IMEXTimeIntegrationSchemes.h

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///////////////////////////////////////////////////////////////////////////////
//
// File: IMEXTimeIntegrationSchemes.h
//
// For more information, please see: http://www.nektar.info
//
// The MIT License
//
// Copyright (c) 2018 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
// 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
// THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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// DEALINGS IN THE SOFTWARE.
//
// Description: Combined header file for all basic IMEX time integration
// schemes.
//
///////////////////////////////////////////////////////////////////////////////
 
// Note : If adding a new integrator be sure to register the
// integrator with the Time Integration Scheme Facatory in
// SchemeInitializor.cpp.
 
#ifndef NEKTAR_LIB_UTILITIES_TIME_INTEGRATION_IMEX_TIME_INTEGRATION_SCHEME
#define NEKTAR_LIB_UTILITIES_TIME_INTEGRATION_IMEX_TIME_INTEGRATION_SCHEME
 
#define LUE LIB_UTILITIES_EXPORT
 
#include <LibUtilities/TimeIntegration/IMEXdirkTimeIntegrationSchemes.h>
#include <LibUtilities/TimeIntegration/TimeIntegrationSchemeGLM.h>
 
namespace Nektar::LibUtilities
{
 
///////////////////////////////////////////////////////////////////////////////
// IMEX Order N
 
class IMEXTimeIntegrationScheme : public TimeIntegrationSchemeGLM
{
public:
    IMEXTimeIntegrationScheme(std::string variant, size_t order,
                              std::vector<NekDouble> freeParams)
        : TimeIntegrationSchemeGLM(variant, order, freeParams)
    {
        if (variant == "dirk" || variant == "DIRK")
        {
            ASSERTL1(freeParams.size() == 2,
                     "IMEX DIRK Time integration scheme invalid number "
                     "of free parameters, expected two "
                     "<implicit stages, explicit stages>, received " +
                         std::to_string(freeParams.size()));
 
            size_t s     = freeParams[0];
            size_t sigma = freeParams[1];
 
            m_integration_phases    = TimeIntegrationAlgorithmGLMVector(1);
            m_integration_phases[0] = TimeIntegrationAlgorithmGLMSharedPtr(
                new TimeIntegrationAlgorithmGLM(this));
 
            if (order == 1 && s == 1 && sigma == 1)
            {
                // This phase is Forward Backward Euler which has two steps.
                IMEXdirkTimeIntegrationScheme::SetupSchemeData_1_1_1(
                    m_integration_phases[0]);
            }
            else
            {
                IMEXdirkTimeIntegrationScheme::SetupSchemeData(
                    m_integration_phases[0], order, freeParams);
            }
        }
        else if (variant == "")
        {
            // Currently up to 4th order is implemented.
            ASSERTL1(1 <= order && order <= 4,
                     "IMEX Time integration scheme bad order (1-4): " +
                         std::to_string(order));
 
            m_integration_phases = TimeIntegrationAlgorithmGLMVector(order);
 
            for (size_t n = 0; n < order; ++n)
            {
                m_integration_phases[n] = TimeIntegrationAlgorithmGLMSharedPtr(
                    new TimeIntegrationAlgorithmGLM(this));
            }
 
            // Last phase
            IMEXTimeIntegrationScheme::SetupSchemeData(
                m_integration_phases[order - 1], order);
 
            // Initial phases
            switch (order)
            {
                case 1:
                    // No intial phase.
                    break;
 
                case 2:
                    IMEXTimeIntegrationScheme::SetupSchemeData(
                        m_integration_phases[0], 1);
                    break;
 
                case 3:
                    IMEXdirkTimeIntegrationScheme::SetupSchemeData(
                        m_integration_phases[0], 3,
                        std::vector<NekDouble>{3, 4});
                    IMEXdirkTimeIntegrationScheme::SetupSchemeData(
                        m_integration_phases[1], 3,
                        std::vector<NekDouble>{3, 4});
                    break;
 
                case 4:
                    IMEXdirkTimeIntegrationScheme::SetupSchemeData(
                        m_integration_phases[0], 3,
                        std::vector<NekDouble>{3, 4});
                    IMEXdirkTimeIntegrationScheme::SetupSchemeData(
                        m_integration_phases[1], 3,
                        std::vector<NekDouble>{3, 4});
                    IMEXdirkTimeIntegrationScheme::SetupSchemeData(
                        m_integration_phases[2], 3,
                        std::vector<NekDouble>{3, 4});
                    break;
 
                default:
                    ASSERTL1(false, "IMEX Time integration scheme bad order: " +
                                        std::to_string(order));
            }
        }
        else
        {
            ASSERTL1(false, "IMEX Time integration scheme bad variant: " +
                                variant + ". Must be blank or 'dirk'");
        }
    }
 
    ~IMEXTimeIntegrationScheme() override = default;
 
    static TimeIntegrationSchemeSharedPtr create(
        std::string variant, size_t order, std::vector<NekDouble> freeParams)
    {
        TimeIntegrationSchemeSharedPtr p =
            MemoryManager<IMEXTimeIntegrationScheme>::AllocateSharedPtr(
                variant, order, freeParams);
 
        return p;
    }
 
    static std::string className;
 
    LUE static void SetupSchemeData(TimeIntegrationAlgorithmGLMSharedPtr &phase,
                                    size_t order)
    {
        constexpr NekDouble ABcoefficients[5] = {0.,
                                                 1.,         // 1st Order
                                                 2. / 3.,    // 2nd Order
                                                 6. / 11.,   // 3rd Order
                                                 12. / 25.}; // 4th Order
 
        // Nsteps = 2 * order
 
        // clang-format off
        constexpr NekDouble UVcoefficients[5][8] =
            { {         0.,    0.,     0.,        0.,
                        0.,    0.,     0.,        0. },
              // 1st Order
              {         1.,    1.,     0.,        0.,
                        0.,    0.,     0.,        0. },
              // 2nd Order
              {  4./ 3.,  -1./ 3.,  4./3.,   -2./ 3.,
                 0.,           0.,     0.,        0. },
              // 3rd Order
              {  18./11.,  -9./11.,  2./11.,  18./11.,
                -18./11.,   6./11.,      0.,       0. },
              // 4th Order
              { 48./25., -36./25., 16./25.,  -3./25.,
                48./25., -72./25., 48./25., -12./25. } };
        // clang-format on
 
        phase->m_schemeType = eIMEX;
        phase->m_order      = order;
        phase->m_name =
            std::string("IMEXOrder" + std::to_string(phase->m_order));
 
        phase->m_numsteps  = 2 * phase->m_order;
        phase->m_numstages = 1;
 
        phase->m_A = Array<OneD, Array<TwoD, NekDouble>>(2);
        phase->m_B = Array<OneD, Array<TwoD, NekDouble>>(2);
 
        phase->m_A[0] =
            Array<TwoD, NekDouble>(phase->m_numstages, phase->m_numstages, 0.0);
        phase->m_B[0] =
            Array<TwoD, NekDouble>(phase->m_numsteps, phase->m_numstages, 0.0);
        phase->m_A[1] =
            Array<TwoD, NekDouble>(phase->m_numstages, phase->m_numstages, 0.0);
        phase->m_B[1] =
            Array<TwoD, NekDouble>(phase->m_numsteps, phase->m_numstages, 0.0);
        phase->m_U =
            Array<TwoD, NekDouble>(phase->m_numstages, phase->m_numsteps, 0.0);
        phase->m_V =
            Array<TwoD, NekDouble>(phase->m_numsteps, phase->m_numsteps, 0.0);
 
        // Coefficients
        phase->m_B[1][phase->m_order][0] = 1.0;
 
        phase->m_A[0][0][0] = ABcoefficients[phase->m_order];
        phase->m_B[0][0][0] = ABcoefficients[phase->m_order];
 
        for (size_t n = 0; n < 2 * phase->m_order; ++n)
        {
            phase->m_U[0][n] = UVcoefficients[phase->m_order][n];
            phase->m_V[0][n] = UVcoefficients[phase->m_order][n];
        }
 
        // V evaluation value shuffling row n column n-1
        for (size_t n = 1; n < 2 * phase->m_order; ++n)
        {
            if (n != phase->m_order)
            {
                phase->m_V[n][n - 1] = 1.0; // constant 1
            }
        }
 
        phase->m_numMultiStepValues         = phase->m_order;
        phase->m_numMultiStepImplicitDerivs = 0;
        phase->m_numMultiStepExplicitDerivs = phase->m_order;
 
        phase->m_timeLevelOffset = Array<OneD, size_t>(phase->m_numsteps);
 
        // Values and derivatives needed.
        for (size_t n = 0; n < phase->m_order; ++n)
        {
            phase->m_timeLevelOffset[n]                  = n;
            phase->m_timeLevelOffset[phase->m_order + n] = n;
        }
 
        phase->CheckAndVerify();
    }
 
protected:
    LUE std::string v_GetFullName() const override
    {
        return m_integration_phases.back()->m_name;
    }
 
    LUE std::string v_GetName() const override
    {
        return std::string("IMEX");
    }
 
    LUE NekDouble v_GetTimeStability() const override
    {
        return 1.0;
    }
 
}; // end class IMEXTimeIntegrationScheme
 
} // namespace Nektar::LibUtilities
 
#endif