NekLinSysIterGMRES.h

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///////////////////////////////////////////////////////////////////////////////
//
// File: NekLinSysIterGMRES.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).
//
// 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"),
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// Software is furnished to do so, subject to the following conditions:
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//
// Description: NekLinSysIterGMRES header
//
///////////////////////////////////////////////////////////////////////////////
 
#ifndef NEKTAR_LIB_UTILITIES_LINEAR_ALGEBRA_NEK_LINSYS_ITERAT_GMRES_H
#define NEKTAR_LIB_UTILITIES_LINEAR_ALGEBRA_NEK_LINSYS_ITERAT_GMRES_H
 
#include <LibUtilities/LinearAlgebra/NekLinSysIter.h>
#include <deque>
 
namespace Nektar::LibUtilities
{
/// A global linear system.
class NekLinSysIterGMRES;
 
class NekLinSysIterGMRES : public NekLinSysIter
{
public:
    /// Support creation through MemoryManager.
    friend class MemoryManager<NekLinSysIterGMRES>;
 
    LIB_UTILITIES_EXPORT static NekLinSysIterSharedPtr create(
        const LibUtilities::SessionReaderSharedPtr &pSession,
        const LibUtilities::CommSharedPtr &vRowComm, const int nDimen,
        const NekSysKey &pKey)
    {
        NekLinSysIterSharedPtr p =
            MemoryManager<NekLinSysIterGMRES>::AllocateSharedPtr(
                pSession, vRowComm, nDimen, pKey);
        p->InitObject();
        return p;
    }
 
    static std::string className;
 
    LIB_UTILITIES_EXPORT NekLinSysIterGMRES(
        const LibUtilities::SessionReaderSharedPtr &pSession,
        const LibUtilities::CommSharedPtr &vRowComm, const int nDimen,
        const NekSysKey &pKey = NekSysKey());
    LIB_UTILITIES_EXPORT ~NekLinSysIterGMRES() override = default;
 
    LIB_UTILITIES_EXPORT int GetMaxLinIte()
    {
        return (m_maxrestart * m_LinSysMaxStorage);
    }
 
    /**
     * @brief Data exported from GMRES for use by the Newton hook-step solver.
     * The data stored here correspond to the most recently completed GMRES
     * restart block.
     */
    struct GMRESHookData
    {
        /// True if hook step data is usable.
        bool valid = false;
        /// Current Krylov subspace dimension, number of done Arnoldi sweeps
        int nswp = 0;
        /// Dimension of the system; length of each Krylov vector
        int nGlobal = 0;
        /// Offset to the non-Dirichlet part of the vector;
        /// active size is nGlobal - nDir
        int nDir = 0;
        /// Initial residual norm beta used in || beta e_1 - H y ||_2
        NekDouble beta = 0.0;
 
        /// Arnoldi basis vectors V_0,...,V_m;
        /// contains nswp + 1 vectors of length nGlobal.
        Array<OneD, Array<OneD, NekDouble>> V;
        /// Arnoldi Hessenberg matrix stored by columns: H[col][row].
        /// H size is (nswp + 1) x nswp.
        Array<OneD, Array<OneD, NekDouble>> H;
        /// Unconstrained reduced GMRES solution y of size nswp.
        Array<OneD, NekDouble> yNewton;
    };
 
    /**
     * @brief Enable or disable export of GMRES Arnoldi data for the hook-step
     *        nonlinear solver.
     * @param flag If true, GMRES exports hook-step data.
     * @return LIB_UTILITIES_EXPORT
     */
    LIB_UTILITIES_EXPORT void EnableHookStepExport(bool flag)
    {
        m_ExportHookData = flag;
    }
 
    /**
     * @brief Get the Hook Data object.
     * Check if GMRESHookData::valid before using the data.
     *
     * @return LIB_UTILITIES_EXPORT const&
     */
    LIB_UTILITIES_EXPORT const GMRESHookData &GetHookData() const
    {
        return m_HookData;
    }
 
    LIB_UTILITIES_EXPORT bool UsingLeftPrecon() const
    {
        return m_NekLinSysLeftPrecon;
    }
 
    LIB_UTILITIES_EXPORT bool UsingRightPrecon() const
    {
        return m_NekLinSysRightPrecon;
    }
 
    LIB_UTILITIES_EXPORT void ApplyRightPrecon(
        const Array<OneD, const NekDouble> &in, Array<OneD, NekDouble> &out)
    {
        Array<OneD, NekDouble> tmpIn(in.size(), 0.0);
        Vmath::Vcopy(in.size(), in, 1, tmpIn, 1);
        m_operator.DoNekSysPrecon(tmpIn, out);
    }
 
protected:
    // This is maximum gmres restart iteration
    int m_maxrestart;
 
    // This is maximum bandwidth of Hessenburg matrix
    // if use truncted Gmres(m)
    int m_KrylovMaxHessMatBand;
 
    // This is the maximum number of solution vectors that can be stored
    // For example, in gmres, it is the max number of Krylov space
    // search directions can be stored
    // It determines the max storage usage
    int m_LinSysMaxStorage;
 
    NekDouble m_prec_factor = 1.0;
 
    bool m_NekLinSysLeftPrecon    = false;
    bool m_NekLinSysRightPrecon   = true;
    bool m_GMRESCentralDifference = false;
 
    // True, if GMRES data needs to be exported to compute the hook step
    bool m_ExportHookData = false;
    // Hook step data needed to compute the hook step
    GMRESHookData m_HookData;
 
    void v_InitObject() override;
 
    int v_SolveSystem(const int nGlobal,
                      const Array<OneD, const NekDouble> &pInput,
                      Array<OneD, NekDouble> &pOutput, const int nDir) override;
 
    void v_DoIterate(const int nGlobal, const Array<OneD, NekDouble> &rhs,
                     Array<OneD, NekDouble> &x, const int nDir, NekDouble &err,
                     int &iter) override;
 
private:
    /// Actual iterative solve-GMRES
    int DoGMRES(const int pNumRows, const Array<OneD, const NekDouble> &pInput,
                Array<OneD, NekDouble> &pOutput, const int pNumDir);
 
    /// Actual iterative gmres solver for one restart
    NekDouble DoGmresRestart(const unsigned int nrestart, const bool truncted,
                             const int nGlobal,
                             const Array<OneD, const NekDouble> &pInput,
                             Array<OneD, NekDouble> &pOutput, const int nDir);
 
    // Arnoldi process
    void DoArnoldi(const int starttem, const int endtem, const int nGlobal,
                   const int nDir, Array<OneD, NekDouble> &w,
                   // V[nd] current search direction
                   Array<OneD, NekDouble> &V1,
                   // V[nd+1] new search direction
                   Array<OneD, NekDouble> &V2,
                   // One line of Hessenburg matrix
                   Array<OneD, NekDouble> &h);
 
    // QR fatorization through Givens rotation
    void DoGivensRotation(const int starttem, const int endtem,
                          Array<OneD, NekDouble> &c, Array<OneD, NekDouble> &s,
                          Array<OneD, NekDouble> &h,
                          Array<OneD, NekDouble> &eta);
 
    // Backward calculation to calculate coeficients
    // of least square problem
    // To notice, Hessenburg's columnns and rows are reverse
    void DoBackward(const int number, Array<OneD, Array<OneD, NekDouble>> &A,
                    const Array<OneD, const NekDouble> &b,
                    Array<OneD, NekDouble> &y);
 
    static std::string lookupIds[];
    static std::string def;
 
    // Hessenburg matrix
    Array<OneD, Array<OneD, NekDouble>> m_hes;
    // Hesseburg matrix after rotation
    Array<OneD, Array<OneD, NekDouble>> m_Upper;
    // Total search directions
    Array<OneD, Array<OneD, NekDouble>> m_V_total;
    Array<OneD, Array<OneD, NekDouble>> m_Z_total;
    std::deque<Array<OneD, NekDouble>> m_delta;
 
    bool m_flexible;
    unsigned int m_GMRESDeltaDirection;
};
} // namespace Nektar::LibUtilities
 
#endif