Implementation of the default H(div)-compatible FEM basis of degree 1 on Quadrilateral cell. More...
#include <Intrepid2_HDIV_QUAD_I1_FEM.hpp>
Inheritance diagram for Intrepid2::Basis_HDIV_QUAD_I1_FEM< DeviceType, outputValueType, pointValueType >:
Public Types | |
| using | BasisBase = Basis< DeviceType, outputValueType, pointValueType > |
| using | OrdinalTypeArray1DHost = typename BasisBase::OrdinalTypeArray1DHost |
| using | OrdinalTypeArray2DHost = typename BasisBase::OrdinalTypeArray2DHost |
| using | OrdinalTypeArray3DHost = typename BasisBase::OrdinalTypeArray3DHost |
| using | OutputViewType = typename BasisBase::OutputViewType |
| using | PointViewType = typename BasisBase::PointViewType |
| using | ScalarViewType = typename BasisBase::ScalarViewType |
 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_HDIV_QUAD_I1_FEM () | |
| Constructor. | |
| virtual void | getValues (OutputViewType outputValues, const PointViewType inputPoints, const EOperator operatorType=OPERATOR_VALUE) const override |
| virtual void | getScratchSpaceSize (ordinal_type &perTeamSpaceSize, ordinal_type &perThreadSpaceSize, const PointViewType inputPointsconst, const EOperator operatorType=OPERATOR_VALUE) const override |
| virtual KOKKOS_INLINE_FUNCTION void | getValues (OutputViewType outputValues, const PointViewType inputPoints, const EOperator operatorType, const typename Kokkos::TeamPolicy< typename DeviceType::execution_space >::member_type &team_member, const typename DeviceType::execution_space::scratch_memory_space &scratchStorage, const ordinal_type subcellDim=-1, const ordinal_type subcellOrdinal=-1) const override |
| virtual void | getDofCoords (ScalarViewType dofCoords) const override |
| virtual void | getDofCoeffs (ScalarViewType dofCoeffs) const override |
| 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 | getScratchSpaceSize (ordinal_type &perTeamSpaceSize, ordinal_type &perThreadSpaceSize, const PointViewType inputPoints, const EOperator operatorType=OPERATOR_VALUE) const |
| Return the size of the scratch space, in bytes, needed for using the team-level implementation of getValues. More... | |
| virtual KOKKOS_INLINE_FUNCTION void | getValues (OutputViewType, const PointViewType, const EOperator, const typename Kokkos::TeamPolicy< ExecutionSpace >::member_type &teamMember, const typename ExecutionSpace::scratch_memory_space &scratchStorage, const ordinal_type subcellDim=-1, const ordinal_type subcellOrdinal=-1) const |
| Team-level evaluation of basis functions on a reference cell. More... | |
| virtual void | getValues (const ExecutionSpace &, OutputViewType, const PointViewType, const EOperator=OPERATOR_VALUE) const |
| Evaluation of a FEM basis on a reference cell. 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... | |
| 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, := P(dofCoords(i)) dofCoeffs(i) are the nodal coefficients associated to basis function i. More... | |
| 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. More... | |
| 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. More... | |
| 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. More... | |
| 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. 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... | |
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. | |
| unsigned | basisCellTopologyKey_ |
| Identifier of the 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 base topology, 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_HDIV_QUAD_I1_FEM< DeviceType, outputValueType, pointValueType >
Implementation of the default H(div)-compatible FEM basis of degree 1 on Quadrilateral cell.
Implements Raviart-Thomas basis of degree 1 on the reference Quadrilateral cell. The basis has cardinality 4 and spans a INCOMPLETE bi-linear polynomial space. Basis functions are dual to a unisolvent set of degrees-of-freedom (DoF) defined and enumerated as follows:
=================================================================================================== | | degree-of-freedom-tag table | | | DoF |----------------------------------------------------------| DoF definition | | ordinal | subc dim | subc ordinal | subc DoF ord |subc num DoF | | |=========|==============|==============|==============|=============|============================| | 0 | 1 | 0 | 0 | 1 | L_0(u) = (u.n)(0,-1) | |---------|--------------|--------------|--------------|-------------|----------------------------| | 1 | 1 | 1 | 0 | 1 | L_1(u) = (u.n)(1,0) | |---------|--------------|--------------|--------------|-------------|----------------------------| | 2 | 1 | 2 | 0 | 1 | L_2(u) = (u.n)(0,1) | |---------|--------------|--------------|--------------|-------------|----------------------------| | 3 | 1 | 3 | 0 | 1 | L_3(u) = (u.n)(-1,0) | |=========|==============|==============|==============|=============|============================| | MAX | maxScDim=2 | maxScOrd=5 | maxDfOrd=0 | - | | |=========|==============|==============|==============|=============|============================|
- Remarks
- In the DOF functional
where 
is the side (edge) tangent, i.e., the choice of normal direction is such that the pair 
is positively oriented.
- Direction of side tangents is determined by the vertex order of the sides in the cell topology and runs from side vertex 0 to side vertex 1, whereas their length is set equal to the side length. For example, side 1 of all Quadrilateral reference cells has vertex order {1,2}, i.e., its tangent runs from vertex 1 of the reference Quadrilateral to vertex 2 of that cell. On the reference Quadrilateral the coordinates of these vertices are (1,-1) and (1,1), respectively. Therefore, the tangent to side 1 is (1,1)-(1,-1) = (0,2) and the normal to that side is (2,0). Because its length already equals side length, no further rescaling of the side tangent is needed.
- The length of the side normal equals the length of the side. As a result, the DoF functional is the value of the normal component of a vector field at the side center times the side length. The resulting basis is equivalent to a basis defined by using the side flux as a DoF functional. Note that all sides of the reference Quadrilateral<> cells have length 2.
- In the DOF functional
Definition at line 146 of file Intrepid2_HDIV_QUAD_I1_FEM.hpp.
Member Function Documentation
template<typename DeviceType = void, typename outputValueType = double, typename pointValueType = double>
|
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 265 of file Intrepid2_HDIV_QUAD_I1_FEM.hpp.
template<typename DeviceType = void, typename outputValueType = double, typename pointValueType = double>
|
inlineoverridevirtual |
Returns basis name.
- Returns
- the name of the basis
Reimplemented from Intrepid2::Basis< DeviceType, outputValueType, pointValueType >.
Definition at line 236 of file Intrepid2_HDIV_QUAD_I1_FEM.hpp.
template<typename DeviceType = void, typename outputValueType = double, typename pointValueType = double>
|
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 along normal to the subCell.
- 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 256 of file Intrepid2_HDIV_QUAD_I1_FEM.hpp.
The documentation for this class was generated from the following files:
- http://docs.trilinos.org/dev/packages/intrepid2/src/Discretization/Basis/Intrepid2_HDIV_QUAD_I1_FEM.hpp
- http://docs.trilinos.org/dev/packages/intrepid2/src/Discretization/Basis/Intrepid2_HDIV_QUAD_I1_FEMDef.hpp
