DiffusionSolver.cpp

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///////////////////////////////////////////////////////////////////////////////
//
// File: DiffusionSolver.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 framework solver
//
///////////////////////////////////////////////////////////////////////////////
 
#include <LibUtilities/BasicUtils/FieldIO.h>
#include <LibUtilities/BasicUtils/SessionReader.h>
#include <MultiRegions/ContField.h>
#include <SpatialDomains/MeshGraph.h>
 
using namespace std;
using namespace Nektar;
 
int main(int argc, char *argv[])
{
    LibUtilities::SessionReaderSharedPtr session;
    LibUtilities::FieldIOSharedPtr fld;
    SpatialDomains::MeshGraphSharedPtr graph;
    MultiRegions::ContFieldSharedPtr field;
    LibUtilities::EquationSharedPtr icond, ex_sol;
    StdRegions::ConstFactorMap factors;
 
    try
    {
        // 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 about the session
        string sessionName  = session->GetSessionName();
        string outFile      = sessionName + ".fld";
        unsigned int nSteps = session->GetParameter("NumSteps");
        NekDouble delta_t   = session->GetParameter("TimeStep");
        NekDouble epsilon   = session->GetParameter("epsilon");
 
        // Create field
        field = MemoryManager<MultiRegions::ContField>::AllocateSharedPtr(
            session, graph, session->GetVariable(0));
 
        // 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 at these points
        icond = session->GetFunction("InitialConditions", "u");
        icond->Evaluate(x0, x1, x2, 0.0, field->UpdatePhys());
 
        // Compute lambda in the Helmholtz problem
        factors[StdRegions::eFactorLambda] = 1.0 / delta_t / epsilon;
 
        // Zero field coefficients for initial guess for linear solver.
        Vmath::Zero(field->GetNcoeffs(), field->UpdateCoeffs(), 1);
 
        // Time integrate using backward Euler
        for (unsigned int n = 0; n < nSteps; ++n)
        {
            Vmath::Smul(nq, -1.0 / delta_t / epsilon, field->GetPhys(), 1,
                        field->UpdatePhys(), 1);
 
            field->HelmSolve(field->GetPhys(), field->UpdateCoeffs(), factors);
 
            field->BwdTrans(field->GetCoeffs(), field->UpdatePhys());
        }
 
        // 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(outFile, FieldDef, FieldData);
 
        // Check for exact solution
        ex_sol = session->GetFunction("ExactSolution", 0);
        if (ex_sol)
        {
            // Allocate storage
            Array<OneD, NekDouble> exact(nq);
 
            //----------------------------------------------
            // Evaluate exact solution
            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;
            //--------------------------------------------
        }
 
        // Finalise session
        session->Finalise();
    }
    catch (const std::runtime_error &e)
    {
        return 1;
    }
    catch (const std::string &eStr)
    {
        cout << "Error: " << eStr << endl;
    }
 
    return 0;
}