GlobalLinSysDirectFull.cpp

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///////////////////////////////////////////////////////////////////////////////
//
// File: GlobalLinSysDirectFull.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).
//
// 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.
//
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// OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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//
// Description: GlobalLinSysDirectFull definition
//
///////////////////////////////////////////////////////////////////////////////
 
#include <MultiRegions/ExpList.h>
#include <MultiRegions/GlobalLinSysDirectFull.h>
 
using namespace std;
 
namespace Nektar::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 std::weak_ptr<ExpList> &pExp,
    const std::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);
}
 
/**
 * Solve the linear system using a full global matrix system.
 */
void GlobalLinSysDirectFull::v_Solve(
    const Array<OneD, const NekDouble> &pLocInput,
    Array<OneD, NekDouble> &pLocOutput,
    const AssemblyMapSharedPtr &pLocToGloMap,
    const Array<OneD, const NekDouble> &pDirForcing)
{
    bool dirForcCalculated = (bool)pDirForcing.size();
    int nDirDofs           = pLocToGloMap->GetNumGlobalDirBndCoeffs();
    int nGlobDofs          = pLocToGloMap->GetNumGlobalCoeffs();
    int nLocDofs           = pLocToGloMap->GetNumLocalCoeffs();
 
    if (nDirDofs)
    {
        std::shared_ptr<MultiRegions::ExpList> expList = m_expList.lock();
        Array<OneD, NekDouble> rhs(nLocDofs);
 
        // Calculate the Dirichlet forcing
        if (dirForcCalculated)
        {
            // Assume pDirForcing is in local space
            ASSERTL0(
                pDirForcing.size() >= nLocDofs,
                "DirForcing is not of sufficient size. Is it in local space?");
            Vmath::Vsub(nLocDofs, pLocInput, 1, pDirForcing, 1, rhs, 1);
        }
        else
        {
            // Calculate initial condition and Dirichlet forcing and subtract it
            // from the rhs
            expList->GeneralMatrixOp(m_linSysKey, pLocOutput, rhs);
 
            // Iterate over all the elements computing Robin BCs where
            // necessary
            for (auto &r : m_robinBCInfo) // add robin mass matrix
            {
                RobinBCInfoSharedPtr rBC;
                Array<OneD, NekDouble> rhsloc;
 
                int n      = r.first;
                int offset = expList->GetCoeff_Offset(n);
 
                LocalRegions::ExpansionSharedPtr vExp = expList->GetExp(n);
                // Add local matrix contribution
                for (rBC = r.second; rBC; rBC = rBC->next)
                {
                    vExp->AddRobinTraceContribution(
                        rBC->m_robinID, rBC->m_robinPrimitiveCoeffs,
                        pLocOutput + offset, rhsloc = rhs + offset);
                }
            }
            Vmath::Vsub(nLocDofs, pLocInput, 1, rhs, 1, rhs, 1);
        }
 
        Array<OneD, NekDouble> diff(nLocDofs);
 
        // Solve for perturbation from initial guess in pOutput
        SolveLinearSystem(nGlobDofs, rhs, diff, pLocToGloMap, nDirDofs);
 
        // Add back initial and boundary condition
        Vmath::Vadd(nLocDofs, diff, 1, pLocOutput, 1, pLocOutput, 1);
    }
    else
    {
        SolveLinearSystem(nGlobDofs, pLocInput, pLocOutput, pLocToGloMap,
                          nDirDofs);
    }
}
 
/**
 * 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 = eFULL;
 
    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(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);
    }
}
 
/// Solve the linear system for given input and output vectors.
void GlobalLinSysDirectFull::v_SolveLinearSystem(
    const int pNumRows, const Array<OneD, const NekDouble> &pInput,
    Array<OneD, NekDouble> &pOutput, const AssemblyMapSharedPtr &pLocToGloMap,
    const int pNumDir)
{
    Array<OneD, NekDouble> tmp(pNumRows);
    Array<OneD, NekDouble> global(pNumRows, 0.0);
 
    pLocToGloMap->Assemble(pInput, tmp);
 
    const int nHomDofs = pNumRows - pNumDir;
    DNekVec Vin(nHomDofs, tmp + pNumDir);
 
    Array<OneD, NekDouble> tmp1 = global + pNumDir;
    DNekVec Vout(nHomDofs, tmp1, eWrapper);
 
    m_linSys->Solve(Vin, Vout);
 
    pLocToGloMap->GlobalToLocal(global, pOutput);
}
 
} // namespace Nektar::MultiRegions