interior of the Tetrahedron. The distribution of these points is specified by the pointType argument to the class constructor. Currently, either equispaced lattice points or Warburton's warp-blend points are available. The dof are enumerated according to the ordering on the lattice (see PointTools).
Definition at line 189 of file Intrepid2_HVOL_TET_Cn_FEM.hpp.
using Intrepid2::Basis_HVOL_TET_Cn_FEM< DeviceType, outputValueType, pointValueType >::OrdinalTypeArray1DHost = typename Basis<DeviceType,outputValueType,pointValueType>::OrdinalTypeArray1DHost |
Definition at line 192 of file Intrepid2_HVOL_TET_Cn_FEM.hpp.
using Intrepid2::Basis_HVOL_TET_Cn_FEM< DeviceType, outputValueType, pointValueType >::OrdinalTypeArray2DHost = typename Basis<DeviceType,outputValueType,pointValueType>::OrdinalTypeArray2DHost |
Definition at line 193 of file Intrepid2_HVOL_TET_Cn_FEM.hpp.
using Intrepid2::Basis_HVOL_TET_Cn_FEM< DeviceType, outputValueType, pointValueType >::OrdinalTypeArray3DHost = typename Basis<DeviceType,outputValueType,pointValueType>::OrdinalTypeArray3DHost |
Definition at line 194 of file Intrepid2_HVOL_TET_Cn_FEM.hpp.
using Intrepid2::Basis_HVOL_TET_Cn_FEM< DeviceType, outputValueType, pointValueType >::OutputViewType = typename Basis<DeviceType,outputValueType,pointValueType>::OutputViewType |
Definition at line 202 of file Intrepid2_HVOL_TET_Cn_FEM.hpp.
using Intrepid2::Basis_HVOL_TET_Cn_FEM< DeviceType, outputValueType, pointValueType >::PointViewType = typename Basis<DeviceType,outputValueType,pointValueType>::PointViewType |
Definition at line 203 of file Intrepid2_HVOL_TET_Cn_FEM.hpp.
typedef Basis<DeviceType,outputValueType,pointValueType>::scalarType Intrepid2::Basis_HVOL_TET_Cn_FEM< DeviceType, outputValueType, pointValueType >::scalarType |
Definition at line 206 of file Intrepid2_HVOL_TET_Cn_FEM.hpp.
using Intrepid2::Basis_HVOL_TET_Cn_FEM< DeviceType, outputValueType, pointValueType >::ScalarViewType = typename Basis<DeviceType,outputValueType,pointValueType>::ScalarViewType |
Definition at line 204 of file Intrepid2_HVOL_TET_Cn_FEM.hpp.
Intrepid2::Basis_HVOL_TET_Cn_FEM< DT, OT, PT >::Basis_HVOL_TET_Cn_FEM | ( | const ordinal_type | order, |
const EPointType | pointType = POINTTYPE_EQUISPACED |
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Constructor.
Definition at line 230 of file Intrepid2_HVOL_TET_Cn_FEMDef.hpp.
References Intrepid2::PointTools::getLattice().
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Coefficients for computing degrees of freedom for Lagrangian basis If P is an element of the space spanned by the basis, \alpha_i := P(dofCoords(i)) \cdot dofCoeffs(i) are the nodal coefficients associated to basis function i.
Rank-1 array for scalar basis with dimension (cardinality) Rank-2 array for vector basis with dimensions (cardinality, cell dimension)
Reimplemented from Intrepid2::Basis< Device, outputValueType, pointValueType >.
Definition at line 249 of file Intrepid2_HVOL_TET_Cn_FEM.hpp.
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Returns spatial locations (coordinates) of degrees of freedom on the reference cell.
Reimplemented from Intrepid2::Basis< Device, outputValueType, pointValueType >.
Definition at line 232 of file Intrepid2_HVOL_TET_Cn_FEM.hpp.
References Intrepid2::Basis< Device, outputValueType, pointValueType >::dofCoords_.
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Creates and returns a Basis object whose DeviceType template argument is Kokkos::HostSpace::device_type, but is otherwise identical to this.
Reimplemented from Intrepid2::Basis< Device, outputValueType, pointValueType >.
Definition at line 280 of file Intrepid2_HVOL_TET_Cn_FEM.hpp.
References Intrepid2::Basis< Device, outputValueType, pointValueType >::basisDegree_.
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Returns basis name.
Reimplemented from Intrepid2::Basis< Device, outputValueType, pointValueType >.
Definition at line 269 of file Intrepid2_HVOL_TET_Cn_FEM.hpp.
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Evaluation of a FEM basis on a reference cell.
Returns values of operatorType acting on FEM basis functions for a set of points in the reference cell for which the basis is defined.
outputValues | [out] - variable rank array with the basis values |
inputPoints | [in] - rank-2 array (P,D) with the evaluation points |
operatorType | [in] - the operator acting on the basis functions |
Reimplemented from Intrepid2::Basis< Device, outputValueType, pointValueType >.
Definition at line 212 of file Intrepid2_HVOL_TET_Cn_FEM.hpp.
References Intrepid2::Basis< Device, outputValueType, pointValueType >::getBaseCellTopology(), Intrepid2::Basis< Device, outputValueType, pointValueType >::getCardinality(), Intrepid2::getValues_HVOL_Args(), Intrepid2::Parameters::MaxNumPtsPerBasisEval, and Intrepid2::Basis_HVOL_TET_Cn_FEM< DeviceType, outputValueType, pointValueType >::vinv_.
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Definition at line 262 of file Intrepid2_HVOL_TET_Cn_FEM.hpp.
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True if orientation is required.
Reimplemented from Intrepid2::Basis< Device, outputValueType, pointValueType >.
Definition at line 275 of file Intrepid2_HVOL_TET_Cn_FEM.hpp.
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Definition at line 289 of file Intrepid2_HVOL_TET_Cn_FEM.hpp.
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inverse of Generalized Vandermonde matrix, whose columns store the expansion coefficients of the nodal basis in terms of phis_
Definition at line 288 of file Intrepid2_HVOL_TET_Cn_FEM.hpp.
Referenced by Intrepid2::Basis_HVOL_TET_Cn_FEM< DeviceType, outputValueType, pointValueType >::getValues().