NekLinSysIterCG.cpp

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///////////////////////////////////////////////////////////////////////////////
//
// File: NekLinSysIterCG.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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// Software is furnished to do so, subject to the following conditions:
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// The above copyright notice and this permission notice shall be included
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//
// Description: NekLinSysIterCG definition
//
///////////////////////////////////////////////////////////////////////////////
 
#include <LibUtilities/LinearAlgebra/NekLinSysIterCG.h>
 
using namespace std;
 
namespace Nektar::LibUtilities
{
/**
 * @class  NekLinSysIterCG
 *
 * Solves a linear system using iterative methods.
 */
string NekLinSysIterCG::className =
    LibUtilities::GetNekLinSysIterFactory().RegisterCreatorFunction(
        "ConjugateGradient", NekLinSysIterCG::create,
        "NekLinSysIterCG solver.");
 
NekLinSysIterCG::NekLinSysIterCG(
    const LibUtilities::SessionReaderSharedPtr &pSession,
    const LibUtilities::CommSharedPtr &vRowComm, const int nDimen,
    const NekSysKey &pKey)
    : NekLinSysIter(pSession, vRowComm, nDimen, pKey)
{
}
 
void NekLinSysIterCG::v_InitObject()
{
    NekLinSysIter::v_InitObject();
}
 
/**
 *
 */
int NekLinSysIterCG::v_SolveSystem(const int nGlobal,
                                   const Array<OneD, const NekDouble> &pInput,
                                   Array<OneD, NekDouble> &pOutput,
                                   const int nDir)
{
    DoConjugateGradient(nGlobal, pInput, pOutput, nDir);
 
    return m_totalIterations;
}
 
/**  
 * Solve a global linear system using the conjugate gradient method.  
 * We solve only for the non-Dirichlet modes. The operator is evaluated  
 * using an auxiliary function m_operator.DoNekSysLhsEval defined by the  
 * specific solver. Distributed math routines are used to support  
 * parallel execution of the solver.  
 *  
 * The implemented algorithm uses a reduced-communication reordering of  
 * the standard PCG method (Demmel, Heath and Vorst, 1993)  
 *  
 * @param       pInput      Input residual  of all DOFs.  
 * @param       pOutput     Solution vector of all DOFs.  
 */
void NekLinSysIterCG::DoConjugateGradient(
    const int nGlobal, const Array<OneD, const NekDouble> &pInput,
    Array<OneD, NekDouble> &pOutput, const int nDir)
{
    // Get vector sizes
    int nNonDir = nGlobal - nDir;
 
    // Allocate array storage
    Array<OneD, NekDouble> w_A(nGlobal, 0.0);
    Array<OneD, NekDouble> s_A(nGlobal, 0.0);
    Array<OneD, NekDouble> p_A(nNonDir, 0.0);
    Array<OneD, NekDouble> r_A(nNonDir, 0.0);
    Array<OneD, NekDouble> q_A(nNonDir, 0.0);
    Array<OneD, NekDouble> tmp;
 
    NekDouble alpha;
    NekDouble beta;
    NekDouble rho;
    NekDouble rho_new;
    NekDouble mu;
    NekDouble eps;
    Array<OneD, NekDouble> vExchange(3, 0.0);
 
    // Copy initial residual from input
    Vmath::Vcopy(nNonDir, pInput + nDir, 1, r_A, 1);
 
    // Zero homogeneous out array ready for solution updates
    // Should not be earlier in case input vector is same as
    // output and above copy has been peformed
    Vmath::Zero(nNonDir, tmp = pOutput + nDir, 1);
 
    // Evaluate initial residual error for exit check
    vExchange[2] = Vmath::Dot2(nNonDir, r_A, r_A, m_map + nDir);
 
    m_rowComm->AllReduce(vExchange[2], Nektar::LibUtilities::ReduceSum);
 
    eps = vExchange[2];
 
    if (m_rhs_magnitude == NekConstants::kNekUnsetDouble)
    {
        Set_Rhs_Magnitude(pInput);
    }
 
    m_totalIterations = 0;
 
    // If input residual is less than tolerance skip solve.
    if (eps < m_NekLinSysTolerance * m_NekLinSysTolerance * m_rhs_magnitude)
    {
        if (m_verbose && m_root)
        {
            cout << "CG iterations made = " << m_totalIterations
                 << " using tolerance of " << m_NekLinSysTolerance
                 << " (error = " << sqrt(eps / m_rhs_magnitude)
                 << ", rhs_mag = " << sqrt(m_rhs_magnitude) << ")" << endl;
        }
        return;
    }
 
    m_operator.DoNekSysPrecon(r_A, tmp = w_A + nDir);
    m_operator.DoNekSysLhsEval(w_A, s_A);
 
    vExchange[0] = Vmath::Dot2(nNonDir, r_A, w_A + nDir, m_map + nDir);
    vExchange[1] = Vmath::Dot2(nNonDir, s_A + nDir, w_A + nDir, m_map + nDir);
 
    m_rowComm->AllReduce(vExchange, Nektar::LibUtilities::ReduceSum);
 
    rho               = vExchange[0];
    mu                = vExchange[1];
    beta              = 0.0;
    alpha             = rho / mu;
    m_totalIterations = 1;
 
    // Continue until convergence
    while (true)
    {
        if (m_totalIterations > m_NekLinSysMaxIterations)
        {
            if (m_root)
            {
                cout << "CG iterations made = " << m_totalIterations
                     << " using tolerance of " << m_NekLinSysTolerance
                     << " (error = " << sqrt(eps / m_rhs_magnitude)
                     << ", rhs_mag = " << sqrt(m_rhs_magnitude) << ")" << endl;
            }
            ROOTONLY_NEKERROR(ErrorUtil::efatal,
                              "Exceeded maximum number of iterations");
        }
 
        // Compute new search direction p_k, q_k
        Vmath::Svtvp(nNonDir, beta, &p_A[0], 1, &w_A[nDir], 1, &p_A[0], 1);
        Vmath::Svtvp(nNonDir, beta, &q_A[0], 1, &s_A[nDir], 1, &q_A[0], 1);
 
        // Update solution x_{k+1}
        Vmath::Svtvp(nNonDir, alpha, &p_A[0], 1, &pOutput[nDir], 1,
                     &pOutput[nDir], 1);
 
        // Update residual vector r_{k+1}
        Vmath::Svtvp(nNonDir, -alpha, &q_A[0], 1, &r_A[0], 1, &r_A[0], 1);
 
        // Apply preconditioner
        m_operator.DoNekSysPrecon(r_A, tmp = w_A + nDir);
 
        // Perform the method-specific matrix-vector multiply operation.
        m_operator.DoNekSysLhsEval(w_A, s_A);
 
        // <r_{k+1}, w_{k+1}>
        vExchange[0] = Vmath::Dot2(nNonDir, r_A, w_A + nDir, m_map + nDir);
 
        // <s_{k+1}, w_{k+1}>
        vExchange[1] =
            Vmath::Dot2(nNonDir, s_A + nDir, w_A + nDir, m_map + nDir);
 
        // <r_{k+1}, r_{k+1}>
        vExchange[2] = Vmath::Dot2(nNonDir, r_A, r_A, m_map + nDir);
 
        // Perform inner-product exchanges
        m_rowComm->AllReduce(vExchange, Nektar::LibUtilities::ReduceSum);
 
        rho_new = vExchange[0];
        mu      = vExchange[1];
        eps     = vExchange[2];
 
        m_totalIterations++;
 
        // Test if norm is within tolerance
        if (eps < m_NekLinSysTolerance * m_NekLinSysTolerance * m_rhs_magnitude)
        {
            if (m_verbose && m_root)
            {
                cout << "CG iterations made = " << m_totalIterations
                     << " using tolerance of " << m_NekLinSysTolerance
                     << " (error = " << sqrt(eps / m_rhs_magnitude)
                     << ", rhs_mag = " << sqrt(m_rhs_magnitude) << ")" << endl;
            }
            break;
        }
 
        // Compute search direction and solution coefficients
        beta  = rho_new / rho;
        alpha = rho_new / (mu - rho_new * beta / alpha);
        rho   = rho_new;
    }
}
} // namespace Nektar::LibUtilities