Expansion.h

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///////////////////////////////////////////////////////////////////////////////
//
// File: Expansion.h
//
// For more information, please see: http://www.nektar.info
//
// The MIT License
//
// Copyright (c) 2006 Division of Applied Mathematics, Brown University (USA),
// Department of Aeronautics, Imperial College London (UK), and Scientific
// Computing and Imaging Institute, University of Utah (USA).
//
// Permission is hereby granted, free of charge, to any person obtaining a
// copy of this software and associated documentation files (the "Software"),
// to deal in the Software without restriction, including without limitation
// the rights to use, copy, modify, merge, publish, distribute, sublicense,
// and/or sell copies of the Software, and to permit persons to whom the
// Software is furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included
// in all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
// OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
// THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
// DEALINGS IN THE SOFTWARE.
//
// Description: Header file for Expansion routines
//
///////////////////////////////////////////////////////////////////////////////
 
#ifndef EXPANSION_H
#define EXPANSION_H
 
#include <LocalRegions/IndexMapKey.h>
#include <LocalRegions/LocalRegionsDeclspec.h>
#include <SpatialDomains/GeomFactors.h>
#include <SpatialDomains/Geometry.h>
#include <StdRegions/StdExpansion.h>
#include <map>
#include <memory>
#include <vector>
 
namespace Nektar::LocalRegions
{
 
class Expansion;
class MatrixKey;
 
typedef Array<OneD, Array<OneD, NekDouble>> NormalVector;
 
enum MetricType
{
    eMetricLaplacian00,
    eMetricLaplacian01,
    eMetricLaplacian02,
    eMetricLaplacian11,
    eMetricLaplacian12,
    eMetricLaplacian22,
    eMetricQuadrature
};
 
typedef std::shared_ptr<Expansion> ExpansionSharedPtr;
typedef std::weak_ptr<Expansion> ExpansionWeakPtr;
typedef std::vector<ExpansionSharedPtr> ExpansionVector;
typedef std::map<MetricType, Array<OneD, NekDouble>> MetricMap;
 
class Expansion : virtual public StdRegions::StdExpansion
{
public:
    LOCAL_REGIONS_EXPORT Expansion(
        SpatialDomains::Geometry *pGeom); // default constructor.
    LOCAL_REGIONS_EXPORT Expansion(const Expansion &pSrc); // copy constructor.
    LOCAL_REGIONS_EXPORT ~Expansion() override;
 
    LOCAL_REGIONS_EXPORT void SetTraceExp(const int traceid,
                                          ExpansionSharedPtr &f);
    LOCAL_REGIONS_EXPORT ExpansionSharedPtr GetTraceExp(const int traceid);
 
    LOCAL_REGIONS_EXPORT ExpansionSharedPtr GetLocTraceExp(const int traceid);
 
    LOCAL_REGIONS_EXPORT StdRegions::StdExpansionSharedPtr GetStdExp() const
    {
        return v_GetStdExp();
    }
 
    LOCAL_REGIONS_EXPORT StdRegions::StdExpansionSharedPtr GetLinStdExp(
        void) const
    {
        return v_GetLinStdExp();
    }
 
    LOCAL_REGIONS_EXPORT DNekScalMatSharedPtr
    GetLocMatrix(const LocalRegions::MatrixKey &mkey);
 
    LOCAL_REGIONS_EXPORT void DropLocMatrix(
        const LocalRegions::MatrixKey &mkey);
 
    LOCAL_REGIONS_EXPORT DNekScalMatSharedPtr GetLocMatrix(
        const StdRegions::MatrixType mtype,
        const StdRegions::ConstFactorMap &factors =
            StdRegions::NullConstFactorMap,
        const StdRegions::VarCoeffMap &varcoeffs = StdRegions::NullVarCoeffMap);
 
    LOCAL_REGIONS_EXPORT SpatialDomains::Geometry *GetGeom() const;
 
    LOCAL_REGIONS_EXPORT void Reset();
 
    LOCAL_REGIONS_EXPORT IndexMapValuesSharedPtr
    CreateIndexMap(const IndexMapKey &ikey);
 
    LOCAL_REGIONS_EXPORT DNekScalBlkMatSharedPtr
    CreateStaticCondMatrix(const MatrixKey &mkey);
 
    LOCAL_REGIONS_EXPORT inline SpatialDomains::GeomFactors *GetGeomFactors()
        const;
 
    LOCAL_REGIONS_EXPORT DNekMatSharedPtr
    BuildTransformationMatrix(const DNekScalMatSharedPtr &r_bnd,
                              const StdRegions::MatrixType matrixType);
 
    LOCAL_REGIONS_EXPORT DNekMatSharedPtr
    BuildVertexMatrix(const DNekScalMatSharedPtr &r_bnd);
 
    LOCAL_REGIONS_EXPORT void ExtractDataToCoeffs(
        const NekDouble *data, const std::vector<unsigned int> &nummodes,
        const int nmodes_offset, NekDouble *coeffs,
        std::vector<LibUtilities::BasisType> &fromType);
 
    LOCAL_REGIONS_EXPORT void AddEdgeNormBoundaryInt(
        const int edge, const std::shared_ptr<Expansion> &EdgeExp,
        const Array<OneD, const NekDouble> &Fx,
        const Array<OneD, const NekDouble> &Fy,
        Array<OneD, NekDouble> &outarray);
    LOCAL_REGIONS_EXPORT void AddEdgeNormBoundaryInt(
        const int edge, const std::shared_ptr<Expansion> &EdgeExp,
        const Array<OneD, const NekDouble> &Fn,
        Array<OneD, NekDouble> &outarray);
    LOCAL_REGIONS_EXPORT void AddFaceNormBoundaryInt(
        const int face, const std::shared_ptr<Expansion> &FaceExp,
        const Array<OneD, const NekDouble> &Fn,
        Array<OneD, NekDouble> &outarray);
    LOCAL_REGIONS_EXPORT void DGDeriv(
        const int dir, const Array<OneD, const NekDouble> &inarray,
        Array<OneD, ExpansionSharedPtr> &EdgeExp,
        Array<OneD, Array<OneD, NekDouble>> &coeffs,
        Array<OneD, NekDouble> &outarray);
    LOCAL_REGIONS_EXPORT NekDouble
    VectorFlux(const Array<OneD, Array<OneD, NekDouble>> &vec);
 
    LOCAL_REGIONS_EXPORT void NormalTraceDerivFactors(
        Array<OneD, Array<OneD, NekDouble>> &factors,
        Array<OneD, Array<OneD, NekDouble>> &d0factors,
        Array<OneD, Array<OneD, NekDouble>> &d1factors);
 
    inline IndexMapValuesSharedPtr GetIndexMap(const IndexMapKey &ikey)
    {
        return m_indexMapManager[ikey];
    }
 
    LOCAL_REGIONS_EXPORT void AlignVectorToCollapsedDir(
        const int dir, const Array<OneD, const NekDouble> &inarray,
        Array<OneD, Array<OneD, NekDouble>> &outarray)
    {
        v_AlignVectorToCollapsedDir(dir, inarray, outarray);
    }
 
    inline ExpansionSharedPtr GetLeftAdjacentElementExp() const;
 
    inline ExpansionSharedPtr GetRightAdjacentElementExp() const;
 
    inline int GetLeftAdjacentElementTrace() const;
 
    inline int GetRightAdjacentElementTrace() const;
 
    inline void SetAdjacentElementExp(int traceid, ExpansionSharedPtr &e);
 
    inline StdRegions::Orientation GetTraceOrient(int trace)
    {
        return v_GetTraceOrient(trace);
    }
 
    inline void SetCoeffsToOrientation(StdRegions::Orientation dir,
                                       Array<OneD, const NekDouble> &inarray,
                                       Array<OneD, NekDouble> &outarray)
    {
        v_SetCoeffsToOrientation(dir, inarray, outarray);
    }
 
    /// Divided by the metric jacobi and quadrature weights
    inline void DivideByQuadratureMetric(
        const Array<OneD, const NekDouble> &inarray,
        Array<OneD, NekDouble> &outarray)
    {
        v_DivideByQuadratureMetric(inarray, outarray);
    }
 
    /**
     * @brief Extract the metric factors to compute the contravariant
     * fluxes along edge \a edge and stores them into \a outarray
     * following the local edge orientation (i.e. anticlockwise
     * convention).
     */
    inline void GetTraceQFactors(const int trace,
                                 Array<OneD, NekDouble> &outarray)
    {
        v_GetTraceQFactors(trace, outarray);
    }
 
    inline void GetTracePhysVals(
        const int trace, const StdRegions::StdExpansionSharedPtr &TraceExp,
        const Array<OneD, const NekDouble> &inarray,
        Array<OneD, NekDouble> &outarray,
        StdRegions::Orientation orient = StdRegions::eNoOrientation)
    {
        v_GetTracePhysVals(trace, TraceExp, inarray, outarray, orient);
    }
 
    inline void GetLocTracePhysVals(
        const int trace, const StdRegions::StdExpansionSharedPtr &TraceExp,
        const Array<OneD, const NekDouble> &inarray,
        Array<OneD, NekDouble> &outarray)
    {
        v_GetLocTracePhysVals(trace, TraceExp, inarray.data(), outarray);
    }
 
    inline void GetTracePhysMap(const int edge, Array<OneD, int> &outarray)
    {
        v_GetTracePhysMap(edge, outarray);
    }
 
    inline void ReOrientTracePhysVals(const StdRegions::Orientation orient,
                                      const Array<OneD, const NekDouble> &in,
                                      Array<OneD, NekDouble> &out,
                                      const int nq0, const int nq1,
                                      bool Forwards = true)
    {
        v_ReOrientTracePhysVals(orient, in, out, nq0, nq1, Forwards);
    }
 
    LOCAL_REGIONS_EXPORT const NormalVector &GetTraceNormal(const int id);
    LOCAL_REGIONS_EXPORT const std::map<int, NormalVector> &GetTraceNormals(
        void);
 
    inline void ComputeTraceNormal(const int id)
    {
        v_ComputeTraceNormal(id);
    }
 
    inline const Array<OneD, const NekDouble> &GetPhysNormals(void)
    {
        return v_GetPhysNormals();
    }
 
    inline void SetPhysNormals(Array<OneD, const NekDouble> &normal)
    {
        v_SetPhysNormals(normal);
    }
 
    inline void SetUpPhysNormals(const int trace)
    {
        v_SetUpPhysNormals(trace);
    }
 
    inline void AddRobinMassMatrix(
        const int traceid, const Array<OneD, const NekDouble> &primCoeffs,
        DNekMatSharedPtr &inoutmat)
    {
        v_AddRobinMassMatrix(traceid, primCoeffs, inoutmat);
    }
 
    inline void TraceNormLen(const int traceid, NekDouble &h, NekDouble &p)
    {
        v_TraceNormLen(traceid, h, p);
    }
 
    inline void AddRobinTraceContribution(
        const int traceid, const Array<OneD, const NekDouble> &primCoeffs,
        const Array<OneD, NekDouble> &incoeffs, Array<OneD, NekDouble> &coeffs)
    {
        v_AddRobinTraceContribution(traceid, primCoeffs, incoeffs, coeffs);
    }
 
    LOCAL_REGIONS_EXPORT const Array<OneD, const NekDouble> &
    GetElmtBndNormDirElmtLen(const int nbnd) const;
 
    LOCAL_REGIONS_EXPORT void StdDerivBaseOnTraceMat(
        Array<OneD, DNekMatSharedPtr> &DerivMat);
 
    LOCAL_REGIONS_EXPORT void PhysDerivBaseOnTraceMat(
        const int traceid, Array<OneD, DNekMatSharedPtr> &DerivMat);
 
    LOCAL_REGIONS_EXPORT void PhysBaseOnTraceMat(const int traceid,
                                                 DNekMatSharedPtr &BdataMat);
    /// Handles generation of geometry factors.
    void GenGeomFactors();
 
protected:
    LibUtilities::NekManager<IndexMapKey, IndexMapValues, IndexMapKey::opLess>
        m_indexMapManager;
 
    std::map<int, ExpansionWeakPtr> m_traceExp;
    SpatialDomains::Geometry *m_geom;
    SpatialDomains::GeomFactorsUniquePtr m_geomFactors;
    MetricMap m_metrics;
    std::map<int, NormalVector> m_traceNormals;
    ExpansionWeakPtr m_elementLeft;
    ExpansionWeakPtr m_elementRight;
    int m_elementTraceLeft  = -1;
    int m_elementTraceRight = -1;
 
    /// the element length in each element boundary(Vertex, edge
    /// or face) normal direction calculated based on the local
    /// m_geomFactors times the standard element length (which is
    /// 2.0)
    std::map<int, Array<OneD, NekDouble>> m_elmtBndNormDirElmtLen;
 
    void ComputeLaplacianMetric();
    void ComputeQuadratureMetric();
    void ComputeGmatcdotMF(const Array<TwoD, const NekDouble> &df,
                           const Array<OneD, const NekDouble> &direction,
                           Array<OneD, Array<OneD, NekDouble>> &dfdir);
 
    Array<OneD, NekDouble> GetMF(const int dir, const int shapedim,
                                 const StdRegions::VarCoeffMap &varcoeffs);
 
    Array<OneD, NekDouble> GetMFDiv(const int dir,
                                    const StdRegions::VarCoeffMap &varcoeffs);
 
    Array<OneD, NekDouble> GetMFMag(const int dir,
                                    const StdRegions::VarCoeffMap &varcoeffs);
 
    LOCAL_REGIONS_EXPORT void v_FwdTrans(
        const Array<OneD, const NekDouble> &inarray,
        Array<OneD, NekDouble> &outarray) override;
 
    LOCAL_REGIONS_EXPORT NekDouble
    v_PhysEvaluate(const Array<OneD, const NekDouble> &coord,
                   const Array<OneD, const NekDouble> &physvals) override;
 
    void v_MultiplyByQuadratureMetric(
        const Array<OneD, const NekDouble> &inarray,
        Array<OneD, NekDouble> &outarray) override;
 
    virtual void v_DivideByQuadratureMetric(
        const Array<OneD, const NekDouble> &inarray,
        Array<OneD, NekDouble> &outarray);
 
    virtual void v_ComputeLaplacianMetric()
    {
    }
 
    LOCAL_REGIONS_EXPORT virtual StdRegions::StdExpansionSharedPtr v_GetStdExp()
        const;
 
    LOCAL_REGIONS_EXPORT virtual StdRegions::StdExpansionSharedPtr v_GetLinStdExp(
        void) const;
 
    int v_GetCoordim() const override
    {
        return m_geom->GetCoordim();
    }
 
    void v_GetCoords(Array<OneD, NekDouble> &coords_1,
                     Array<OneD, NekDouble> &coords_2,
                     Array<OneD, NekDouble> &coords_3) override;
 
    virtual DNekScalMatSharedPtr v_GetLocMatrix(
        const LocalRegions::MatrixKey &mkey);
 
    virtual void v_DropLocMatrix(const LocalRegions::MatrixKey &mkey);
 
    virtual DNekMatSharedPtr v_BuildTransformationMatrix(
        const DNekScalMatSharedPtr &r_bnd,
        const StdRegions::MatrixType matrixType);
 
    virtual DNekMatSharedPtr v_BuildVertexMatrix(
        const DNekScalMatSharedPtr &r_bnd);
 
    virtual void v_ExtractDataToCoeffs(
        const NekDouble *data, const std::vector<unsigned int> &nummodes,
        const int nmodes_offset, NekDouble *coeffs,
        std::vector<LibUtilities::BasisType> &fromType);
 
    virtual void v_AddEdgeNormBoundaryInt(
        const int edge, const std::shared_ptr<Expansion> &EdgeExp,
        const Array<OneD, const NekDouble> &Fx,
        const Array<OneD, const NekDouble> &Fy,
        Array<OneD, NekDouble> &outarray);
    virtual void v_AddEdgeNormBoundaryInt(
        const int edge, const std::shared_ptr<Expansion> &EdgeExp,
        const Array<OneD, const NekDouble> &Fn,
        Array<OneD, NekDouble> &outarray);
    virtual void v_AddFaceNormBoundaryInt(
        const int face, const std::shared_ptr<Expansion> &FaceExp,
        const Array<OneD, const NekDouble> &Fn,
        Array<OneD, NekDouble> &outarray);
    virtual void v_DGDeriv(const int dir,
                           const Array<OneD, const NekDouble> &inarray,
                           Array<OneD, ExpansionSharedPtr> &EdgeExp,
                           Array<OneD, Array<OneD, NekDouble>> &coeffs,
                           Array<OneD, NekDouble> &outarray);
    virtual NekDouble v_VectorFlux(
        const Array<OneD, Array<OneD, NekDouble>> &vec);
 
    virtual void v_NormalTraceDerivFactors(
        Array<OneD, Array<OneD, NekDouble>> &factors,
        Array<OneD, Array<OneD, NekDouble>> &d0factors,
        Array<OneD, Array<OneD, NekDouble>> &d1factors);
 
    virtual void v_AlignVectorToCollapsedDir(
        const int dir, const Array<OneD, const NekDouble> &inarray,
        Array<OneD, Array<OneD, NekDouble>> &outarray);
 
    virtual StdRegions::Orientation v_GetTraceOrient(int trace);
 
    void v_SetCoeffsToOrientation(StdRegions::Orientation dir,
                                  Array<OneD, const NekDouble> &inarray,
                                  Array<OneD, NekDouble> &outarray) override;
 
    virtual void v_GetTraceQFactors(const int trace,
                                    Array<OneD, NekDouble> &outarray);
 
    virtual void v_GetTracePhysVals(
        const int trace, const StdRegions::StdExpansionSharedPtr &TraceExp,
        const Array<OneD, const NekDouble> &inarray,
        Array<OneD, NekDouble> &outarray, StdRegions::Orientation orient);
 
    virtual void v_GetLocTracePhysVals(
        const int trace, const StdRegions::StdExpansionSharedPtr &TraceExp,
        const NekDouble *inarray, Array<OneD, NekDouble> &outarray);
 
    virtual void v_GetTracePhysMap(const int edge, Array<OneD, int> &outarray);
 
    virtual void v_ReOrientTracePhysVals(const StdRegions::Orientation orient,
                                         const Array<OneD, const NekDouble> &in,
                                         Array<OneD, NekDouble> &out,
                                         const int nq0, const int nq1,
                                         bool Forwards);
 
    virtual void v_ComputeTraceNormal(const int id);
 
    virtual const Array<OneD, const NekDouble> &v_GetPhysNormals();
 
    virtual void v_SetPhysNormals(Array<OneD, const NekDouble> &normal);
 
    virtual void v_SetUpPhysNormals(const int id);
 
    virtual void v_AddRobinMassMatrix(
        const int face, const Array<OneD, const NekDouble> &primCoeffs,
        DNekMatSharedPtr &inoutmat);
 
    virtual void v_AddRobinTraceContribution(
        const int traceid, const Array<OneD, const NekDouble> &primCoeffs,
        const Array<OneD, NekDouble> &incoeffs, Array<OneD, NekDouble> &coeffs);
 
    virtual void v_TraceNormLen(const int traceid, NekDouble &h, NekDouble &p);
 
    virtual void v_GenTraceExp(const int traceid, ExpansionSharedPtr &exp);
 
private:
};
 
/**
 * @brief Get the geometric factors for this object, generating them if
 * required.
 */
inline SpatialDomains::GeomFactors *Expansion::GetGeomFactors() const
{
    return m_geomFactors.get();
}
 
/**
 * @brief Generate the geometric factors (i.e. derivatives of \f$\chi\f$) and
 * related metrics.
 *
 * @see SpatialDomains::GeomFactors
 */
inline void Expansion::GenGeomFactors()
{
    LibUtilities::PointsKeyVector keyTgt = GetPointsKeys();
    m_geomFactors                        = m_geom->GenGeomFactors(keyTgt);
}
 
// This returns a local trace expansion which might be replaced by a global
// trace (for example by the DG trace which could be of a different order or
// Dirichlet BCs)
inline ExpansionSharedPtr Expansion::GetTraceExp(const int traceid)
{
    ASSERTL1(traceid < GetNtraces(), "Trace is out of range.");
 
    ExpansionSharedPtr returnval;
 
    if (m_traceExp.count(traceid))
    {
        // Use stored value
        returnval = m_traceExp[traceid].lock();
    }
    else
    {
        // Generate trace exp
        v_GenTraceExp(traceid, returnval);
    }
 
    return returnval;
}
 
// Generate a local Trace expansion
inline ExpansionSharedPtr Expansion::GetLocTraceExp(const int traceid)
{
    ASSERTL1(traceid < GetNtraces(), "Trace is out of range.");
 
    ExpansionSharedPtr returnval;
 
    // Generate local trace exp
    v_GenTraceExp(traceid, returnval);
 
    return returnval;
}
 
inline void Expansion::SetTraceExp(const int traceid, ExpansionSharedPtr &exp)
{
    ASSERTL1(traceid < GetNtraces(), "Trace out of range.");
 
    m_traceExp[traceid] = exp;
}
 
inline ExpansionSharedPtr Expansion::GetLeftAdjacentElementExp() const
{
    ASSERTL1(m_elementLeft.lock().get(), "Left adjacent element not set.");
    return m_elementLeft.lock();
}
 
inline ExpansionSharedPtr Expansion::GetRightAdjacentElementExp() const
{
    ASSERTL1(m_elementLeft.lock().get(), "Right adjacent element not set.");
 
    return m_elementRight.lock();
}
 
inline int Expansion::GetLeftAdjacentElementTrace() const
{
    return m_elementTraceLeft;
}
 
inline int Expansion::GetRightAdjacentElementTrace() const
{
    return m_elementTraceRight;
}
 
inline void Expansion::SetAdjacentElementExp(int traceid,
                                             ExpansionSharedPtr &exp)
{
    if (m_elementLeft.lock().get())
    {
        m_elementRight      = exp;
        m_elementTraceRight = traceid;
    }
    else
    {
        m_elementLeft      = exp;
        m_elementTraceLeft = traceid;
    }
}
 
void GetTraceQuadRange(const LibUtilities::ShapeType shapeType,
                       const LibUtilities::BasisKeyVector &bkeys, int traceid,
                       std::vector<int> &q_begin, std::vector<int> &q_end);
 
} // namespace Nektar::LocalRegions
 
#endif