Intrepid
Classes | Static Public Member Functions | List of all members
Intrepid::FunctionSpaceTools Class Reference

Defines expert-level interfaces for the evaluation of functions and operators in physical space (supported for FE, FV, and FD methods) and FE reference space; in addition, provides several function transformation utilities. More...

#include <Intrepid_FunctionSpaceTools.hpp>

Classes

struct  integrateTempSpec
 
struct  tensorMultiplyDataDataTempSpec
 
struct  tensorMultiplyDataDataTempSpec< Scalar, ArrayOutData, ArrayInDataLeft, ArrayInDataRight, 3 >
 
struct  tensorMultiplyDataDataTempSpec< Scalar, ArrayOutData, ArrayInDataLeft, ArrayInDataRight, 4 >
 
struct  tensorMultiplyDataDataTempSpec< Scalar, ArrayOutData, ArrayInDataLeft, ArrayInDataRight,-1 >
 

Static Public Member Functions

template<class Scalar , class ArrayTypeOut , class ArrayTypeIn >
static void HGRADtransformVALUE (ArrayTypeOut &outVals, const ArrayTypeIn &inVals)
 Transformation of a (scalar) value field in the H-grad space, defined at points on a reference cell, stored in the user-provided container inVals and indexed by (F,P), into the output container outVals, defined on cells in physical space and indexed by (C,F,P). More...
 
template<class Scalar , class ArrayTypeOut , class ArrayTypeJac , class ArrayTypeIn >
static void HGRADtransformGRAD (ArrayTypeOut &outVals, const ArrayTypeJac &jacobianInverse, const ArrayTypeIn &inVals, const char transpose= 'T')
 Transformation of a gradient field in the H-grad space, defined at points on a reference cell, stored in the user-provided container inVals and indexed by (F,P,D), into the output container outVals, defined on cells in physical space and indexed by (C,F,P,D). More...
 
template<class Scalar , class ArrayTypeOut , class ArrayTypeJac , class ArrayTypeIn >
static void HCURLtransformVALUE (ArrayTypeOut &outVals, const ArrayTypeJac &jacobianInverse, const ArrayTypeIn &inVals, const char transpose= 'T')
 Transformation of a (vector) value field in the H-curl space, defined at points on a reference cell, stored in the user-provided container inVals and indexed by (F,P,D), into the output container outVals, defined on cells in physical space and indexed by (C,F,P,D). More...
 
template<class Scalar , class ArrayTypeOut , class ArrayTypeJac , class ArrayTypeDet , class ArrayTypeIn >
static void HCURLtransformCURL (ArrayTypeOut &outVals, const ArrayTypeJac &jacobian, const ArrayTypeDet &jacobianDet, const ArrayTypeIn &inVals, const char transpose= 'N')
 Transformation of a curl field in the H-curl space, defined at points on a reference cell, stored in the user-provided container inVals and indexed by (F,P,D), into the output container outVals, defined on cells in physical space and indexed by (C,F,P,D). More...
 
template<class Scalar , class ArrayTypeOut , class ArrayTypeJac , class ArrayTypeDet , class ArrayTypeIn >
static void HDIVtransformVALUE (ArrayTypeOut &outVals, const ArrayTypeJac &jacobian, const ArrayTypeDet &jacobianDet, const ArrayTypeIn &inVals, const char transpose= 'N')
 Transformation of a (vector) value field in the H-div space, defined at points on a reference cell, stored in the user-provided container inVals and indexed by (F,P,D), into the output container outVals, defined on cells in physical space and indexed by (C,F,P,D). More...
 
template<class Scalar , class ArrayTypeOut , class ArrayTypeDet , class ArrayTypeIn >
static void HDIVtransformDIV (ArrayTypeOut &outVals, const ArrayTypeDet &jacobianDet, const ArrayTypeIn &inVals)
 Transformation of a divergence field in the H-div space, defined at points on a reference cell, stored in the user-provided container inVals and indexed by (F,P), into the output container outVals, defined on cells in physical space and indexed by (C,F,P). More...
 
template<class Scalar , class ArrayTypeOut , class ArrayTypeDet , class ArrayTypeIn >
static void HVOLtransformVALUE (ArrayTypeOut &outVals, const ArrayTypeDet &jacobianDet, const ArrayTypeIn &inVals)
 Transformation of a (scalar) value field in the H-vol space, defined at points on a reference cell, stored in the user-provided container inVals and indexed by (F,P), into the output container outVals, defined on cells in physical space and indexed by (C,F,P). More...
 
template<class Scalar >
static void integrate (Intrepid::FieldContainer< Scalar > &outputValues, const Intrepid::FieldContainer< Scalar > &leftValues, const Intrepid::FieldContainer< Scalar > &rightValues, const ECompEngine compEngine, const bool sumInto=false)
 Contracts leftValues and rightValues arrays on the point and possibly space dimensions and stores the result in outputValues; this is a generic, high-level integration routine that calls either FunctionSpaceTools::operatorIntegral, or FunctionSpaceTools::functionalIntegral, or FunctionSpaceTools::dataIntegral methods, depending on the rank of the outputValues array. More...
 
template<class Scalar , class ArrayOut , class ArrayInLeft , class ArrayInRight >
static void integrate (ArrayOut &outputValues, const ArrayInLeft &leftValues, const ArrayInRight &rightValues, const ECompEngine compEngine, const bool sumInto=false)
 
template<class Scalar , class ArrayOutFields , class ArrayInFieldsLeft , class ArrayInFieldsRight >
static void operatorIntegral (ArrayOutFields &outputFields, const ArrayInFieldsLeft &leftFields, const ArrayInFieldsRight &rightFields, const ECompEngine compEngine, const bool sumInto=false)
 Contracts the point (and space) dimensions P (and D1 and D2) of two rank-3, 4, or 5 containers with dimensions (C,L,P) and (C,R,P), or (C,L,P,D1) and (C,R,P,D1), or (C,L,P,D1,D2) and (C,R,P,D1,D2), and returns the result in a rank-3 container with dimensions (C,L,R). More...
 
template<class Scalar , class ArrayOutFields , class ArrayInData , class ArrayInFields >
static void functionalIntegral (ArrayOutFields &outputFields, const ArrayInData &inputData, const ArrayInFields &inputFields, const ECompEngine compEngine, const bool sumInto=false)
 Contracts the point (and space) dimensions P (and D1 and D2) of a rank-3, 4, or 5 container and a rank-2, 3, or 4 container, respectively, with dimensions (C,F,P) and (C,P), or (C,F,P,D1) and (C,P,D1), or (C,F,P,D1,D2) and (C,P,D1,D2), respectively, and returns the result in a rank-2 container with dimensions (C,F). More...
 
template<class Scalar , class ArrayOutData , class ArrayInDataLeft , class ArrayInDataRight >
static void dataIntegral (ArrayOutData &outputData, const ArrayInDataLeft &inputDataLeft, const ArrayInDataRight &inputDataRight, const ECompEngine compEngine, const bool sumInto=false)
 Contracts the point (and space) dimensions P (and D1 and D2) of two rank-2, 3, or 4 containers with dimensions (C,P), or (C,P,D1), or (C,P,D1,D2), respectively, and returns the result in a rank-1 container with dimensions (C). More...
 
template<class Scalar , class ArrayOut , class ArrayDet , class ArrayWeights >
static void computeCellMeasure (ArrayOut &outVals, const ArrayDet &inDet, const ArrayWeights &inWeights)
 Returns the weighted integration measures outVals with dimensions (C,P) used for the computation of cell integrals, by multiplying absolute values of the user-provided cell Jacobian determinants inDet with dimensions (C,P) with the user-provided integration weights inWeights with dimensions (P). More...
 
template<class Scalar , class ArrayOut , class ArrayJac , class ArrayWeights >
static void computeFaceMeasure (ArrayOut &outVals, const ArrayJac &inJac, const ArrayWeights &inWeights, const int whichFace, const shards::CellTopology &parentCell)
 Returns the weighted integration measures outVals with dimensions (C,P) used for the computation of face integrals, based on the provided cell Jacobian array inJac with dimensions (C,P,D,D) and the provided integration weights inWeights with dimensions (P). More...
 
template<class Scalar , class ArrayOut , class ArrayJac , class ArrayWeights >
static void computeEdgeMeasure (ArrayOut &outVals, const ArrayJac &inJac, const ArrayWeights &inWeights, const int whichEdge, const shards::CellTopology &parentCell)
 Returns the weighted integration measures outVals with dimensions (C,P) used for the computation of edge integrals, based on the provided cell Jacobian array inJac with dimensions (C,P,D,D) and the provided integration weights inWeights with dimensions (P). More...
 
template<class Scalar , class ArrayTypeOut , class ArrayTypeMeasure , class ArrayTypeIn >
static void multiplyMeasure (ArrayTypeOut &outVals, const ArrayTypeMeasure &inMeasure, const ArrayTypeIn &inVals)
 Multiplies fields inVals by weighted measures inMeasure and returns the field array outVals; this is a simple redirection to the call FunctionSpaceTools::scalarMultiplyDataField. More...
 
template<class Scalar , class ArrayOutFields , class ArrayInData , class ArrayInFields >
static void scalarMultiplyDataField (ArrayOutFields &outputFields, ArrayInData &inputData, ArrayInFields &inputFields, const bool reciprocal=false)
 Scalar multiplication of data and fields; please read the description below. More...
 
template<class Scalar , class ArrayOutData , class ArrayInDataLeft , class ArrayInDataRight >
static void scalarMultiplyDataData (ArrayOutData &outputData, ArrayInDataLeft &inputDataLeft, ArrayInDataRight &inputDataRight, const bool reciprocal=false)
 Scalar multiplication of data and data; please read the description below. More...
 
template<class Scalar , class ArrayOutFields , class ArrayInData , class ArrayInFields >
static void dotMultiplyDataField (ArrayOutFields &outputFields, const ArrayInData &inputData, const ArrayInFields &inputFields)
 Dot product of data and fields; please read the description below. More...
 
template<class Scalar , class ArrayOutData , class ArrayInDataLeft , class ArrayInDataRight >
static void dotMultiplyDataData (ArrayOutData &outputData, const ArrayInDataLeft &inputDataLeft, const ArrayInDataRight &inputDataRight)
 Dot product of data and data; please read the description below. More...
 
template<class Scalar , class ArrayOutFields , class ArrayInData , class ArrayInFields >
static void vectorMultiplyDataField (ArrayOutFields &outputFields, const ArrayInData &inputData, const ArrayInFields &inputFields)
 Cross or outer product of data and fields; please read the description below. More...
 
template<class Scalar , class ArrayOutData , class ArrayInDataLeft , class ArrayInDataRight >
static void vectorMultiplyDataData (ArrayOutData &outputData, const ArrayInDataLeft &inputDataLeft, const ArrayInDataRight &inputDataRight)
 Cross or outer product of data and data; please read the description below. More...
 
template<class Scalar , class ArrayOutFields , class ArrayInData , class ArrayInFields >
static void tensorMultiplyDataField (ArrayOutFields &outputFields, const ArrayInData &inputData, const ArrayInFields &inputFields, const char transpose= 'N')
 Matrix-vector or matrix-matrix product of data and fields; please read the description below. More...
 
template<class Scalar , class ArrayOutData , class ArrayInDataLeft , class ArrayInDataRight >
static void tensorMultiplyDataData (ArrayOutData &outputData, const ArrayInDataLeft &inputDataLeft, const ArrayInDataRight &inputDataRight, const char transpose= 'N')
 Matrix-vector or matrix-matrix product of data and data; please read the description below. More...
 
template<class Scalar , class ArrayTypeInOut , class ArrayTypeSign >
static void applyLeftFieldSigns (ArrayTypeInOut &inoutOperator, const ArrayTypeSign &fieldSigns)
 Applies left (row) signs, stored in the user-provided container fieldSigns and indexed by (C,L), to the operator inoutOperator indexed by (C,L,R). More...
 
template<class Scalar , class ArrayTypeInOut , class ArrayTypeSign >
static void applyRightFieldSigns (ArrayTypeInOut &inoutOperator, const ArrayTypeSign &fieldSigns)
 Applies right (column) signs, stored in the user-provided container fieldSigns and indexed by (C,R), to the operator inoutOperator indexed by (C,L,R). More...
 
template<class Scalar , class ArrayTypeInOut , class ArrayTypeSign >
static void applyFieldSigns (ArrayTypeInOut &inoutFunction, const ArrayTypeSign &fieldSigns)
 Applies field signs, stored in the user-provided container fieldSigns and indexed by (C,F), to the function inoutFunction indexed by (C,F), (C,F,P), (C,F,P,D1) or (C,F,P,D1,D2). More...
 
template<class Scalar , class ArrayOutPointVals , class ArrayInCoeffs , class ArrayInFields >
static void evaluate (ArrayOutPointVals &outPointVals, const ArrayInCoeffs &inCoeffs, const ArrayInFields &inFields)
 Computes point values outPointVals of a discrete function specified by the basis inFields and coefficients inCoeffs. More...
 

Detailed Description

Defines expert-level interfaces for the evaluation of functions and operators in physical space (supported for FE, FV, and FD methods) and FE reference space; in addition, provides several function transformation utilities.

Definition at line 69 of file Intrepid_FunctionSpaceTools.hpp.

Member Function Documentation

template<class Scalar , class ArrayTypeInOut , class ArrayTypeSign >
void Intrepid::FunctionSpaceTools::applyFieldSigns ( ArrayTypeInOut &  inoutFunction,
const ArrayTypeSign &  fieldSigns 
)
static

Applies field signs, stored in the user-provided container fieldSigns and indexed by (C,F), to the function inoutFunction indexed by (C,F), (C,F,P), (C,F,P,D1) or (C,F,P,D1,D2). 

   Returns

\[ \mbox{inoutFunction}(c,f,*) = \mbox{fieldSigns}(c,f)*\mbox{inoutFunction}(c,f,*) \]

See Section Pullbacks for discussion of field signs.

C - num. integration domains
F - num. fields
P - num. integration points
D1 - spatial dimension
D2 - spatial dimension
Parameters
inoutFunction[in/out] - Input / output function array.
fieldSigns[in] - Right field signs.

Definition at line 1636 of file Intrepid_FunctionSpaceToolsDef.hpp.

template<class Scalar , class ArrayTypeInOut , class ArrayTypeSign >
void Intrepid::FunctionSpaceTools::applyLeftFieldSigns ( ArrayTypeInOut &  inoutOperator,
const ArrayTypeSign &  fieldSigns 
)
static

Applies left (row) signs, stored in the user-provided container fieldSigns and indexed by (C,L), to the operator inoutOperator indexed by (C,L,R). 

   Mathematically, this method computes the matrix-matrix product

\[ \mathbf{K}^{c} = \mbox{diag}(\sigma^c_0,\ldots,\sigma^c_{L-1}) \mathbf{K}^c \]

where $\mathbf{K}^{c} \in \mathbf{R}^{L\times R}$ is array of matrices indexed by cell number c and stored in the rank-3 array inoutOperator, and $\{\sigma^c_l\}_{l=0}^{L-1}$ is array of left field signs indexed by cell number c and stored in the rank-2 container fieldSigns; see Section Pullbacks for discussion of field signs. This operation is required for operators generated by HCURL and HDIV-conforming vector-valued finite element basis functions; see Sections Pullbacks and Section Evaluation of finite element operators and functionals for applications of this method.

C - num. integration domains
L - num. left fields
R - num. right fields
Parameters
inoutOperator[in/out] - Input / output operator array.
fieldSigns[in] - Left field signs.

Definition at line 1585 of file Intrepid_FunctionSpaceToolsDef.hpp.

template<class Scalar , class ArrayTypeInOut , class ArrayTypeSign >
void Intrepid::FunctionSpaceTools::applyRightFieldSigns ( ArrayTypeInOut &  inoutOperator,
const ArrayTypeSign &  fieldSigns 
)
static

Applies right (column) signs, stored in the user-provided container fieldSigns and indexed by (C,R), to the operator inoutOperator indexed by (C,L,R). 

   Mathematically, this method computes the matrix-matrix product

\[ \mathbf{K}^{c} = \mathbf{K}^c \mbox{diag}(\sigma^c_0,\ldots,\sigma^c_{R-1}) \]

where $\mathbf{K}^{c} \in \mathbf{R}^{L\times R}$ is array of matrices indexed by cell number c and stored in the rank-3 container inoutOperator, and $\{\sigma^c_r\}_{r=0}^{R-1}$ is array of right field signs indexed by cell number c and stored in the rank-2 container fieldSigns; see Section Pullbacks for discussion of field signs. This operation is required for operators generated by HCURL and HDIV-conforming vector-valued finite element basis functions; see Sections Pullbacks and Section Evaluation of finite element operators and functionals for applications of this method.

C - num. integration domains
L - num. left fields
R - num. right fields
Parameters
inoutOperator[in/out] - Input / output operator array.
fieldSigns[in] - Right field signs.

Definition at line 1610 of file Intrepid_FunctionSpaceToolsDef.hpp.

template<class Scalar , class ArrayOut , class ArrayDet , class ArrayWeights >
void Intrepid::FunctionSpaceTools::computeCellMeasure ( ArrayOut &  outVals,
const ArrayDet &  inDet,
const ArrayWeights &  inWeights 
)
inlinestatic

Returns the weighted integration measures outVals with dimensions (C,P) used for the computation of cell integrals, by multiplying absolute values of the user-provided cell Jacobian determinants inDet with dimensions (C,P) with the user-provided integration weights inWeights with dimensions (P). 

     Returns a rank-2 array (C, P) array such that

\[ \mbox{outVals}(c,p) = |\mbox{det}(DF_{c}(\widehat{x}_p))|\omega_{p} \,, \]

where $\{(\widehat{x}_p,\omega_p)\}$ is a cubature rule defined on a reference cell (a set of integration points and their associated weights; see Intrepid::Cubature::getCubature for getting cubature rules on reference cells).

Warning
The user is responsible for providing input arrays with consistent data: the determinants in inDet should be evaluated at integration points on the reference cell corresponding to the weights in inWeights.
Remarks
See Intrepid::CellTools::setJacobian for computation of DF and Intrepid::CellTools::setJacobianDet for computation of its determinant.
C - num. integration domains dim0 in all containers
P - num. integration points dim1 in all containers
Parameters
outVals[out] - Output array with weighted cell measures.
inDet[in] - Input array containing determinants of cell Jacobians.
inWeights[in] - Input integration weights.

Definition at line 1337 of file Intrepid_FunctionSpaceToolsDef.hpp.

template<class Scalar , class ArrayOut , class ArrayJac , class ArrayWeights >
void Intrepid::FunctionSpaceTools::computeEdgeMeasure ( ArrayOut &  outVals,
const ArrayJac &  inJac,
const ArrayWeights &  inWeights,
const int  whichEdge,
const shards::CellTopology &  parentCell 
)
static

Returns the weighted integration measures outVals with dimensions (C,P) used for the computation of edge integrals, based on the provided cell Jacobian array inJac with dimensions (C,P,D,D) and the provided integration weights inWeights with dimensions (P). 

     Returns a rank-2 array (C, P) array such that

\[ \mbox{outVals}(c,p) = \left\|\frac{d \Phi_c(\widehat{x}_p)}{d s}\right\|\omega_{p} \,, \]

where:

  • $\{(\widehat{x}_p,\omega_p)\}$ is a cubature rule defined on reference edge $\widehat{\mathcal{E}}$, with ordinal whichEdge relative to the specified parent reference cell;
  • $ \Phi_c : R \mapsto \mathcal{E} $ is parameterization of the physical edge corresponding to $\widehat{\mathcal{E}}$; see Section Parametrization of physical 1- and 2-subcells.
Warning
The user is responsible for providing input arrays with consistent data: the Jacobians in inJac should be evaluated at integration points on the reference edge corresponding to the weights in inWeights.
Remarks
Cubature rules on reference edges are defined by a two-step process:
See Intrepid::CellTools::setJacobian for computation of DF and Intrepid::CellTools::setJacobianDet for computation of its determinant.
C - num. integration domains dim0 in all input containers
P - num. integration points dim1 in all input containers
D - spatial dimension dim2 and dim3 in Jacobian container
Parameters
outVals[out] - Output array with weighted edge measures.
inJac[in] - Input array containing cell Jacobians.
inWeights[in] - Input integration weights.
whichEdge[in] - Index of the edge subcell relative to the parent cell; defines the domain of integration.
parentCell[in] - Parent cell topology.

Definition at line 1389 of file Intrepid_FunctionSpaceToolsDef.hpp.

References Intrepid::CellTools< Scalar >::getPhysicalEdgeTangents(), and Intrepid::RealSpaceTools< Scalar >::vectorNorm().

template<class Scalar , class ArrayOut , class ArrayJac , class ArrayWeights >
void Intrepid::FunctionSpaceTools::computeFaceMeasure ( ArrayOut &  outVals,
const ArrayJac &  inJac,
const ArrayWeights &  inWeights,
const int  whichFace,
const shards::CellTopology &  parentCell 
)
static

Returns the weighted integration measures outVals with dimensions (C,P) used for the computation of face integrals, based on the provided cell Jacobian array inJac with dimensions (C,P,D,D) and the provided integration weights inWeights with dimensions (P). 

     Returns a rank-2 array (C, P) array such that

\[ \mbox{outVals}(c,p) = \left\|\frac{\partial\Phi_c(\widehat{x}_p)}{\partial u}\times \frac{\partial\Phi_c(\widehat{x}_p)}{\partial v}\right\|\omega_{p} \,, \]

where:

  • $\{(\widehat{x}_p,\omega_p)\}$ is a cubature rule defined on reference face $\widehat{\mathcal{F}}$, with ordinal whichFace relative to the specified parent reference cell;
  • $ \Phi_c : R \mapsto \mathcal{F} $ is parameterization of the physical face corresponding to $\widehat{\mathcal{F}}$; see Section Parametrization of physical 1- and 2-subcells.
Warning
The user is responsible for providing input arrays with consistent data: the Jacobians in inJac should be evaluated at integration points on the reference face corresponding to the weights in inWeights.
Remarks
Cubature rules on reference faces are defined by a two-step process:
  • A cubature rule is defined on the parametrization domain R of the face (R is the standard 2-simplex {(0,0),(1,0),(0,1)} or the standard 2-cube [-1,1] X [-1,1]).
  • The points are mapped to a reference face using Intrepid::CellTools::mapToReferenceSubcell
See Intrepid::CellTools::setJacobian for computation of DF and Intrepid::CellTools::setJacobianDet for computation of its determinant.
C - num. integration domains dim0 in all input containers
P - num. integration points dim1 in all input containers
D - spatial dimension dim2 and dim3 in Jacobian container
Parameters
outVals[out] - Output array with weighted face measures.
inJac[in] - Input array containing cell Jacobians.
inWeights[in] - Input integration weights.
whichFace[in] - Index of the face subcell relative to the parent cell; defines the domain of integration.
parentCell[in] - Parent cell topology.

Definition at line 1360 of file Intrepid_FunctionSpaceToolsDef.hpp.

References Intrepid::CellTools< Scalar >::getPhysicalFaceNormals(), and Intrepid::RealSpaceTools< Scalar >::vectorNorm().

template<class Scalar , class ArrayOutData , class ArrayInDataLeft , class ArrayInDataRight >
void Intrepid::FunctionSpaceTools::dataIntegral ( ArrayOutData &  outputData,
const ArrayInDataLeft &  inputDataLeft,
const ArrayInDataRight &  inputDataRight,
const ECompEngine  compEngine,
const bool  sumInto = false 
)
static

Contracts the point (and space) dimensions P (and D1 and D2) of two rank-2, 3, or 4 containers with dimensions (C,P), or (C,P,D1), or (C,P,D1,D2), respectively, and returns the result in a rank-1 container with dimensions (C).

C - num. integration domains dim0 in both input containers
P - num. integration points dim1 in both input containers
D1 - first spatial (tensor) dimension index dim2 in both input containers
D2 - second spatial (tensor) dimension index dim3 in both input containers
Parameters
outputData[out] - Output data array.
inputDataLeft[in] - Left data input array.
inputDataRight[in] - Right data input array.
compEngine[in] - Computational engine.
sumInto[in] - If TRUE, sum into given output array, otherwise overwrite it. Default: FALSE.

Definition at line 1307 of file Intrepid_FunctionSpaceToolsDef.hpp.

template<class Scalar , class ArrayOutData , class ArrayInDataLeft , class ArrayInDataRight >
void Intrepid::FunctionSpaceTools::dotMultiplyDataData ( ArrayOutData &  outputData,
const ArrayInDataLeft &  inputDataLeft,
const ArrayInDataRight &  inputDataRight 
)
static

Dot product of data and data; please read the description below. 

   There are two use cases:
   \li
   dot product of a rank-2, 3 or 4 container \a <b>inputDataRight</b> with dimensions (C,P)
   (C,P,D1) or (C,P,D1,D2), representing the values of a scalar, vector or a
   tensor set of data, by the values in a rank-2, 3 or 4 container \a <b>inputDataLeft</b> indexed by
   (C,P), (C,P,D1), or (C,P,D1,D2) representing the values of scalar, vector or
   tensor data, OR
   \li
   dot product of a rank-2, 3 or 4 container \a <b>inputDataRight</b> with dimensions (P),
   (P,D1) or (P,D1,D2), representing the values of scalar, vector or tensor
   data, by the values in a rank-2 container \a <b>inputDataLeft</b> indexed by (C,P), (C,P,D1) or
   (C,P,D1,D2), representing the values of scalar, vector, or tensor data;
   the output value container \a <b>outputData</b> is indexed by (C,P),
   regardless of which of the two use cases is considered.

   For input fields containers without a dimension index, this operation reduces to
   scalar multiplication.
C - num. integration domains
P - num. integration points
D1 - first spatial (tensor) dimension index
D2 - second spatial (tensor) dimension index
Parameters
outputData[out] - Output (dot product) data array.
inputDataLeft[in] - Left input data array.
inputDataRight[in] - Right input data array.

Definition at line 1461 of file Intrepid_FunctionSpaceToolsDef.hpp.

template<class Scalar , class ArrayOutFields , class ArrayInData , class ArrayInFields >
void Intrepid::FunctionSpaceTools::dotMultiplyDataField ( ArrayOutFields &  outputFields,
const ArrayInData &  inputData,
const ArrayInFields &  inputFields 
)
static

Dot product of data and fields; please read the description below. 

   There are two use cases:
   \li
   dot product of a rank-3, 4 or 5 container \a <b>inputFields</b> with dimensions (C,F,P)
   (C,F,P,D1) or (C,F,P,D1,D2), representing the values of a set of scalar, vector
   or tensor fields, by the values in a rank-2, 3 or 4 container \a <b>inputData</b> indexed by
   (C,P), (C,P,D1), or (C,P,D1,D2) representing the values of scalar, vector or
   tensor data, OR
   \li
   dot product of a rank-2, 3 or 4 container \a <b>inputFields</b> with dimensions (F,P),
   (F,P,D1) or (F,P,D1,D2), representing the values of a scalar, vector or tensor
   field, by the values in a rank-2 container \a <b>inputData</b> indexed by (C,P), (C,P,D1) or
   (C,P,D1,D2), representing the values of scalar, vector or tensor data;
   the output value container \a <b>outputFields</b> is indexed by (C,F,P),
   regardless of which of the two use cases is considered.

   For input fields containers without a dimension index, this operation reduces to
   scalar multiplication.
C - num. integration domains
F - num. fields
P - num. integration points
D1 - first spatial (tensor) dimension index
D2 - second spatial (tensor) dimension index
Parameters
outputFields[out] - Output (dot product) fields array.
inputData[in] - Data array.
inputFields[in] - Input fields array.

Definition at line 1451 of file Intrepid_FunctionSpaceToolsDef.hpp.

template<class Scalar , class ArrayOutPointVals , class ArrayInCoeffs , class ArrayInFields >
void Intrepid::FunctionSpaceTools::evaluate ( ArrayOutPointVals &  outPointVals,
const ArrayInCoeffs &  inCoeffs,
const ArrayInFields &  inFields 
)
static

Computes point values outPointVals of a discrete function specified by the basis inFields and coefficients inCoeffs. 

   The array \a <b>inFields</b> with dimensions (C,F,P), (C,F,P,D1),
   or (C,F,P,D1,D2) represents the signed, transformed field (basis) values at
   points in REFERENCE frame; the \a <b>outPointVals</b> array with
   dimensions (C,P), (C,P,D1), or (C,P,D1,D2), respectively, represents
   values of a discrete function at points in PHYSICAL frame.
   The array \a <b>inCoeffs</b> dimensioned (C,F) supplies the coefficients
   for the field (basis) array.

   Returns rank-2,3 or 4 array such that

\[ outPointValues(c,p,*) = \sum_{f=0}^{F-1} \sigma_{c,f} u_{c,f}(x_p) \]

where $\{u_{c,f}\}_{f=0}^{F-1} $ is scalar, vector or tensor valued finite element basis defined on physical cell $\mathcal{C}$ and $\{\sigma_{c,f}\}_{f=0}^{F-1} $ are the field signs of the basis functions; see Section Pullbacks. This method implements the last step in a four step process; please see Section Evaluation of finite element fields for details about the first three steps that prepare the necessary data for this method.

C - num. integration domains
F - num. fields
P - num. integration points
D1 - spatial dimension
D2 - spatial dimension
Parameters
outPointVals[out] - Output point values of a discrete function.
inCoeffs[in] - Coefficients associated with the fields (basis) array.
inFields[in] - Field (basis) values.

Definition at line 1729 of file Intrepid_FunctionSpaceToolsDef.hpp.

template<class Scalar , class ArrayOutFields , class ArrayInData , class ArrayInFields >
void Intrepid::FunctionSpaceTools::functionalIntegral ( ArrayOutFields &  outputFields,
const ArrayInData &  inputData,
const ArrayInFields &  inputFields,
const ECompEngine  compEngine,
const bool  sumInto = false 
)
static

Contracts the point (and space) dimensions P (and D1 and D2) of a rank-3, 4, or 5 container and a rank-2, 3, or 4 container, respectively, with dimensions (C,F,P) and (C,P), or (C,F,P,D1) and (C,P,D1), or (C,F,P,D1,D2) and (C,P,D1,D2), respectively, and returns the result in a rank-2 container with dimensions (C,F). 

      For a fixed index "C", (C,F) represents a (column) vector of length F.
C - num. integration domains dim0 in both input containers
F - num. fields dim1 in fields input container
P - num. integration points dim2 in fields input container and dim1 in tensor data container
D1 - first spatial (tensor) dimension index dim3 in fields input container and dim2 in tensor data container
D2 - second spatial (tensor) dimension index dim4 in fields input container and dim3 in tensor data container
Parameters
outputFields[out] - Output fields array.
inputData[in] - Data array.
inputFields[in] - Input fields array.
compEngine[in] - Computational engine.
sumInto[in] - If TRUE, sum into given output array, otherwise overwrite it. Default: FALSE.

Definition at line 1277 of file Intrepid_FunctionSpaceToolsDef.hpp.

template<class Scalar , class ArrayTypeOut , class ArrayTypeJac , class ArrayTypeDet , class ArrayTypeIn >
void Intrepid::FunctionSpaceTools::HCURLtransformCURL ( ArrayTypeOut &  outVals,
const ArrayTypeJac &  jacobian,
const ArrayTypeDet &  jacobianDet,
const ArrayTypeIn &  inVals,
const char  transpose = 'N' 
)
static

Transformation of a curl field in the H-curl space, defined at points on a reference cell, stored in the user-provided container inVals and indexed by (F,P,D), into the output container outVals, defined on cells in physical space and indexed by (C,F,P,D). 

     Computes pullback of curls of \e HCURL functions

$\Phi^*(\widehat{\bf u}_f) = \left(J^{-1}_{c} DF_{c}\cdot\nabla\times\widehat{\bf u}_f\right)\circ F^{-1}_{c}$ for points in one or more physical cells that are images of a given set of points in the reference cell:

\[ \{ x_{c,p} \}_{p=0}^P = \{ F_{c} (\widehat{x}_p) \}_{p=0}^{P}\qquad 0\le c < C \,. \]

In this case $ F^{-1}_{c}(x_{c,p}) = \widehat{x}_p $ and the user-provided container should contain the curls of the vector function set $\{\widehat{\bf u}_f\}_{f=0}^{F}$ at the reference points:

\[ inVals(f,p,*) = \nabla\times\widehat{\bf u}_f(\widehat{x}_p) \,. \]

The method returns

\[ outVals(c,f,p,*) = \left(J^{-1}_{c} DF_{c}\cdot\nabla\times\widehat{\bf u}_f\right)\circ F^{-1}_{c}(x_{c,p}) = J^{-1}_{c}(\widehat{x}_p) DF_{c}(\widehat{x}_p)\cdot\nabla\times\widehat{\bf u}_f(\widehat{x}_p) \qquad 0\le c < C \,. \]

See Section Pullbacks for more details about pullbacks.

|------|----------------------|--------------------------------------------------|
| | Index | Dimension |
|------|----------------------|--------------------------------------------------|
| C | cell | 0 <= C < num. integration domains |
| F | field | 0 <= F < dim. of the basis |
| P | point | 0 <= P < num. integration points |
| D | space dim | 0 <= D < spatial dimension |
|------|----------------------|--------------------------------------------------|

Definition at line 81 of file Intrepid_FunctionSpaceToolsDef.hpp.

template<class Scalar , class ArrayTypeOut , class ArrayTypeJac , class ArrayTypeIn >
void Intrepid::FunctionSpaceTools::HCURLtransformVALUE ( ArrayTypeOut &  outVals,
const ArrayTypeJac &  jacobianInverse,
const ArrayTypeIn &  inVals,
const char  transpose = 'T' 
)
static

Transformation of a (vector) value field in the H-curl space, defined at points on a reference cell, stored in the user-provided container inVals and indexed by (F,P,D), into the output container outVals, defined on cells in physical space and indexed by (C,F,P,D). 

     Computes pullback of \e HCURL functions

$\Phi^*(\widehat{\bf u}_f) = \left((DF_c)^{-{\sf T}}\cdot\widehat{\bf u}_f\right)\circ F^{-1}_{c}$ for points in one or more physical cells that are images of a given set of points in the reference cell:

\[ \{ x_{c,p} \}_{p=0}^P = \{ F_{c} (\widehat{x}_p) \}_{p=0}^{P}\qquad 0\le c < C \,. \]

In this case $ F^{-1}_{c}(x_{c,p}) = \widehat{x}_p $ and the user-provided container should contain the values of the vector function set $\{\widehat{\bf u}_f\}_{f=0}^{F}$ at the reference points:

\[ inVals(f,p,*) = \widehat{\bf u}_f(\widehat{x}_p) \,. \]

The method returns

\[ outVals(c,f,p,*) = \left((DF_c)^{-{\sf T}}\cdot\widehat{\bf u}_f\right)\circ F^{-1}_{c}(x_{c,p}) = (DF_c)^{-{\sf T}}(\widehat{x}_p)\cdot\widehat{\bf u}_f(\widehat{x}_p) \qquad 0\le c < C \,. \]

See Section Pullbacks for more details about pullbacks.

|------|----------------------|--------------------------------------------------|
| | Index | Dimension |
|------|----------------------|--------------------------------------------------|
| C | cell | 0 <= C < num. integration domains |
| F | field | 0 <= F < dim. of native basis |
| P | point | 0 <= P < num. integration points |
| D | space dim | 0 <= D < spatial dimension |
|------|----------------------|--------------------------------------------------|

Definition at line 71 of file Intrepid_FunctionSpaceToolsDef.hpp.

template<class Scalar , class ArrayTypeOut , class ArrayTypeDet , class ArrayTypeIn >
void Intrepid::FunctionSpaceTools::HDIVtransformDIV ( ArrayTypeOut &  outVals,
const ArrayTypeDet &  jacobianDet,
const ArrayTypeIn &  inVals 
)
static

Transformation of a divergence field in the H-div space, defined at points on a reference cell, stored in the user-provided container inVals and indexed by (F,P), into the output container outVals, defined on cells in physical space and indexed by (C,F,P). 

     Computes pullback of the divergence of \e HDIV functions

$\Phi^*(\widehat{\bf u}_f) = \left(J^{-1}_{c}\nabla\cdot\widehat{\bf u}_{f}\right) \circ F^{-1}_{c} $ for points in one or more physical cells that are images of a given set of points in the reference cell:

\[ \{ x_{c,p} \}_{p=0}^P = \{ F_{c} (\widehat{x}_p) \}_{p=0}^{P}\qquad 0\le c < C \,. \]

In this case $ F^{-1}_{c}(x_{c,p}) = \widehat{x}_p $ and the user-provided container should contain the divergencies of the vector function set $\{\widehat{\bf u}_f\}_{f=0}^{F}$ at the reference points:

\[ inVals(f,p) = \nabla\cdot\widehat{\bf u}_f(\widehat{x}_p) \,. \]

The method returns

\[ outVals(c,f,p,*) = \left(J^{-1}_{c}\nabla\cdot\widehat{\bf u}_{f}\right) \circ F^{-1}_{c} (x_{c,p}) = J^{-1}_{c}(\widehat{x}_p) \nabla\cdot\widehat{\bf u}_{f} (\widehat{x}_p) \qquad 0\le c < C \,. \]

See Section Pullbacks for more details about pullbacks.

|------|----------------------|--------------------------------------------------|
| | Index | Dimension |
|------|----------------------|--------------------------------------------------|
| C | cell | 0 <= C < num. integration domains |
| F | field | 0 <= F < dim. of the basis |
| P | point | 0 <= P < num. integration points |
|------|----------------------|--------------------------------------------------|

Definition at line 105 of file Intrepid_FunctionSpaceToolsDef.hpp.

template<class Scalar , class ArrayTypeOut , class ArrayTypeJac , class ArrayTypeDet , class ArrayTypeIn >
void Intrepid::FunctionSpaceTools::HDIVtransformVALUE ( ArrayTypeOut &  outVals,
const ArrayTypeJac &  jacobian,
const ArrayTypeDet &  jacobianDet,
const ArrayTypeIn &  inVals,
const char  transpose = 'N' 
)
static

Transformation of a (vector) value field in the H-div space, defined at points on a reference cell, stored in the user-provided container inVals and indexed by (F,P,D), into the output container outVals, defined on cells in physical space and indexed by (C,F,P,D). 

     Computes pullback of \e HDIV functions

$\Phi^*(\widehat{\bf u}_f) = \left(J^{-1}_{c} DF_{c}\cdot\widehat{\bf u}_f\right)\circ F^{-1}_{c} $ for points in one or more physical cells that are images of a given set of points in the reference cell:

\[ \{ x_{c,p} \}_{p=0}^P = \{ F_{c} (\widehat{x}_p) \}_{p=0}^{P}\qquad 0\le c < C \,. \]

In this case $ F^{-1}_{c}(x_{c,p}) = \widehat{x}_p $ and the user-provided container should contain the values of the vector function set $\{\widehat{\bf u}_f\}_{f=0}^{F}$ at the reference points:

\[ inVals(f,p,*) = \widehat{\bf u}_f(\widehat{x}_p) \,. \]

The method returns

\[ outVals(c,f,p,*) = \left(J^{-1}_{c} DF_{c}\cdot \widehat{\bf u}_f\right)\circ F^{-1}_{c}(x_{c,p}) = J^{-1}_{c}(\widehat{x}_p) DF_{c}(\widehat{x}_p)\cdot\widehat{\bf u}_f(\widehat{x}_p) \qquad 0\le c < C \,. \]

See Section Pullbacks for more details about pullbacks.

|------|----------------------|--------------------------------------------------|
| | Index | Dimension |
|------|----------------------|--------------------------------------------------|
| C | cell | 0 <= C < num. integration domains |
| F | field | 0 <= F < dim. of the basis |
| P | point | 0 <= P < num. integration points |
| D | space dim | 0 <= D < spatial dimension |
|------|----------------------|--------------------------------------------------|

Definition at line 93 of file Intrepid_FunctionSpaceToolsDef.hpp.

template<class Scalar , class ArrayTypeOut , class ArrayTypeJac , class ArrayTypeIn >
void Intrepid::FunctionSpaceTools::HGRADtransformGRAD ( ArrayTypeOut &  outVals,
const ArrayTypeJac &  jacobianInverse,
const ArrayTypeIn &  inVals,
const char  transpose = 'T' 
)
static

Transformation of a gradient field in the H-grad space, defined at points on a reference cell, stored in the user-provided container inVals and indexed by (F,P,D), into the output container outVals, defined on cells in physical space and indexed by (C,F,P,D). 

     Computes pullback of gradients of \e HGRAD functions

$\Phi^*(\nabla\widehat{u}_f) = \left((DF_c)^{-{\sf T}}\cdot\nabla\widehat{u}_f\right)\circ F^{-1}_{c}$ for points in one or more physical cells that are images of a given set of points in the reference cell:

\[ \{ x_{c,p} \}_{p=0}^P = \{ F_{c} (\widehat{x}_p) \}_{p=0}^{P}\qquad 0\le c < C \,. \]

In this case $ F^{-1}_{c}(x_{c,p}) = \widehat{x}_p $ and the user-provided container should contain the gradients of the function set $\{\widehat{u}_f\}_{f=0}^{F}$ at the reference points:

\[ inVals(f,p,*) = \nabla\widehat{u}_f(\widehat{x}_p) \,. \]

The method returns

\[ outVals(c,f,p,*) = \left((DF_c)^{-{\sf T}}\cdot\nabla\widehat{u}_f\right)\circ F^{-1}_{c}(x_{c,p}) = (DF_c)^{-{\sf T}}(\widehat{x}_p)\cdot\nabla\widehat{u}_f(\widehat{x}_p) \qquad 0\le c < C \,. \]

See Section Pullbacks for more details about pullbacks.

|------|----------------------|--------------------------------------------------|
| | Index | Dimension |
|------|----------------------|--------------------------------------------------|
| C | cell | 0 <= C < num. integration domains |
| F | field | 0 <= F < dim. of the basis |
| P | point | 0 <= P < num. integration points |
| D | space dim | 0 <= D < spatial dimension |
|------|----------------------|--------------------------------------------------|

Definition at line 61 of file Intrepid_FunctionSpaceToolsDef.hpp.

template<class Scalar , class ArrayTypeOut , class ArrayTypeIn >
void Intrepid::FunctionSpaceTools::HGRADtransformVALUE ( ArrayTypeOut &  outVals,
const ArrayTypeIn &  inVals 
)
static

Transformation of a (scalar) value field in the H-grad space, defined at points on a reference cell, stored in the user-provided container inVals and indexed by (F,P), into the output container outVals, defined on cells in physical space and indexed by (C,F,P). 

     Computes pullback of \e HGRAD functions \form#242 
     for points in one or more physical cells that are images of a given set of points in the reference cell:

\[ \{ x_{c,p} \}_{p=0}^P = \{ F_{c} (\widehat{x}_p) \}_{p=0}^{P}\qquad 0\le c < C \,. \]

In this case $ F^{-1}_{c}(x_{c,p}) = \widehat{x}_p $ and the user-provided container should contain the values of the function set $\{\widehat{u}_f\}_{f=0}^{F}$ at the reference points:

\[ inVals(f,p) = \widehat{u}_f(\widehat{x}_p) \,. \]

The method returns

\[ outVals(c,f,p) = \widehat{u}_f\circ F^{-1}_{c}(x_{c,p}) = \widehat{u}_f(\widehat{x}_p) = inVals(f,p) \qquad 0\le c < C \,, \]

i.e., it simply replicates the values in the user-provided container to every cell. See Section Pullbacks for more details about pullbacks.

|------|----------------------|--------------------------------------------------|
| | Index | Dimension |
|------|----------------------|--------------------------------------------------|
| C | cell | 0 <= C < num. integration domains |
| F | field | 0 <= F < dim. of the basis |
| P | point | 0 <= P < num. integration points |
|------|----------------------|--------------------------------------------------|

Definition at line 53 of file Intrepid_FunctionSpaceToolsDef.hpp.

template<class Scalar , class ArrayTypeOut , class ArrayTypeDet , class ArrayTypeIn >
void Intrepid::FunctionSpaceTools::HVOLtransformVALUE ( ArrayTypeOut &  outVals,
const ArrayTypeDet &  jacobianDet,
const ArrayTypeIn &  inVals 
)
static

Transformation of a (scalar) value field in the H-vol space, defined at points on a reference cell, stored in the user-provided container inVals and indexed by (F,P), into the output container outVals, defined on cells in physical space and indexed by (C,F,P). 

     Computes pullback of \e HVOL functions

$\Phi^*(\widehat{u}_f) = \left(J^{-1}_{c}\widehat{u}_{f}\right) \circ F^{-1}_{c} $ for points in one or more physical cells that are images of a given set of points in the reference cell:

\[ \{ x_{c,p} \}_{p=0}^P = \{ F_{c} (\widehat{x}_p) \}_{p=0}^{P}\qquad 0\le c < C \,. \]

In this case $ F^{-1}_{c}(x_{c,p}) = \widehat{x}_p $ and the user-provided container should contain the values of the functions in the set $\{\widehat{\bf u}_f\}_{f=0}^{F}$ at the reference points:

\[ inVals(f,p) = \widehat{u}_f(\widehat{x}_p) \,. \]

The method returns

\[ outVals(c,f,p,*) = \left(J^{-1}_{c}\widehat{u}_{f}\right) \circ F^{-1}_{c} (x_{c,p}) = J^{-1}_{c}(\widehat{x}_p) \widehat{u}_{f} (\widehat{x}_p) \qquad 0\le c < C \,. \]

See Section Pullbacks for more details about pullbacks.

|------|----------------------|--------------------------------------------------|
| | Index | Dimension |
|------|----------------------|--------------------------------------------------|
| C | cell | 0 <= C < num. integration domains |
| F | field | 0 <= F < dim. of the basis |
| P | point | 0 <= P < num. integration points |
|------|----------------------|--------------------------------------------------|

Definition at line 114 of file Intrepid_FunctionSpaceToolsDef.hpp.

template<class Scalar >
void Intrepid::FunctionSpaceTools::integrate ( Intrepid::FieldContainer< Scalar > &  outputValues,
const Intrepid::FieldContainer< Scalar > &  leftValues,
const Intrepid::FieldContainer< Scalar > &  rightValues,
const ECompEngine  compEngine,
const bool  sumInto = false 
)
static

Contracts leftValues and rightValues arrays on the point and possibly space dimensions and stores the result in outputValues; this is a generic, high-level integration routine that calls either FunctionSpaceTools::operatorIntegral, or FunctionSpaceTools::functionalIntegral, or FunctionSpaceTools::dataIntegral methods, depending on the rank of the outputValues array.

Parameters
outputValues[out] - Output array.
leftValues[in] - Left input array.
rightValues[in] - Right input array.
compEngine[in] - Computational engine.
sumInto[in] - If TRUE, sum into given output array, otherwise overwrite it. Default: FALSE.

Definition at line 122 of file Intrepid_FunctionSpaceToolsDef.hpp.

References Intrepid::FieldContainer< Scalar, ArrayTypeId >::dimension(), and Intrepid::FieldContainer< Scalar, ArrayTypeId >::rank().

template<class Scalar , class ArrayTypeOut , class ArrayTypeMeasure , class ArrayTypeIn >
void Intrepid::FunctionSpaceTools::multiplyMeasure ( ArrayTypeOut &  outVals,
const ArrayTypeMeasure &  inMeasure,
const ArrayTypeIn &  inVals 
)
static

Multiplies fields inVals by weighted measures inMeasure and returns the field array outVals; this is a simple redirection to the call FunctionSpaceTools::scalarMultiplyDataField.

Parameters
outVals[out] - Output array with scaled field values.
inMeasure[in] - Input array containing weighted measures.
inVals[in] - Input fields.

Definition at line 1419 of file Intrepid_FunctionSpaceToolsDef.hpp.

template<class Scalar , class ArrayOutFields , class ArrayInFieldsLeft , class ArrayInFieldsRight >
void Intrepid::FunctionSpaceTools::operatorIntegral ( ArrayOutFields &  outputFields,
const ArrayInFieldsLeft &  leftFields,
const ArrayInFieldsRight &  rightFields,
const ECompEngine  compEngine,
const bool  sumInto = false 
)
static

Contracts the point (and space) dimensions P (and D1 and D2) of two rank-3, 4, or 5 containers with dimensions (C,L,P) and (C,R,P), or (C,L,P,D1) and (C,R,P,D1), or (C,L,P,D1,D2) and (C,R,P,D1,D2), and returns the result in a rank-3 container with dimensions (C,L,R). 

     For a fixed index "C", (C,L,R) represents a rectangular L X R matrix
     where L and R may be different.
C - num. integration domains dim0 in both input containers
L - num. "left" fields dim1 in "left" container
R - num. "right" fields dim1 in "right" container
P - num. integration points dim2 in both input containers
D1- vector (1st tensor) dimension dim3 in both input containers
D2- 2nd tensor dimension dim4 in both input containers
Parameters
outputFields[out] - Output array.
leftFields[in] - Left input array.
rightFields[in] - Right input array.
compEngine[in] - Computational engine.
sumInto[in] - If TRUE, sum into given output array, otherwise overwrite it. Default: FALSE.

Definition at line 1246 of file Intrepid_FunctionSpaceToolsDef.hpp.

template<class Scalar , class ArrayOutData , class ArrayInDataLeft , class ArrayInDataRight >
void Intrepid::FunctionSpaceTools::scalarMultiplyDataData ( ArrayOutData &  outputData,
ArrayInDataLeft &  inputDataLeft,
ArrayInDataRight &  inputDataRight,
const bool  reciprocal = false 
)
static

Scalar multiplication of data and data; please read the description below. 

   There are two use cases:
   \li
   multiplies a rank-2, 3, or 4 container \a <b>inputDataRight</b> with dimensions (C,P),
   (C,P,D1) or (C,P,D1,D2), representing the values of a set of scalar, vector
   or tensor data, by the values in a rank-2 container \a <b>inputDataLeft</b> indexed by (C,P),
   representing the values of scalar data, OR
   \li
   multiplies a rank-1, 2, or 3 container \a <b>inputDataRight</b> with dimensions (P),
   (P,D1) or (P,D1,D2), representing the values of scalar, vector or
   tensor data, by the values in a rank-2 container \a <b>inputDataLeft</b> indexed by (C,P),
   representing the values of scalar data;
   the output value container \a <b>outputData</b> is indexed by (C,P), (C,P,D1) or (C,P,D1,D2),
   regardless of which of the two use cases is considered.
C - num. integration domains
P - num. integration points
D1 - first spatial (tensor) dimension index
D2 - second spatial (tensor) dimension index
Note
The arguments inputDataLeft, inputDataRight can be changed! This enables in-place multiplication.
Parameters
outputData[out] - Output data array.
inputDataLeft[in] - Left (multiplying) data array.
inputDataRight[in] - Right (being multiplied) data array.
reciprocal[in] - If TRUE, divides input fields by the data (instead of multiplying). Default: FALSE.

Definition at line 1440 of file Intrepid_FunctionSpaceToolsDef.hpp.

template<class Scalar , class ArrayOutFields , class ArrayInData , class ArrayInFields >
void Intrepid::FunctionSpaceTools::scalarMultiplyDataField ( ArrayOutFields &  outputFields,
ArrayInData &  inputData,
ArrayInFields &  inputFields,
const bool  reciprocal = false 
)
static

Scalar multiplication of data and fields; please read the description below. 

   There are two use cases:
   \li
   multiplies a rank-3, 4, or 5 container \a <b>inputFields</b> with dimensions (C,F,P),
   (C,F,P,D1) or (C,F,P,D1,D2), representing the values of a set of scalar, vector
   or tensor fields, by the values in a rank-2 container \a <b>inputData</b> indexed by (C,P),
   representing the values of scalar data, OR
   \li
   multiplies a rank-2, 3, or 4 container \a <b>inputFields</b> with dimensions (F,P),
   (F,P,D1) or (F,P,D1,D2), representing the values of a scalar, vector or a
   tensor field, by the values in a rank-2 container \a <b>inputData</b> indexed by (C,P),
   representing the values of scalar data;
   the output value container \a <b>outputFields</b> is indexed by (C,F,P), (C,F,P,D1)
   or (C,F,P,D1,D2), regardless of which of the two use cases is considered.
C - num. integration domains
F - num. fields
P - num. integration points
D1 - first spatial (tensor) dimension index
D2 - second spatial (tensor) dimension index
Note
The argument inputFields can be changed! This enables in-place multiplication.
Parameters
outputFields[out] - Output (product) fields array.
inputData[in] - Data (multiplying) array.
inputFields[in] - Input (being multiplied) fields array.
reciprocal[in] - If TRUE, divides input fields by the data (instead of multiplying). Default: FALSE.

Definition at line 1429 of file Intrepid_FunctionSpaceToolsDef.hpp.

template<class Scalar , class ArrayOutData , class ArrayInDataLeft , class ArrayInDataRight >
void Intrepid::FunctionSpaceTools::tensorMultiplyDataData ( ArrayOutData &  outputData,
const ArrayInDataLeft &  inputDataLeft,
const ArrayInDataRight &  inputDataRight,
const char  transpose = 'N' 
)
static

Matrix-vector or matrix-matrix product of data and data; please read the description below. 

   There are four use cases:
   \li
   matrix-vector product of a rank-3 container \a <b>inputDataRight</b> with dimensions (C,P,D),
   representing the values of a set of vector data, on the left by the values in a rank-2, 3, or 4
   container \a <b>inputDataLeft</b> indexed by (C,P), (C,P,D) or (C,P,D,D), respectively,
   representing the values of tensor data, OR
   \li
   matrix-vector product of a rank-2 container \a <b>inputDataRight</b> with dimensions (P,D),
   representing the values of vector data, on the left by the values in a rank-2, 3, or 4
   container \a <b>inputDataLeft</b> indexed by (C,P), (C,P,D) or (C,P,D,D), respectively,
   representing the values of tensor data, OR
   \li
   matrix-matrix product of a rank-4 container \a <b>inputDataRight</b> with dimensions (C,P,D,D),
   representing the values of a set of tensor data, on the left by the values in a rank-2, 3, or 4
   container \a <b>inputDataLeft</b> indexed by (C,P), (C,P,D) or (C,P,D,D), respectively,
   representing the values of tensor data, OR
   \li
   matrix-matrix product of a rank-3 container \a <b>inputDataRight</b> with dimensions (P,D,D),
   representing the values of tensor data, on the left by the values in a rank-2, 3, or 4
   container \a <b>inputDataLeft</b> indexed by (C,P), (C,P,D) or (C,P,D,D), respectively,
   representing the values of tensor data;
   for matrix-vector products, the output value container \a <b>outputData</b>
   is indexed by (C,P,D);
   for matrix-matrix products, the output value container \a <b>outputData</b>
   is indexed by (C,P,D1,D2).
Remarks
The rank of inputDataLeft implicitly defines the type of tensor data:
  • rank = 2 corresponds to a constant diagonal tensor $ diag(a,\ldots,a) $
  • rank = 3 corresponds to a nonconstant diagonal tensor $ diag(a_1,\ldots,a_d) $
  • rank = 4 corresponds to a full tensor $ \{a_{ij}\}$
Note
It is assumed that all tensors are square!
The method is defined for spatial dimensions D = 1, 2, 3
C - num. integration domains
P - num. integration points
D - spatial dimension
Parameters
outputData[out] - Output (matrix-vector product) data array.
inputDataLeft[in] - Left input data array.
inputDataRight[in] - Right input data array.
transpose[in] - If 'T', use transposed tensor; if 'N', no transpose. Default: 'N'.

Definition at line 1577 of file Intrepid_FunctionSpaceToolsDef.hpp.

template<class Scalar , class ArrayOutFields , class ArrayInData , class ArrayInFields >
void Intrepid::FunctionSpaceTools::tensorMultiplyDataField ( ArrayOutFields &  outputFields,
const ArrayInData &  inputData,
const ArrayInFields &  inputFields,
const char  transpose = 'N' 
)
static

Matrix-vector or matrix-matrix product of data and fields; please read the description below. 

   There are four use cases:
   \li
   matrix-vector product of a rank-4 container \a <b>inputFields</b> with dimensions (C,F,P,D),
   representing the values of a set of vector fields, on the left by the values in a rank-2, 3, or 4
   container \a <b>inputData</b> indexed by (C,P), (C,P,D) or (C,P,D,D), respectively,
   representing the values of tensor data, OR
   \li
   matrix-vector product of a rank-3 container \a <b>inputFields</b> with dimensions (F,P,D),
   representing the values of a vector field, on the left by the values in a rank-2, 3, or 4
   container \a <b>inputData</b> indexed by (C,P), (C,P,D) or (C,P,D,D), respectively,
   representing the values of tensor data, OR
   \li
   matrix-matrix product of a rank-5 container \a <b>inputFields</b> with dimensions (C,F,P,D,D),
   representing the values of a set of tensor fields, on the left by the values in a rank-2, 3, or 4
   container \a <b>inputData</b> indexed by (C,P), (C,P,D) or (C,P,D,D), respectively,
   representing the values of tensor data, OR
   \li
   matrix-matrix product of a rank-4 container \a <b>inputFields</b> with dimensions (F,P,D,D),
   representing the values of a tensor field, on the left by the values in a rank-2, 3, or 4
   container \a <b>inputData</b> indexed by (C,P), (C,P,D) or (C,P,D,D), respectively,
   representing the values of tensor data;
   for matrix-vector products, the output value container \a <b>outputFields</b> is
   indexed by (C,F,P,D);
   for matrix-matrix products the output value container \a <b>outputFields</b> is
   indexed by (C,F,P,D,D).
Remarks
The rank of inputData implicitly defines the type of tensor data:
  • rank = 2 corresponds to a constant diagonal tensor $ diag(a,\ldots,a) $
  • rank = 3 corresponds to a nonconstant diagonal tensor $ diag(a_1,\ldots,a_d) $
  • rank = 4 corresponds to a full tensor $ \{a_{ij}\}$
Note
It is assumed that all tensors are square!
The method is defined for spatial dimensions D = 1, 2, 3
C - num. integration domains
F - num. fields
P - num. integration points
D - spatial dimension
Parameters
outputFields[out] - Output (matrix-vector or matrix-matrix product) fields array.
inputData[in] - Data array.
inputFields[in] - Input fields array.
transpose[in] - If 'T', use transposed left data tensor; if 'N', no transpose. Default: 'N'.

Definition at line 1517 of file Intrepid_FunctionSpaceToolsDef.hpp.

template<class Scalar , class ArrayOutData , class ArrayInDataLeft , class ArrayInDataRight >
void Intrepid::FunctionSpaceTools::vectorMultiplyDataData ( ArrayOutData &  outputData,
const ArrayInDataLeft &  inputDataLeft,
const ArrayInDataRight &  inputDataRight 
)
static

Cross or outer product of data and data; please read the description below. 

   There are four use cases:
   \li
   cross product of a rank-3 container \a <b>inputDataRight</b> with dimensions (C,P,D),
   representing the values of a set of vector data, on the left by the values in a rank-3
   container \a <b>inputDataLeft</b> indexed by (C,P,D) representing the values of vector data, OR
   \li
   cross product of a rank-2 container \a <b>inputDataRight</b> with dimensions (P,D),
   representing the values of vector data, on the left by the values in a rank-3 container
   \a <b>inputDataLeft</b> indexed by (C,P,D), representing the values of vector data, OR
   \li
   outer product of a rank-3 container \a <b>inputDataRight</b> with dimensions (C,P,D),
   representing the values of a set of vector data, on the left by the values in a rank-3
   container \a <b>inputDataLeft</b> indexed by (C,P,D) representing the values of vector data, OR
   \li
   outer product of a rank-2 container \a <b>inputDataRight</b> with dimensions (P,D),
   representing the values of vector data, on the left by the values in a rank-3 container
   \a <b>inputDataLeft</b> indexed by (C,P,D), representing the values of vector data;
   for cross products, the output value container \a <b>outputData</b> is indexed by
   (C,P,D) in 3D (vector output) and by (C,P) in 2D (scalar output);
   for outer products, the output value container \a <b>outputData</b> is indexed by (C,P,D,D).
C - num. integration domains
P - num. integration points
D - spatial dimension, must be 2 or 3
Parameters
outputData[out] - Output (cross or outer product) data array.
inputDataLeft[in] - Left input data array.
inputDataRight[in] - Right input data array.

Definition at line 1494 of file Intrepid_FunctionSpaceToolsDef.hpp.

template<class Scalar , class ArrayOutFields , class ArrayInData , class ArrayInFields >
void Intrepid::FunctionSpaceTools::vectorMultiplyDataField ( ArrayOutFields &  outputFields,
const ArrayInData &  inputData,
const ArrayInFields &  inputFields 
)
static

Cross or outer product of data and fields; please read the description below. 

   There are four use cases:
   \li
   cross product of a rank-4 container \a <b>inputFields</b> with dimensions (C,F,P,D),
   representing the values of a set of vector fields, on the left by the values in a rank-3
   container \a <b>inputData</b> indexed by (C,P,D), representing the values of vector data, OR
   \li
   cross product of a rank-3 container \a <b>inputFields</b> with dimensions (F,P,D),
   representing the values of a vector field, on the left by the values in a rank-3 container
   \a <b>inputData</b> indexed by (C,P,D), representing the values of vector data, OR
   \li
   outer product of a rank-4 container \a <b>inputFields</b> with dimensions (C,F,P,D),
   representing the values of a set of vector fields, on the left by the values in a rank-3
   container \a <b>inputData</b> indexed by (C,P,D), representing the values of vector data, OR
   \li
   outer product of a rank-3 container \a <b>inputFields</b> with dimensions (F,P,D),
   representing the values of a vector field, on the left by the values in a rank-3 container
   \a <b>inputData</b> indexed by (C,P,D), representing the values of vector data;
   for cross products, the output value container \a <b>outputFields</b> is indexed by
   (C,F,P,D) in 3D (vector output) and by (C,F,P) in 2D (scalar output);
   for outer products, the output value container \a <b>outputFields</b> is indexed by (C,F,P,D,D).
C - num. integration domains
F - num. fields
P - num. integration points
D - spatial dimension, must be 2 or 3
Parameters
outputFields[out] - Output (cross or outer product) fields array.
inputData[in] - Data array.
inputFields[in] - Input fields array.

Definition at line 1471 of file Intrepid_FunctionSpaceToolsDef.hpp.

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