Intrepid2
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Intrepid2::Basis_HCURL_TET_In_FEM< DeviceType, outputValueType, pointValueType > Class Template Reference

Implementation of the default H(curl)-compatible Nedelec (first kind) basis of arbitrary degree on Tetrahedron cell. More...

#include <Intrepid2_HCURL_TET_In_FEM.hpp>

Inheritance diagram for Intrepid2::Basis_HCURL_TET_In_FEM< DeviceType, outputValueType, pointValueType >:
Intrepid2::Basis< DeviceType, outputValueType, pointValueType >

Public Types

using BasisBase = Basis< DeviceType, outputValueType, pointValueType >
 
typedef Basis< DeviceType,
outputValueType,
pointValueType >::scalarType 		scalarType
 
using ExecutionSpace = typename DeviceType::execution_space
 (Kokkos) Execution space for basis.
 
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 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 Types inherited from Intrepid2::Basis< DeviceType, outputValueType, pointValueType >
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_HCURL_TET_In_FEM (const ordinal_type order, const EPointType pointType=POINTTYPE_EQUISPACED)
 Constructor.
 
virtual void getValues (const ExecutionSpace &space, OutputViewType outputValues, const PointViewType inputPoints, const EOperator operatorType=OPERATOR_VALUE) const override
 Evaluation of a FEM basis on a reference cell. More...
 
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, := P(dofCoords(i)) dofCoeffs(i) are the nodal coefficients associated to basis function i. More...
 
void getExpansionCoeffs (ScalarViewType coeffs) const
 
virtual const char * getName () const override
 Returns basis name. More...
 
virtual bool requireOrientation () const override
 True if orientation is required.
 
BasisPtr< DeviceType,
outputValueType,
pointValueType > 		getSubCellRefBasis (const ordinal_type subCellDim, const ordinal_type subCellOrd) const override
 returns the basis associated to a subCell. More...
 
BasisPtr< typename
Kokkos::HostSpace::device_type,
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. More...
 
- Public Member Functions inherited from Intrepid2::Basis< DeviceType, outputValueType, pointValueType >
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). More...
 
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. More...
 
virtual void getValues (OutputViewType outputValues, const PointViewType inputPoints, const EOperator operatorType=OPERATOR_VALUE) const
 
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. More...
 
virtual void getValues (OutputViewType, const PointViewType, const PointViewType, const EOperator=OPERATOR_VALUE) const
 Evaluation of an FVD basis evaluation on a physical cell. More...
 
OrdinalTypeArray1DHost getFieldOrdinalsForDegree (OrdinalTypeArray1DHost &degrees) 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. More...
 
std::vector< int > getFieldOrdinalsForDegree (std::vector< int > &degrees) 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. More...
 
OrdinalTypeArray1DHost getFieldOrdinalsForH1Degree (OrdinalTypeArray1DHost &degrees) 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. More...
 
std::vector< int > getFieldOrdinalsForH1Degree (std::vector< int > &degrees) 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. More...
 
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. More...
 
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. More...
 
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. More...
 
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. More...
 
int getPolynomialDegreeLength () const
 For hierarchical bases, returns the number of entries required to specify the polynomial degree of a basis function.
 
ordinal_type getCardinality () const
 Returns cardinality of the basis. More...
 
ordinal_type getDegree () const
 Returns the degree of the basis. More...
 
EFunctionSpace getFunctionSpace () const
 Returns the function space for the basis. More...
 
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. More...
 
EBasis getBasisType () const
 Returns the basis type. More...
 
ECoordinates getCoordinateSystem () const
 Returns the type of coordinate system for which the basis is defined. More...
 
ordinal_type getDofCount (const ordinal_type subcDim, const ordinal_type subcOrd) const
 DoF count for specified subcell. More...
 
ordinal_type getDofOrdinal (const ordinal_type subcDim, const ordinal_type subcOrd, const ordinal_type subcDofOrd) const
 DoF tag to ordinal lookup. More...
 
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. More...
 
const OrdinalTypeArray2DHost getAllDofTags () const
 Retrieves all DoF tags. More...
 
ordinal_type getDomainDimension () const
 Returns the spatial dimension of the domain of the basis; this is equal to getBaseCellTopology().getDimension() + getNumTensorialExtrusions(). More...
 

Private Attributes

Kokkos::DynRankView
< scalarType, DeviceType > 		coeffs_
 expansion coefficients of the nodal basis in terms of the orthgonal one
 
EPointType pointType_
 type of lattice used for creating the DoF coordinates
 

Additional Inherited Members

- Protected Member Functions inherited from Intrepid2::Basis< DeviceType, outputValueType, pointValueType >
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. More...
 
- Protected Attributes inherited from Intrepid2::Basis< DeviceType, outputValueType, pointValueType >
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_
 The function space in which the basis is defined.
 
OrdinalTypeArray2DHost ordinalToTag_
 "true" if tagToOrdinal_ and ordinalToTag_ have been initialized More...
 
OrdinalTypeArray3DHost tagToOrdinal_
 DoF tag to ordinal lookup table. More...
 
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, := P(dofCoords_(i)) dofCoeffs_(i) are the nodal coefficients associated to basis functions i. More...
 
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. More...
 
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. More...
 

Detailed Description

template<typename DeviceType = void, typename outputValueType = double, typename pointValueType = double>
class Intrepid2::Basis_HCURL_TET_In_FEM< DeviceType, outputValueType, pointValueType >

Implementation of the default H(curl)-compatible Nedelec (first kind) basis of arbitrary degree on Tetrahedron cell. 

      The lowest order space
      is indexted with 1 rather than 0.
      Implements nodal basis of degree n (n>=1) on the reference Tetrahedron cell. The basis has
      cardinality n*(n+2)*(n+3)/2 and spans an INCOMPLETE
      polynomial space of degree n. Basis functions are dual
      to a unisolvent set of degrees-of-freedom (DoF) defined by

      \li The tangential component of the vector field at n
      points per edge.  These are the first 6 * n dof.
      \li The components in the directions of the tangents to
      each face (see CellTools) on a lattice of order n+1 with
      offset 1 (see PointTools) on each face.  These are the
      next 4 * n*(n-1) dof.
      \li The x,y,z components on a lattice of order n+1 with
      offset 1 on the interior of the tetrahedron, the remaining
      degrees of freedom.

      If the pointType argument to the constructor specifies equispaced points, then the edge points
      will be equispaced on each edge and the interior points equispaced also.  If
      the pointType argument specifies warp-blend points, then Gauss-Lobatto points of order n
      are chosen on each edge and the interior of warp-blend
      lattice is chosen on each face and the interior.

 

Definition at line 207 of file Intrepid2_HCURL_TET_In_FEM.hpp.


Member Function Documentation








template<typename DeviceType  = void, typename outputValueType  = double, typename pointValueType  = double> 



  

  
      

        

          virtual void Intrepid2::Basis_HCURL_TET_In_FEM< DeviceType, outputValueType, pointValueType >::getDofCoeffs 
          (
          ScalarViewType 
          )
           const
        

      

  		
  
inlineoverridevirtual  
  







Coefficients for computing degrees of freedom for Lagrangian basis If P is an element of the space spanned by the basis,  := P(dofCoords(i))  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< DeviceType, outputValueType, pointValueType >.



Definition at line 272 of file Intrepid2_HCURL_TET_In_FEM.hpp.



References Intrepid2::Basis< DeviceType, outputValueType, pointValueType >::dofCoeffs_, Intrepid2::Basis< DeviceType, outputValueType, pointValueType >::getBaseCellTopology(), and Intrepid2::Basis< DeviceType, outputValueType, pointValueType >::getCardinality().













template<typename DeviceType  = void, typename outputValueType  = double, typename pointValueType  = double> 



  

  
      

        

          BasisPtr<typename Kokkos::HostSpace::device_type,outputValueType,pointValueType> Intrepid2::Basis_HCURL_TET_In_FEM< DeviceType, outputValueType, pointValueType >::getHostBasis 
          (
          )
           const
        

      

  		
  
inlineoverridevirtual  
  







Creates and returns a Basis object whose DeviceType template argument is Kokkos::HostSpace::device_type, but is otherwise identical to this. 


Returns
Pointer to the new Basis object. 



Reimplemented from Intrepid2::Basis< DeviceType, outputValueType, pointValueType >.



Definition at line 329 of file Intrepid2_HCURL_TET_In_FEM.hpp.



References Intrepid2::Basis< DeviceType, outputValueType, pointValueType >::basisDegree_, and Intrepid2::Basis_HCURL_TET_In_FEM< DeviceType, outputValueType, pointValueType >::pointType_.













template<typename DeviceType  = void, typename outputValueType  = double, typename pointValueType  = double> 



  

  
      

        

          virtual const char* Intrepid2::Basis_HCURL_TET_In_FEM< DeviceType, outputValueType, pointValueType >::getName 
          (
          )
           const
        

      

  		
  
inlineoverridevirtual  
  







Returns basis name. 


Returns
the name of the basis 



Reimplemented from Intrepid2::Basis< DeviceType, outputValueType, pointValueType >.



Definition at line 295 of file Intrepid2_HCURL_TET_In_FEM.hpp.













template<typename DeviceType  = void, typename outputValueType  = double, typename pointValueType  = double> 



  

  
      

        

          BasisPtr<DeviceType,outputValueType,pointValueType> Intrepid2::Basis_HCURL_TET_In_FEM< DeviceType, outputValueType, pointValueType >::getSubCellRefBasis 
          (
          const ordinal_type 
          subCellDim, 
        

        

          
          
          const ordinal_type 
          subCellOrd 
        

        

          
          )
           const
        

      

  		
  
inlineoverridevirtual  
  







returns the basis associated to a subCell. 


The bases of the subCell are the restriction to the subCell of the bases of the parent cell, projected to the subCell plane.


Parameters

  

    
[in]subCellDim- dimension of subCell 

    
[in]subCellOrd- position of the subCell among of the subCells having the same dimension 

  

  




Returns
pointer to the subCell basis of dimension subCellDim and position subCellOrd 



Reimplemented from Intrepid2::Basis< DeviceType, outputValueType, pointValueType >.



Definition at line 315 of file Intrepid2_HCURL_TET_In_FEM.hpp.



References Intrepid2::Basis< DeviceType, outputValueType, pointValueType >::basisDegree_, and Intrepid2::Basis_HCURL_TET_In_FEM< DeviceType, outputValueType, pointValueType >::pointType_.













template<typename DeviceType  = void, typename outputValueType  = double, typename pointValueType  = double> 



  

  
      

        

          virtual void Intrepid2::Basis_HCURL_TET_In_FEM< DeviceType, outputValueType, pointValueType >::getValues 
          (
          const ExecutionSpace & 
          , 
        

        

          
          
          OutputViewType 
          , 
        

        

          
          
          const PointViewType 
          , 
        

        

          
          
          const EOperator 
           = OPERATOR_VALUE 
        

        

          
          )
           const
        

      

  		
  
inlineoverridevirtual  
  







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.


Parameters

  

    
space[in] - execution space instance 

    
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

  

  




Remarks
For rank and dimension specifications of the output array see Section MD array template arguments for basis methods. Dimensions of ArrayScalar arguments are checked at runtime if HAVE_INTREPID2_DEBUG is defined.



A FEM basis spans a COMPLETE or INCOMPLETE polynomial space on the reference cell which is a smooth function space. Thus, all operator types that are meaningful for the approximated function space are admissible. When the order of the operator exceeds the degree of the basis, the output array is filled with the appropriate number of zeros. 



Reimplemented from Intrepid2::Basis< DeviceType, outputValueType, pointValueType >.



Definition at line 232 of file Intrepid2_HCURL_TET_In_FEM.hpp.



References Intrepid2::Basis_HCURL_TET_In_FEM< DeviceType, outputValueType, pointValueType >::coeffs_, Intrepid2::Basis< DeviceType, outputValueType, pointValueType >::getBaseCellTopology(), Intrepid2::Basis< DeviceType, outputValueType, pointValueType >::getCardinality(), and Intrepid2::Parameters::MaxNumPtsPerBasisEval.







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





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