GlobalLinSysDirectFull.cpp

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///////////////////////////////////////////////////////////////////////////////
//
// File GlobalLinSys.cpp
//
// 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).
//
// License for the specific language governing rights and limitations under
// 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
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// The above copyright notice and this permission notice shall be included
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// OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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//
// Description: GlobalLinSys definition
//
///////////////////////////////////////////////////////////////////////////////

#include <MultiRegions/GlobalLinSysDirectFull.h>
#include <MultiRegions/ExpList.h>

namespace Nektar
{
    namespace MultiRegions
    {
        /**
         * @class GlobalLinSysDirect
         *
         * Consider a linear system
         *   \f$\boldsymbol{M\hat{u}}_g=\boldsymbol{\hat{f}}\f$
         * to be solved, where \f$\boldsymbol{M}\f$ is a matrix of type
         * specified by \a mkey. This function assembles the global system
         * matrix \f$\boldsymbol{M}\f$ out of the elemental submatrices
         * \f$\boldsymbol{M}^e\f$. This is equivalent to:
         * \f[ \boldsymbol{M}=\boldsymbol{\mathcal{A}}^T
         * \underline{\boldsymbol{M}}^e\boldsymbol{\mathcal{A}}.\f]
         * where the matrix \f$\boldsymbol{\mathcal{A}}\f$ is a sparse
         * permutation matrix of size \f$N_{\mathrm{eof}}\times
         * N_{\mathrm{dof}}\f$. However, due to the size and sparsity of the
         * matrix \f$\boldsymbol{\mathcal{A}}\f$, it is more efficient to
         * assemble the global matrix using the mapping array \a
         * map\f$[e][i]\f$ contained in the input argument \a locToGloMap.
         * The global assembly is then evaluated as:
         * \f[ \boldsymbol{M}\left[\mathrm{\texttt{map}}[e][i]\right]
         * \left[\mathrm{\texttt{map}}[e][j]\right]
         *       =\mathrm{\texttt{sign}}[e][i]\cdot
         * \mathrm{\texttt{sign}}[e][j] \cdot\boldsymbol{M}^e[i][j]\f]
         * where the values \a sign\f$[e][i]\f$ ensure the correct connectivity.
         */

        /**
         * Registers the class with the Factory.
         */
        string GlobalLinSysDirectFull::className
                = GetGlobalLinSysFactory().RegisterCreatorFunction(
                    "DirectFull",
                    GlobalLinSysDirectFull::create,
                    "Direct Full.");


        /// Constructor for full direct matrix solve.
        GlobalLinSysDirectFull::GlobalLinSysDirectFull(
                    const GlobalLinSysKey &pLinSysKey,
                    const boost::weak_ptr<ExpList> &pExp,
                    const boost::shared_ptr<AssemblyMap>
                                                            &pLocToGloMap)
            : GlobalLinSys(pLinSysKey, pExp, pLocToGloMap),
              GlobalLinSysDirect(pLinSysKey, pExp, pLocToGloMap)
        {

            ASSERTL1(m_linSysKey.GetGlobalSysSolnType()==eDirectFullMatrix,
                     "This routine should only be used when using a Full Direct"
                     " matrix solve");
            ASSERTL1(pExp.lock()->GetComm()->GetSize() == 1,
                     "Direct full matrix solve can only be used in serial.");

            AssembleFullMatrix(pLocToGloMap);
        }


        GlobalLinSysDirectFull::~GlobalLinSysDirectFull()
        {

        }


        /**
         * Solve the linear system using a full global matrix system.
         */
        void GlobalLinSysDirectFull::v_Solve(
                    const Array<OneD, const NekDouble>  &pInput,
                          Array<OneD,       NekDouble>  &pOutput,
                    const AssemblyMapSharedPtr &pLocToGloMap,
                    const Array<OneD, const NekDouble>  &pDirForcing)
        {
            bool dirForcCalculated = (bool) pDirForcing.num_elements();
            int nDirDofs  = pLocToGloMap->GetNumGlobalDirBndCoeffs();
            int nGlobDofs = pLocToGloMap->GetNumGlobalCoeffs();
            Array<OneD, NekDouble> tmp(nGlobDofs);
            
            if(nDirDofs)
            {
                // calculate the dirichlet forcing
                if(dirForcCalculated)
                {
                    Vmath::Vsub(nGlobDofs,
                                pInput.get(),      1,
                                pDirForcing.get(), 1,
                                tmp.get(),         1);
                }
                else
                {
                    // Calculate Dirichlet forcing and subtract it from the rhs
                    m_expList.lock()->GeneralMatrixOp(
                        m_linSysKey, pOutput, tmp, eGlobal);
                    
                    Vmath::Vsub(nGlobDofs, 
                                pInput.get(), 1,
                                tmp.get(),    1,
                                tmp.get(),    1);
                }

                Array<OneD, NekDouble> out(nGlobDofs,0.0);
                SolveLinearSystem(nGlobDofs, tmp, out, pLocToGloMap, nDirDofs);
                Vmath::Vadd(nGlobDofs-nDirDofs,    &out    [nDirDofs], 1,
                            &pOutput[nDirDofs], 1, &pOutput[nDirDofs], 1);
            }
            else
            {
                SolveLinearSystem(nDirDofs, pInput, pOutput, pLocToGloMap);
            }
        }


        /**
         * Assemble a full matrix from the block matrix stored in
         * #m_blkMatrices and the given local to global mapping information.
         * @param   locToGloMap Local to global mapping information.
         */
        void GlobalLinSysDirectFull::AssembleFullMatrix(
                        const AssemblyMapSharedPtr& pLocToGloMap)
        {
            int i,j,n,cnt,gid1,gid2;
            NekDouble sign1,sign2,value;
            int totDofs     = pLocToGloMap->GetNumGlobalCoeffs();
            int NumDirBCs   = pLocToGloMap->GetNumGlobalDirBndCoeffs();

            unsigned int rows = totDofs - NumDirBCs;
            unsigned int cols = totDofs - NumDirBCs;
            NekDouble zero = 0.0;

            DNekMatSharedPtr Gmat;
            int bwidth = pLocToGloMap->GetFullSystemBandWidth();
            MatrixStorage matStorage;

            switch(m_linSysKey.GetMatrixType())
            {
                // case for all symmetric matices
                case StdRegions::eMass:
                case StdRegions::eHelmholtz:
                case StdRegions::eLaplacian:
                case StdRegions::eHybridDGHelmBndLam:
                {
                    if( (2*(bwidth+1)) < rows)
                    {
                        matStorage = ePOSITIVE_DEFINITE_SYMMETRIC_BANDED;
                        Gmat = MemoryManager<DNekMat>
                                        ::AllocateSharedPtr(rows, cols, zero,
                                                            matStorage,
                                                            bwidth, bwidth);
                    }
                    else
                    {
                        matStorage = ePOSITIVE_DEFINITE_SYMMETRIC;
                        Gmat = MemoryManager<DNekMat>
                                        ::AllocateSharedPtr(rows, cols, zero,
                                                            matStorage);
                    }
                    break;
                }
                case StdRegions::eLinearAdvectionReaction:
                case StdRegions::eLinearAdvectionDiffusionReaction:
                {
                    matStorage = eFULL;
                    Gmat = MemoryManager<DNekMat>
                                        ::AllocateSharedPtr(rows, cols, zero,
                                                            matStorage);
                    break;
                }
                default:
                {
                    NEKERROR(ErrorUtil::efatal, "Add MatrixType to switch "
                                                "statement");
                }
            }

            // fill global matrix
            DNekScalMatSharedPtr loc_mat;

            int loc_lda;
            for(n = cnt = 0; n < m_expList.lock()->GetNumElmts(); ++n)
            {
                loc_mat = GetBlock(m_expList.lock()->GetOffset_Elmt_Id(n));
                loc_lda = loc_mat->GetRows();

                for(i = 0; i < loc_lda; ++i)
                {
                    gid1 = pLocToGloMap->GetLocalToGlobalMap(cnt + i)-NumDirBCs;
                    sign1 = pLocToGloMap->GetLocalToGlobalSign(cnt + i);
                    if(gid1 >= 0)
                    {
                        for(j = 0; j < loc_lda; ++j)
                        {
                            gid2 = pLocToGloMap->GetLocalToGlobalMap(cnt + j)
                                                                    - NumDirBCs;
                            sign2 = pLocToGloMap->GetLocalToGlobalSign(cnt + j);
                            if(gid2 >= 0)
                            {
                                // When global matrix is symmetric,
                                // only add the value for the upper
                                // triangular part in order to avoid
                                // entries to be entered twice
                                if((matStorage == eFULL)||(gid2 >= gid1))
                                {
                                    value = Gmat->GetValue(gid1,gid2)
                                                + sign1*sign2*(*loc_mat)(i,j);
                                    Gmat->SetValue(gid1,gid2,value);
                                }
                            }
                        }
                    }
                }
                cnt   += loc_lda;
            }

            if(rows)
            {
                PointerWrapper w = eWrapper;
                m_linSys = MemoryManager<DNekLinSys>::AllocateSharedPtr(Gmat,w);
            }
        }
    }
}