AdamsBashforthTimeIntegrationSchemes.h

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///////////////////////////////////////////////////////////////////////////////
//
// File: AdamsBashforthTimeIntegrationSchemes.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
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
// DEALINGS IN THE SOFTWARE.
//
// Description: Combined header file for all Adams Bashforth based 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_AB_TIME_INTEGRATION_SCHEME
#define NEKTAR_LIB_UTILITIES_TIME_INTEGRATION_AB_TIME_INTEGRATION_SCHEME
 
#define LUE LIB_UTILITIES_EXPORT
 
#include <LibUtilities/TimeIntegration/RungeKuttaTimeIntegrationSchemes.h>
#include <LibUtilities/TimeIntegration/TimeIntegrationSchemeGLM.h>
 
namespace Nektar::LibUtilities
{
 
///////////////////////////////////////////////////////////////////////////////
// Adams Bashforth Order N
 
class AdamsBashforthTimeIntegrationScheme : public TimeIntegrationSchemeGLM
{
public:
    AdamsBashforthTimeIntegrationScheme(std::string variant, size_t order,
                                        std::vector<NekDouble> freeParams)
        : TimeIntegrationSchemeGLM(variant, order, freeParams)
    {
        // Currently up to 4th order is implemented.
        ASSERTL1(1 <= order && order <= 4,
                 "AdamsBashforth 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));
        }
 
        // Next to last phase
        if (order > 1)
        {
            AdamsBashforthTimeIntegrationScheme::SetupSchemeData(
                m_integration_phases[order - 2], order - 1);
        }
 
        // Last phase
        AdamsBashforthTimeIntegrationScheme::SetupSchemeData(
            m_integration_phases[order - 1], order);
 
        // Initial phases
        switch (order)
        {
            case 1:
                // No intial phases.
                break;
 
            case 2:
                // Intial phase set above
                break;
 
            case 3:
                // Order 2
                RungeKuttaTimeIntegrationScheme::SetupSchemeData(
                    m_integration_phases[0], "", 2, std::vector<NekDouble>());
                break;
 
            case 4:
                // SSP Order 3
                RungeKuttaTimeIntegrationScheme::SetupSchemeData(
                    m_integration_phases[0], "SSP", 3,
                    std::vector<NekDouble>());
                // SSP Order 3
                RungeKuttaTimeIntegrationScheme::SetupSchemeData(
                    m_integration_phases[1], "SSP", 3,
                    std::vector<NekDouble>());
                break;
 
            default:
                ASSERTL1(false,
                         "AdamsBashforth Time integration scheme bad order: " +
                             std::to_string(order));
        }
    }
 
    ~AdamsBashforthTimeIntegrationScheme() override = default;
 
    static TimeIntegrationSchemeSharedPtr create(
        std::string variant, size_t order, std::vector<NekDouble> freeParams)
    {
        TimeIntegrationSchemeSharedPtr p = MemoryManager<
            AdamsBashforthTimeIntegrationScheme>::AllocateSharedPtr(variant,
                                                                    order,
                                                                    freeParams);
 
        return p;
    }
 
    static std::string className;
 
    LUE static void SetupSchemeData(TimeIntegrationAlgorithmGLMSharedPtr &phase,
                                    size_t order)
    {
        // clang-format off
        constexpr NekDouble coefficients[5][4] =
            { {      0.,       0.,      0.,      0. },
              // 1st Order
              {      1.,       0.,      0.,      0. },
              // 2nd Order
              {  3./ 2.,  -1./ 2.,      0.,      0. },
              // 3rd Order
              { 23./12., -16./12.,  5./12.,      0. },
              // 4th Order
              { 55./24., -59./24., 37./24., -9./24.} };
        // clang-format on
 
        phase->m_schemeType = eExplicit;
        phase->m_order      = order;
        phase->m_name =
            std::string("AdamsBashforthOrder" + std::to_string(phase->m_order));
 
        phase->m_numsteps  = phase->m_order;
        phase->m_numstages = 1;
 
        phase->m_A = Array<OneD, Array<TwoD, NekDouble>>(1);
        phase->m_B = Array<OneD, Array<TwoD, NekDouble>>(1);
 
        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_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
 
        // B Coefficient for first row first column
        phase->m_B[0][0][0] = coefficients[phase->m_order][0];
 
        // B evaluation value shuffling second row first column
        if (phase->m_order > 1)
        {
            phase->m_B[0][1][0] = 1.0;
        }
 
        // U Curent time step evaluation first row first column
        phase->m_U[0][0] = 1.0;
        phase->m_V[0][0] = 1.0;
 
        // V Coefficients for first row additional columns
        for (size_t n = 1; n < phase->m_order; ++n)
        {
            phase->m_V[0][n] = coefficients[phase->m_order][n];
        }
 
        // V evaluation value shuffling row n column n-1
        for (size_t n = 2; n < phase->m_order; ++n)
        {
            phase->m_V[n][n - 1] = 1.0;
        }
 
        phase->m_numMultiStepValues         = 1;
        phase->m_numMultiStepImplicitDerivs = 0;
        phase->m_numMultiStepExplicitDerivs = phase->m_order - 1;
        phase->m_timeLevelOffset    = Array<OneD, size_t>(phase->m_numsteps);
        phase->m_timeLevelOffset[0] = 0;
 
        // For order > 1 derivatives are needed.
        for (size_t n = 1; n < phase->m_order; ++n)
        {
            phase->m_timeLevelOffset[n] = n;
        }
 
        phase->CheckAndVerify();
    }
 
protected:
    LUE std::string v_GetName() const override
    {
        return std::string("AdamsBashforth");
    }
 
    LUE NekDouble v_GetTimeStability() const override
    {
        if (GetOrder() == 1)
        {
            return 2.0;
        }
        else if (GetOrder() == 2)
        {
            return 1.0;
        }
        else if (GetOrder() == 3)
        {
            return 0.545454545454545;
        }
        else if (GetOrder() == 4)
        {
            return 0.3;
        }
        else
        {
            return 2.0;
        }
    }
 
}; // end class AdamsBashforthTimeIntegrationScheme
 
} // namespace Nektar::LibUtilities
 
#endif