ImplicitTimeIntegrationSchemeSDC.h

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///////////////////////////////////////////////////////////////////////////////
//
// File: ImplicitTimeIntegrationSchemeSDC.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).
//
// 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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// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
// DEALINGS IN THE SOFTWARE.
//
// Description: Header file of time integration scheme SDC base class
//
///////////////////////////////////////////////////////////////////////////////
 
#ifndef NEKTAR_LIB_UTILITIES_TIME_INTEGRATION_IMPLICIT_TIME_INTEGRATION_SCHEME_SDC
#define NEKTAR_LIB_UTILITIES_TIME_INTEGRATION_IMPLICIT_TIME_INTEGRATION_SCHEME_SDC
 
#define LUE LIB_UTILITIES_EXPORT
 
#include <string>
 
#include <LibUtilities/BasicUtils/VmathArray.hpp>
#include <LibUtilities/TimeIntegration/TimeIntegrationSchemeSDC.h>
 
namespace Nektar
{
namespace LibUtilities
{
class ImplicitTimeIntegrationSchemeSDC : public TimeIntegrationSchemeSDC
{
public:
    ImplicitTimeIntegrationSchemeSDC(std::string variant, unsigned int order,
                                     std::vector<NekDouble> freeParams)
        : TimeIntegrationSchemeSDC(variant, order, freeParams)
    {
        ASSERTL0(variant == "GaussRadauLegendre",
                 "only GaussRadauLegendre variant "
                 "(quadrature) type available for ImplicitSDC");
        ASSERTL0(0.0 < freeParams[0],
                 "Spectral Deferred Correction Time integration "
                 "scheme bad parameter numbers (> 0.0): " +
                     std::to_string(freeParams[0]));
 
        m_name       = "ImplicitSpectralDeferredCorrection";
        m_schemeType = eImplicit;
    }
 
    static TimeIntegrationSchemeSharedPtr create(
        std::string variant, unsigned int order,
        std::vector<NekDouble> freeParams)
    {
        TimeIntegrationSchemeSharedPtr p =
            MemoryManager<ImplicitTimeIntegrationSchemeSDC>::AllocateSharedPtr(
                variant, order, freeParams);
 
        return p;
    }
 
    static std::string className;
 
protected:
    LUE virtual void v_InitializeScheme(
        const NekDouble deltaT, ConstDoubleArray &y_0, const NekDouble time,
        const TimeIntegrationSchemeOperators &op) override;
 
    LUE virtual void v_ResidualEval(
        const NekDouble &delta_t, const int n,
        const TimeIntegrationSchemeOperators &op) override;
 
    LUE virtual void v_ResidualEval(
        const NekDouble &delta_t,
        const TimeIntegrationSchemeOperators &op) override;
 
    LUE virtual void v_ComputeInitialGuess(
        const NekDouble &delta_t,
        const TimeIntegrationSchemeOperators &op) override;
 
    LUE virtual void v_SDCIterationLoop(
        const NekDouble &delta_t,
        const TimeIntegrationSchemeOperators &op) override;
 
}; // end class ImplicitTimeIntegrationSchemeSDC
 
/**
 * @brief Worker method to initialize the integration scheme.
 */
void ImplicitTimeIntegrationSchemeSDC::v_InitializeScheme(
    const NekDouble deltaT, ConstDoubleArray &y_0, const NekDouble time,
    const TimeIntegrationSchemeOperators &op)
{
    TimeIntegrationSchemeSDC::v_InitializeScheme(deltaT, y_0, time, op);
}
 
/**
 * @brief Worker method to compute the residual.
 */
void ImplicitTimeIntegrationSchemeSDC::v_ResidualEval(
    const NekDouble &delta_t, const int n,
    const TimeIntegrationSchemeOperators &op)
{
    // Compute residual
    op.DoOdeRhs(m_Y[n], m_F[n], m_time + delta_t * m_points[n]);
}
 
void ImplicitTimeIntegrationSchemeSDC::v_ResidualEval(
    const NekDouble &delta_t, const TimeIntegrationSchemeOperators &op)
{
    // Compute residual
    for (unsigned int n = 0; n < m_nQuadPts; ++n)
    {
        v_ResidualEval(delta_t, n, op);
    }
}
 
/**
 * @brief Worker method to compute the initial SDC guess.
 */
void ImplicitTimeIntegrationSchemeSDC::v_ComputeInitialGuess(
    const NekDouble &delta_t, const TimeIntegrationSchemeOperators &op)
{
    // Compute initial guess
    for (unsigned int n = 0; n < m_nQuadPts - 1; ++n)
    {
        // Use implicit Euler as a first guess
        NekDouble dtn = delta_t * (m_points[n + 1] - m_points[n]);
        op.DoImplicitSolve(m_Y[n], m_Y[n + 1],
                           m_time + delta_t * m_points[n + 1], dtn);
 
        // Compute residual from updated solution
        for (unsigned int i = 0; i < m_nvars; ++i)
        {
            Vmath::Vsub(m_npoints, m_Y[n + 1][i], 1, m_Y[n][i], 1,
                        m_F[n + 1][i], 1);
            Vmath::Smul(m_npoints, 1.0 / dtn, m_F[n + 1][i], 1, m_F[n + 1][i],
                        1);
        }
    }
}
 
/**
 * @brief Worker method to compute the SDC iteration.
 */
void ImplicitTimeIntegrationSchemeSDC::v_SDCIterationLoop(
    const NekDouble &delta_t, const TimeIntegrationSchemeOperators &op)
{
    unsigned int kstart = 1;
    for (unsigned int k = kstart; k < m_order; ++k)
    {
        // Update integrated residual
        UpdateIntegratedResidual(delta_t);
 
        // Loop over quadrature points
        for (unsigned int n = 0; n < m_nQuadPts - 1; ++n)
        {
            NekDouble dtn = delta_t * (m_points[n + 1] - m_points[n]);
 
            // Update solution
            for (unsigned int i = 0; i < m_nvars; ++i)
            {
                // Add Fint contribution
                Vmath::Vadd(m_npoints, m_Y[n][i], 1, m_Fint[n][i], 1, m_tmp[i],
                            1);
 
                // Add implicit contribution
                Vmath::Svtvp(m_npoints, -m_theta * dtn, m_F[n + 1][i], 1,
                             m_tmp[i], 1, m_tmp[i], 1);
            }
 
            // Solve implicit system
            op.DoImplicitSolve(m_tmp, m_Y[n + 1],
                               m_time + delta_t * m_points[n + 1],
                               m_theta * dtn);
 
            // Compute residual from updated solution
            for (unsigned int i = 0; i < m_nvars; ++i)
            {
                Vmath::Vsub(m_npoints, m_Y[n + 1][i], 1, m_tmp[i], 1,
                            m_F[n + 1][i], 1);
                Vmath::Smul(m_npoints, 1.0 / (m_theta * dtn), m_F[n + 1][i], 1,
                            m_F[n + 1][i], 1);
            }
        }
    }
}
 
} // end namespace LibUtilities
} // end namespace Nektar
 
#endif