/usr/include/trilinos/Intrepid_FunctionSpaceToolsInPlace.hpp is in libtrilinos-intrepid-dev 12.12.1-5.
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// ************************************************************************
//
// Intrepid Package
// Copyright (2007) Sandia Corporation
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// @HEADER
/** \file Intrepid_FunctionSpaceToolsInPlace.hpp
\brief Header file for the Intrepid::FunctionSpaceToolsInPlace class.
\author Created by R. Kirby
*/
#ifndef INTREPID_FUNCTIONSPACETOOLSINPLACE_HPP
#define INTREPID_FUNCTIONSPACETOOLSINPLACE_HPP
#include "Intrepid_ConfigDefs.hpp"
#include "Intrepid_ArrayTools.hpp"
#include "Intrepid_RealSpaceTools.hpp"
#include "Intrepid_FieldContainer.hpp"
#include "Intrepid_CellTools.hpp"
namespace Intrepid {
/** \class Intrepid::FunctionSpaceToolsInPlace
\brief 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.
The functionality here largely mirrors that in Intrepid::FunctionSpaceTools,
except that the input data is overwrriten with the result of the particular
transformation. This can reduce intermediate storage when the input values
are not required by later calculations.
A new feature compared to Intrepid::FunctionSpaceTools is that of "dual"
transforms that are useful in alternate workflow patterns. At the innermost
loop nest, we may have a computation of the form (T_1 D_1 u).(T_2 D_2 v), and
we would like to rewrite this as (T_2^t T_1 D_1 u).(D_2 v). The transposes
of each of these transformations are supplied in this routine.
*/
class FunctionSpaceToolsInPlace {
public:
/** \brief Transformation of a (scalar) value field in the H-grad space, defined at points on a
reference cell, stored in the user-provided container <var><b>inVals</b></var>
and indexed by (F,P), into the output container <var><b>outVals</b></var>,
defined on cells in physical space and indexed by (C,F,P).
Computes pullback of \e HGRAD functions \f$\Phi^*(\widehat{u}_f) = \widehat{u}_f\circ F^{-1}_{c} \f$
for points in one or more physical cells that are images of a given set of points in the reference cell:
\f[
\{ x_{c,p} \}_{p=0}^P = \{ F_{c} (\widehat{x}_p) \}_{p=0}^{P}\qquad 0\le c < C \,.
\f]
In this case \f$ F^{-1}_{c}(x_{c,p}) = \widehat{x}_p \f$ and the user-provided container
should contain the values of the function set \f$\{\widehat{u}_f\}_{f=0}^{F}\f$ at the
reference points:
\f[
inVals(f,p) = \widehat{u}_f(\widehat{x}_p) \,.
\f]
The method returns
\f[
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 \,,
\f]
i.e., it simply replicates the values in the user-provided container to every cell.
See Section \ref sec_pullbacks for more details about pullbacks.
\code
|------|----------------------|--------------------------------------------------|
| | Index | Dimension |
|------|----------------------|--------------------------------------------------|
| C | cell | 0 <= C < num. integration domains |
| F | field | 0 <= F < number of fields per cell to transform |
| P | point | 0 <= P < num. integration points |
|------|----------------------|--------------------------------------------------|
\endcode
*/
template<class Scalar, class ArrayType>
static void HGRADtransformVALUE(ArrayType & inOutVals );
/** \brief Since there is no matrix involved, this is the same transformation
as HGRADtransformVALUE */
template<class Scalar, class ArrayType>
static void HGRADtransformVALUEDual(ArrayType & inOutVals );
/** \brief Transformation of a gradient field in the H-grad space, defined at points on a
reference cell, stored in the user-provided container <var><b>inVals</b></var>
and indexed by (F,P,D), into the output container <var><b>outVals</b></var>,
defined on cells in physical space and indexed by (C,F,P,D).
Computes pullback of gradients of \e HGRAD functions
\f$\Phi^*(\nabla\widehat{u}_f) = \left((DF_c)^{-{\sf T}}\cdot\nabla\widehat{u}_f\right)\circ F^{-1}_{c}\f$
for points in one or more physical cells that are images of a given set of points in the reference cell:
\f[
\{ x_{c,p} \}_{p=0}^P = \{ F_{c} (\widehat{x}_p) \}_{p=0}^{P}\qquad 0\le c < C \,.
\f]
In this case \f$ F^{-1}_{c}(x_{c,p}) = \widehat{x}_p \f$ and the user-provided container
should contain the gradients of the function set \f$\{\widehat{u}_f\}_{f=0}^{F}\f$ at the
reference points:
\f[
inVals(f,p,*) = \nabla\widehat{u}_f(\widehat{x}_p) \,.
\f]
The method returns
\f[
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 \,.
\f]
See Section \ref sec_pullbacks for more details about pullbacks.
\code
|------|----------------------|--------------------------------------------------|
| | Index | Dimension |
|------|----------------------|--------------------------------------------------|
| C | cell | 0 <= C < num. integration domains |
| F | field | 0 <= F < number of fields per cell |
| P | point | 0 <= P < num. integration points |
| D | space dim | 0 <= D < spatial dimension |
|------|----------------------|--------------------------------------------------|
\endcode
*/
template<class Scalar, class ArrayType, class ArrayTypeJac>
static void HGRADtransformGRAD(ArrayType & inOutVals,
const ArrayTypeJac & jacobianInverse,
const char transpose = 'T');
/** \brief Applies the transpose of the HGRADtransformGRAD to the data */
template<class Scalar, class ArrayType, class ArrayTypeJac>
static void HGRADtransformGRADDual(ArrayType & inOutVals,
const ArrayTypeJac & jacobianInverse,
const char transpose = 'T');
/** \brief Transformation of a (vector) value field in the H-curl space, defined at points on a
reference cell, stored in the user-provided container <var><b>inVals</b></var>
and indexed by (F,P,D), into the output container <var><b>outVals</b></var>,
defined on cells in physical space and indexed by (C,F,P,D).
Computes pullback of \e HCURL functions
\f$\Phi^*(\widehat{\bf u}_f) = \left((DF_c)^{-{\sf T}}\cdot\widehat{\bf u}_f\right)\circ F^{-1}_{c}\f$
for points in one or more physical cells that are images of a given set of points in the reference cell:
\f[
\{ x_{c,p} \}_{p=0}^P = \{ F_{c} (\widehat{x}_p) \}_{p=0}^{P}\qquad 0\le c < C \,.
\f]
In this case \f$ F^{-1}_{c}(x_{c,p}) = \widehat{x}_p \f$ and the user-provided container
should contain the values of the vector function set \f$\{\widehat{\bf u}_f\}_{f=0}^{F}\f$ at the
reference points:
\f[
inVals(f,p,*) = \widehat{\bf u}_f(\widehat{x}_p) \,.
\f]
The method returns
\f[
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 \,.
\f]
See Section \ref sec_pullbacks for more details about pullbacks.
\code
|------|----------------------|--------------------------------------------------|
| | 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 |
|------|----------------------|--------------------------------------------------|
\endcode
*/
template<class Scalar, class ArrayType, class ArrayTypeJac>
static void HCURLtransformVALUE(ArrayType & inOutVals,
const ArrayTypeJac & jacobianInverse,
const char transpose = 'T');
/** \brief Applies the dual of the HCURLtransformVALUE transformation */
template<class Scalar, class ArrayType, class ArrayTypeJac>
static void HCURLtransformVALUEDual(ArrayType & outVals,
const ArrayTypeJac & jacobianInverse,
const char transpose = 'T');
/** \brief Transformation of a curl field in the H-curl space, defined at points on a
reference cell, stored in the user-provided container <var><b>inVals</b></var>
and indexed by (F,P,D), into the output container <var><b>outVals</b></var>,
defined on cells in physical space and indexed by (C,F,P,D).
Computes pullback of curls of \e HCURL functions
\f$\Phi^*(\widehat{\bf u}_f) = \left(J^{-1}_{c} DF_{c}\cdot\nabla\times\widehat{\bf u}_f\right)\circ F^{-1}_{c}\f$
for points in one or more physical cells that are images of a given set of points in the reference cell:
\f[
\{ x_{c,p} \}_{p=0}^P = \{ F_{c} (\widehat{x}_p) \}_{p=0}^{P}\qquad 0\le c < C \,.
\f]
In this case \f$ F^{-1}_{c}(x_{c,p}) = \widehat{x}_p \f$ and the user-provided container
should contain the curls of the vector function set \f$\{\widehat{\bf u}_f\}_{f=0}^{F}\f$ at the
reference points:
\f[
inVals(f,p,*) = \nabla\times\widehat{\bf u}_f(\widehat{x}_p) \,.
\f]
The method returns
\f[
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 \,.
\f]
See Section \ref sec_pullbacks for more details about pullbacks.
\code
|------|----------------------|--------------------------------------------------|
| | 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 |
|------|----------------------|--------------------------------------------------|
\endcode
*/
template<class Scalar, class ArrayType, class ArrayTypeJac, class ArrayTypeDet>
static void HCURLtransformCURL(ArrayType & inOutVals,
const ArrayTypeJac & jacobian,
const ArrayTypeDet & jacobianDet,
const char transpose = 'N');
/** \brief Applies the dual of the HCURLtransformCURL transformation */
template<class Scalar, class ArrayType, class ArrayTypeJac, class ArrayTypeDet>
static void HCURLtransformCURLDual(ArrayType & outVals,
const ArrayTypeJac & jacobian,
const ArrayTypeDet & jacobianDet,
const char transpose = 'N');
/** \brief Transformation of a (vector) value field in the H-div space, defined at points on a
reference cell, stored in the user-provided container <var><b>inVals</b></var>
and indexed by (F,P,D), into the output container <var><b>outVals</b></var>,
defined on cells in physical space and indexed by (C,F,P,D).
Computes pullback of \e HDIV functions
\f$\Phi^*(\widehat{\bf u}_f) = \left(J^{-1}_{c} DF_{c}\cdot\widehat{\bf u}_f\right)\circ F^{-1}_{c} \f$
for points in one or more physical cells that are images of a given set of points in the reference cell:
\f[
\{ x_{c,p} \}_{p=0}^P = \{ F_{c} (\widehat{x}_p) \}_{p=0}^{P}\qquad 0\le c < C \,.
\f]
In this case \f$ F^{-1}_{c}(x_{c,p}) = \widehat{x}_p \f$ and the user-provided container
should contain the values of the vector function set \f$\{\widehat{\bf u}_f\}_{f=0}^{F}\f$ at the
reference points:
\f[
inVals(f,p,*) = \widehat{\bf u}_f(\widehat{x}_p) \,.
\f]
The method returns
\f[
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 \,.
\f]
See Section \ref sec_pullbacks for more details about pullbacks.
\code
|------|----------------------|--------------------------------------------------|
| | 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 |
|------|----------------------|--------------------------------------------------|
\endcode
*/
template<class Scalar, class ArrayType, class ArrayTypeJac, class ArrayTypeDet>
static void HDIVtransformVALUE(ArrayType & inOutVals,
const ArrayTypeJac & jacobian,
const ArrayTypeDet & jacobianDet,
const char transpose = 'N');
/** \brief Applies the dual of HDIVtransformVALUE */
template<class Scalar, class ArrayType, class ArrayTypeJac, class ArrayTypeDet>
static void HDIVtransformVALUEDual(ArrayType & outVals,
const ArrayTypeJac & jacobian,
const ArrayTypeDet & jacobianDet,
const char transpose = 'N');
/** \brief Transformation of a divergence field in the H-div space, defined at points on a
reference cell, stored in the user-provided container <var><b>inVals</b></var>
and indexed by (F,P), into the output container <var><b>outVals</b></var>,
defined on cells in physical space and indexed by (C,F,P).
Computes pullback of the divergence of \e HDIV functions
\f$\Phi^*(\widehat{\bf u}_f) = \left(J^{-1}_{c}\nabla\cdot\widehat{\bf u}_{f}\right) \circ F^{-1}_{c} \f$
for points in one or more physical cells that are images of a given set of points in the reference cell:
\f[
\{ x_{c,p} \}_{p=0}^P = \{ F_{c} (\widehat{x}_p) \}_{p=0}^{P}\qquad 0\le c < C \,.
\f]
In this case \f$ F^{-1}_{c}(x_{c,p}) = \widehat{x}_p \f$ and the user-provided container
should contain the divergencies of the vector function set \f$\{\widehat{\bf u}_f\}_{f=0}^{F}\f$ at the
reference points:
\f[
inVals(f,p) = \nabla\cdot\widehat{\bf u}_f(\widehat{x}_p) \,.
\f]
The method returns
\f[
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 \,.
\f]
See Section \ref sec_pullbacks for more details about pullbacks.
\code
|------|----------------------|--------------------------------------------------|
| | Index | Dimension |
|------|----------------------|--------------------------------------------------|
| C | cell | 0 <= C < num. integration domains |
| F | field | 0 <= F < dim. of the basis |
| P | point | 0 <= P < num. integration points |
|------|----------------------|--------------------------------------------------|
\endcode
*/
template<class Scalar, class ArrayType, class ArrayTypeDet>
static void HDIVtransformDIV(ArrayType & inOutVals,
const ArrayTypeDet & jacobianDet);
/** \brief Applies the dual of HDIVtransformDIV, which is the same */
template<class Scalar, class ArrayType, class ArrayTypeDet>
static void HDIVtransformDIVDual(ArrayType & inOutVals,
const ArrayTypeDet & jacobianDet);
/** \brief Transformation of a (scalar) value field in the H-vol space, defined at points on a
reference cell, stored in the user-provided container <var><b>inVals</b></var>
and indexed by (F,P), into the output container <var><b>outVals</b></var>,
defined on cells in physical space and indexed by (C,F,P).
Computes pullback of \e HVOL functions
\f$\Phi^*(\widehat{u}_f) = \left(J^{-1}_{c}\widehat{u}_{f}\right) \circ F^{-1}_{c} \f$
for points in one or more physical cells that are images of a given set of points in the reference cell:
\f[
\{ x_{c,p} \}_{p=0}^P = \{ F_{c} (\widehat{x}_p) \}_{p=0}^{P}\qquad 0\le c < C \,.
\f]
In this case \f$ F^{-1}_{c}(x_{c,p}) = \widehat{x}_p \f$ and the user-provided container
should contain the values of the functions in the set \f$\{\widehat{\bf u}_f\}_{f=0}^{F}\f$ at the
reference points:
\f[
inVals(f,p) = \widehat{u}_f(\widehat{x}_p) \,.
\f]
The method returns
\f[
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 \,.
\f]
See Section \ref sec_pullbacks for more details about pullbacks.
\code
|------|----------------------|--------------------------------------------------|
| | Index | Dimension |
|------|----------------------|--------------------------------------------------|
| C | cell | 0 <= C < num. integration domains |
| F | field | 0 <= F < dim. of the basis |
| P | point | 0 <= P < num. integration points |
|------|----------------------|--------------------------------------------------|
\endcode
*/
template<class Scalar, class ArrayType, class ArrayTypeDet>
static void HVOLtransformVALUE(ArrayType & inOutVals,
const ArrayTypeDet & jacobianDet);
/** \brief Applies the dual of HVOLtransformVALUE */
template<class Scalar, class ArrayType, class ArrayTypeDet>
static void HVOLtransformVALUEDual(ArrayType & inOutVals,
const ArrayTypeDet & jacobianDet);
template<class Scalar, class ArrayType, class ArrayTypeMeasure>
static void multiplyMeasure(ArrayType & inOutVals,
const ArrayTypeMeasure & inMeasure);
}; // end FunctionSpaceToolsInPlace
} // end namespace Intrepid
// include templated definitions
#include <Intrepid_FunctionSpaceToolsInPlaceDef.hpp>
#endif
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