StdExpansion2D.h

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///////////////////////////////////////////////////////////////////////////////
//
// File: StdExpansion2D.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
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//
// Description: Daughter of StdExpansion. This class contains routine
// which are common to 2D expansion. Typically this inolves physiocal
// space operations.
//
///////////////////////////////////////////////////////////////////////////////
 
#ifndef STDEXP2D_H
#define STDEXP2D_H
 
#include <StdRegions/StdExpansion.h>
 
namespace Nektar::StdRegions
{
class StdExpansion2D : virtual public StdExpansion
{
public:
    STD_REGIONS_EXPORT StdExpansion2D(int numcoeffs,
                                      const LibUtilities::BasisKey &Ba,
                                      const LibUtilities::BasisKey &Bb);
    STD_REGIONS_EXPORT StdExpansion2D()                        = default;
    STD_REGIONS_EXPORT StdExpansion2D(const StdExpansion2D &T) = default;
    STD_REGIONS_EXPORT ~StdExpansion2D() override              = default;
 
    // Generic operations in different element
 
    /** \brief Calculate the 2D derivative in the local
     *  tensor/collapsed coordinate at the physical points
     *
     *  This function is independent of the expansion basis and can
     *  therefore be defined for all tensor product distribution of
     *  quadrature points in a generic manner.  The key operations are:
     *
     *  - \f$ \frac{d}{d\eta_1} \rightarrow {\bf D^T_0 u } \f$ \n
     *  - \f$ \frac{d}{d\eta_2} \rightarrow {\bf D_1 u } \f$
     *
     *  \param inarray array of physical points to be differentiated
     *  \param  outarray_d0 the resulting array of derivative in the
     *  \f$\eta_1\f$ direction will be stored in outarray_d0 as output
     *  of the function
     *  \param outarray_d1 the resulting array of derivative in the
     *  \f$\eta_2\f$ direction will be stored in outarray_d1 as output
     *  of the function
     *
     *  Recall that:
     *  \f$
     *  \hspace{1cm} \begin{array}{llll}
     *  \mbox{Shape}    & \mbox{Cartesian coordinate range} &
     *  \mbox{Collapsed coord.}      &
     *  \mbox{Collapsed coordinate definition}\\
     *  \mbox{Quadrilateral}  & -1 \leq \xi_1,\xi_2 \leq  1
     *  & -1 \leq \eta_1,\eta_2 \leq 1
     *  & \eta_1 = \xi_1, \eta_2 = \xi_2\\
     *  \mbox{Triangle}  & -1 \leq \xi_1,\xi_2; \xi_1+\xi_2 \leq  0
     *  & -1 \leq \eta_1,\eta_2 \leq 1
     *  & \eta_1 = \frac{2(1+\xi_1)}{(1-\xi_2)}-1, \eta_2 = \xi_2 \\
     *  \end{array} \f$
     */
    STD_REGIONS_EXPORT void PhysTensorDeriv(
        const Array<OneD, const NekDouble> &inarray,
        Array<OneD, NekDouble> &outarray_d0,
        Array<OneD, NekDouble> &outarray_d1);
 
    STD_REGIONS_EXPORT NekDouble
    Integral(const Array<OneD, const NekDouble> &inarray,
             const Array<OneD, const NekDouble> &w0,
             const Array<OneD, const NekDouble> &w1);
 
    // find derivative of u (inarray) at all coords points
    STD_REGIONS_EXPORT inline NekDouble BaryTensorDeriv(
        const Array<OneD, NekDouble> &coord,
        const Array<OneD, const NekDouble> &inarray,
        std::array<NekDouble, 3> &firstOrderDerivs)
    {
        const int nq0 = m_base[0]->GetNumPoints();
        const int nq1 = m_base[1]->GetNumPoints();
 
        const NekDouble *ptr = &inarray[0];
        Array<OneD, NekDouble> deriv0(nq1, 0.0);
        Array<OneD, NekDouble> phys0(nq1, 0.0);
 
        for (int j = 0; j < nq1; ++j, ptr += nq0)
        {
            phys0[j] =
                StdExpansion::BaryEvaluate<0, true>(coord[0], ptr, deriv0[j]);
        }
        firstOrderDerivs[0] =
            StdExpansion::BaryEvaluate<1, false>(coord[1], &deriv0[0]);
 
        return StdExpansion::BaryEvaluate<1, true>(coord[1], &phys0[0],
                                                   firstOrderDerivs[1]);
    }
 
    STD_REGIONS_EXPORT void BwdTrans_SumFacKernel(
        const Array<OneD, const NekDouble> &base0,
        const Array<OneD, const NekDouble> &base1,
        const Array<OneD, const NekDouble> &inarray,
        Array<OneD, NekDouble> &outarray, Array<OneD, NekDouble> &wsp,
        bool doCheckCollDir0 = true, bool doCheckCollDir1 = true);
 
    STD_REGIONS_EXPORT void IProductWRTBase_SumFacKernel(
        const Array<OneD, const NekDouble> &base0,
        const Array<OneD, const NekDouble> &base1,
        const Array<OneD, const NekDouble> &inarray,
        Array<OneD, NekDouble> &outarray, Array<OneD, NekDouble> &wsp,
        bool doCheckCollDir0 = true, bool doCheckCollDir1 = true);
 
protected:
    /** \brief This function evaluates the expansion at a single
     *  (arbitrary) point of the domain
     *
     *  This function is a wrapper around the virtual function
     *  \a v_PhysEvaluate()
     *
     *  Based on the value of the expansion at the quadrature points,
     *  this function calculates the value of the expansion at an
     *  arbitrary single points (with coordinates \f$ \mathbf{x_c}\f$
     *  given by the pointer \a coords). This operation, equivalent to
     *  \f[ u(\mathbf{x_c})  = \sum_p \phi_p(\mathbf{x_c}) \hat{u}_p \f]
     *  is evaluated using Lagrangian interpolants through the quadrature
     *  points:
     *  \f[ u(\mathbf{x_c}) = \sum_p h_p(\mathbf{x_c}) u_p\f]
     *
     *  This function requires that the physical value array
     *  \f$\mathbf{u}\f$ (implemented as the attribute #m_phys)
     *  is set.
     *
     *  \param coords the coordinates of the single point
     *  \return returns the value of the expansion at the single point
     */
    STD_REGIONS_EXPORT NekDouble
    v_PhysEvaluate(const Array<OneD, const NekDouble> &coords,
                   const Array<OneD, const NekDouble> &physvals) override;
 
    STD_REGIONS_EXPORT NekDouble
    v_PhysEvaluate(const Array<OneD, DNekMatSharedPtr> &I,
                   const Array<OneD, const NekDouble> &physvals) override;
 
    STD_REGIONS_EXPORT NekDouble
    v_PhysEvaluate(const Array<OneD, NekDouble> &coord,
                   const Array<OneD, const NekDouble> &inarray,
                   std::array<NekDouble, 3> &firstOrderDerivs) override;
 
    STD_REGIONS_EXPORT virtual void v_BwdTrans_SumFacKernel(
        const Array<OneD, const NekDouble> &base0,
        const Array<OneD, const NekDouble> &base1,
        const Array<OneD, const NekDouble> &inarray,
        Array<OneD, NekDouble> &outarray, Array<OneD, NekDouble> &wsp,
        bool doCheckCollDir0, bool doCheckCollDir1) = 0;
 
    STD_REGIONS_EXPORT virtual void v_IProductWRTBase_SumFacKernel(
        const Array<OneD, const NekDouble> &base0,
        const Array<OneD, const NekDouble> &base1,
        const Array<OneD, const NekDouble> &inarray,
        Array<OneD, NekDouble> &outarray, Array<OneD, NekDouble> &wsp,
        bool doCheckCollDir0, bool doCheckCollDir1) = 0;
 
    STD_REGIONS_EXPORT void v_LaplacianMatrixOp_MatFree(
        const Array<OneD, const NekDouble> &inarray,
        Array<OneD, NekDouble> &outarray,
        const StdRegions::StdMatrixKey &mkey) override;
    STD_REGIONS_EXPORT void v_HelmholtzMatrixOp_MatFree(
        const Array<OneD, const NekDouble> &inarray,
        Array<OneD, NekDouble> &outarray,
        const StdRegions::StdMatrixKey &mkey) override;
 
    STD_REGIONS_EXPORT void v_GetTraceCoeffMap(
        const unsigned int traceid,
        Array<OneD, unsigned int> &maparray) override;
 
    STD_REGIONS_EXPORT void v_GetElmtTraceToTraceMap(
        const unsigned int eid, Array<OneD, unsigned int> &maparray,
        Array<OneD, int> &signarray, Orientation edgeOrient, int P,
        int Q) override;
 
    STD_REGIONS_EXPORT void v_GetTraceToElementMap(
        const int eid, Array<OneD, unsigned int> &maparray,
        Array<OneD, int> &signarray, Orientation edgeOrient = eForwards,
        int P = -1, int Q = -1) override;
 
    STD_REGIONS_EXPORT void v_GenStdMatBwdDeriv(const int dir,
                                                DNekMatSharedPtr &mat) override;
 
private:
    int v_GetShapeDimension() const final
    {
        return 2;
    }
};
 
typedef std::shared_ptr<StdExpansion2D> StdExpansion2DSharedPtr;
 
} // namespace Nektar::StdRegions
 
#endif // STDEXP2D_H