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	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

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	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	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 &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...

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_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 ${\bf n}=(t_2,-t_1)$ where ${\bf t}=(t_1,t_2)$ is the side (edge) tangent, i.e., the choice of normal direction is such that the pair $({\bf n},{\bf t})$ 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.

Definition at line 179 of file Intrepid2_HDIV_QUAD_I1_FEM.hpp.

Member Function Documentation

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

BasisPtr<typename Kokkos::HostSpace::device_type,outputValueType,pointValueType> Intrepid2::Basis_HDIV_QUAD_I1_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 280 of file Intrepid2_HDIV_QUAD_I1_FEM.hpp.

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

virtual const char* Intrepid2::Basis_HDIV_QUAD_I1_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 251 of file Intrepid2_HDIV_QUAD_I1_FEM.hpp.

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

BasisPtr<DeviceType,outputValueType,pointValueType> Intrepid2::Basis_HDIV_QUAD_I1_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 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 271 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

Public Types

Public Member Functions

Additional Inherited Members

Detailed Description

template<typename DeviceType = void, typename outputValueType = double, typename pointValueType = double> class Intrepid2::Basis_HDIV_QUAD_I1_FEM< DeviceType, outputValueType, pointValueType >

Member Function Documentation

template<typename DeviceType = void, typename outputValueType = double, typename pointValueType = double>
class Intrepid2::Basis_HDIV_QUAD_I1_FEM< DeviceType, outputValueType, pointValueType >