DiffusionSolverTimeInt.cpp

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///////////////////////////////////////////////////////////////////////////////
//
// File: DiffusionSolverTimeInt.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).
//
// 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: Diffusion solver
//
///////////////////////////////////////////////////////////////////////////////
 
#include <cstdlib>
 
#include <LibUtilities/BasicUtils/FieldIO.h>
#include <LibUtilities/BasicUtils/SessionReader.h>
#include <LibUtilities/TimeIntegration/TimeIntegrationScheme.h>
#include <LibUtilities/TimeIntegration/TimeIntegrationSchemeOperators.h>
 
#include <MultiRegions/ContField.h>
#include <SpatialDomains/MeshGraph.h>
 
using namespace std;
using namespace Nektar;
 
class Diffusion
{
public:
    Diffusion(int argc, char *argv[]);
    ~Diffusion();
 
    void TimeIntegrate();
 
    void DoImplicitSolve(
        const Array<OneD, const Array<OneD, NekDouble>> &inarray,
        Array<OneD, Array<OneD, NekDouble>> &outarray, const NekDouble time,
        const NekDouble lambda);
 
private:
    LibUtilities::SessionReaderSharedPtr session;
    LibUtilities::FieldIOSharedPtr fld;
    string sessionName;
    SpatialDomains::MeshGraphSharedPtr graph;
    MultiRegions::ContFieldSharedPtr field;
 
    LibUtilities::TimeIntegrationSchemeSharedPtr intScheme;
    LibUtilities::TimeIntegrationSchemeOperators ode;
    Array<OneD, Array<OneD, NekDouble>> fields;
 
    LibUtilities::TimeIntScheme timeInt;
    unsigned int nSteps;
    NekDouble delta_t;
    NekDouble epsilon;
    NekDouble lambda;
 
    void WriteSolution();
    void ExactSolution();
};
 
Diffusion::Diffusion(int argc, char *argv[])
{
    // Create session reader.
    session = LibUtilities::SessionReader::CreateInstance(argc, argv);
 
    // Read the geometry and the expansion information
    graph = SpatialDomains::MeshGraph::Read(session);
 
    // Create Field I/O object.
    fld = LibUtilities::FieldIO::CreateDefault(session);
 
    // Get some information from the session
    sessionName = session->GetSessionName();
 
    // Create time integration scheme.
    if (session->DefinesTimeIntScheme())
    {
        timeInt = session->GetTimeIntScheme();
    }
    else
    {
        timeInt.method = session->GetSolverInfo("TimeIntegrationMethod");
    }
 
    nSteps  = session->GetParameter("NumSteps");
    delta_t = session->GetParameter("TimeStep");
    epsilon = session->GetParameter("epsilon");
    lambda  = 1.0 / delta_t / epsilon;
 
    // Set up the field
    field = MemoryManager<MultiRegions::ContField>::AllocateSharedPtr(
        session, graph, session->GetVariable(0));
 
    fields    = Array<OneD, Array<OneD, NekDouble>>(1);
    fields[0] = field->UpdatePhys();
 
    // Get coordinates of physical points
    unsigned int nq = field->GetNpoints();
    Array<OneD, NekDouble> x0(nq), x1(nq), x2(nq);
    field->GetCoords(x0, x1, x2);
 
    // Evaluate initial condition
    LibUtilities::EquationSharedPtr icond =
        session->GetFunction("InitialConditions", "u");
    icond->Evaluate(x0, x1, x2, 0.0, field->UpdatePhys());
}
 
Diffusion::~Diffusion()
{
    session->Finalise();
}
 
void Diffusion::TimeIntegrate()
{
    intScheme = LibUtilities::GetTimeIntegrationSchemeFactory().CreateInstance(
        timeInt.method, timeInt.variant, timeInt.order, timeInt.freeParams);
 
    ode.DefineImplicitSolve(&Diffusion::DoImplicitSolve, this);
 
    // Initialise the scheme for actual time integration scheme
    intScheme->InitializeScheme(delta_t, fields, 0.0, ode);
 
    // Zero field coefficients for initial guess for linear solver.
    Vmath::Zero(field->GetNcoeffs(), field->UpdateCoeffs(), 1);
 
    for (int n = 0; n < nSteps; ++n)
    {
        fields = intScheme->TimeIntegrate(n, delta_t);
    }
 
    Vmath::Vcopy(field->GetNpoints(), fields[0], 1, field->UpdatePhys(), 1);
 
    WriteSolution();
    ExactSolution();
}
 
void Diffusion::DoImplicitSolve(
    const Array<OneD, const Array<OneD, NekDouble>> &inarray,
    Array<OneD, Array<OneD, NekDouble>> &outarray,
    [[maybe_unused]] const NekDouble time, const NekDouble lambda)
{
    StdRegions::ConstFactorMap factors;
    factors[StdRegions::eFactorLambda] = 1.0 / lambda / epsilon;
 
    for (int i = 0; i < inarray.size(); ++i)
    {
        // Multiply RHS by 1.0/timestep/lambda
        Vmath::Smul(field->GetNpoints(), -factors[StdRegions::eFactorLambda],
                    inarray[i], 1, outarray[i], 1);
 
        // Solve a system of equations with Helmholtz solver
        field->HelmSolve(outarray[i], field->UpdateCoeffs(), factors);
 
        // Transform to physical space and store in solution vector
        field->BwdTrans(field->GetCoeffs(), outarray[i]);
    }
}
 
void Diffusion::WriteSolution()
{
    // Write solution to file
    std::vector<LibUtilities::FieldDefinitionsSharedPtr> FieldDef =
        field->GetFieldDefinitions();
    std::vector<std::vector<NekDouble>> FieldData(FieldDef.size());
    for (int i = 0; i < FieldDef.size(); ++i)
    {
        FieldDef[i]->m_fields.push_back("u");
        field->AppendFieldData(FieldDef[i], FieldData[i]);
    }
    fld->Write(session->GetSessionName() + ".fld", FieldDef, FieldData);
}
 
void Diffusion::ExactSolution()
{
    unsigned int nq = field->GetNpoints();
    Array<OneD, NekDouble> x0(nq), x1(nq), x2(nq);
    field->GetCoords(x0, x1, x2);
 
    LibUtilities::EquationSharedPtr ex_sol =
        session->GetFunction("ExactSolution", 0);
 
    if (ex_sol)
    {
        // evaluate exact solution
        Array<OneD, NekDouble> exact(nq);
        ex_sol->Evaluate(x0, x1, x2, (nSteps)*delta_t, exact);
 
        // Calculate errors
        cout << "L inf error:      " << field->Linf(field->GetPhys(), exact)
             << endl;
        cout << "L 2 error:        " << field->L2(field->GetPhys(), exact)
             << endl;
        cout << "H 1 error:        " << field->H1(field->GetPhys(), exact)
             << endl;
    }
}
 
int main(int argc, char *argv[])
{
    try
    {
        Diffusion ops(argc, argv);
        ops.TimeIntegrate();
    }
    catch (const std::runtime_error &e)
    {
        exit(-1);
    }
    catch (const std::string &eStr)
    {
        cout << "Error: " << eStr << endl;
        exit(-1);
    }
}