ImageWarpingSystem.cpp

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///////////////////////////////////////////////////////////////////////////////
//
// File: ImageWarpingSystem.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: Image warping solve routines
//
///////////////////////////////////////////////////////////////////////////////
 
#include <ImageWarpingSolver/EquationSystems/ImageWarpingSystem.h>
#include <MultiRegions/ContField.h>
 
namespace Nektar
{
 
std::string ImageWarpingSystem::className =
    GetEquationSystemFactory().RegisterCreatorFunction(
        "ImageWarpingSystem", ImageWarpingSystem::create,
        "Image warping system.");
 
/**
 *
 */
ImageWarpingSystem::ImageWarpingSystem(
    const LibUtilities::SessionReaderSharedPtr &pSession,
    const SpatialDomains::MeshGraphSharedPtr &pGraph)
    : UnsteadySystem(pSession, pGraph), AdvectionSystem(pSession, pGraph)
{
}
 
/**
 *
 */
void ImageWarpingSystem::v_InitObject(bool DeclareField)
{
    AdvectionSystem::v_InitObject(DeclareField);
 
    // Define Velocity fields
    m_velocity = Array<OneD, Array<OneD, NekDouble>>(m_spacedim);
    int nq     = m_fields[0]->GetNpoints();
 
    for (int i = 0; i < m_spacedim; ++i)
    {
        m_velocity[i] = Array<OneD, NekDouble>(nq, 0.0);
    }
 
    // Bit of a hack: redefine u/v fields so they are continuous for
    // Helmholtz solve.
    MultiRegions::ContFieldSharedPtr fld =
        MemoryManager<MultiRegions::ContField>::AllocateSharedPtr(
            m_session, m_graph, m_session->GetVariable(2));
    m_fields[2] = fld;
    m_fields[3] = MemoryManager<MultiRegions::ContField>::AllocateSharedPtr(
        *fld, m_graph, m_session->GetVariable(3));
 
    // Tell UnsteadySystem to only integrate first two fields (i.e. I and
    // phi).
    m_intVariables.push_back(0);
    m_intVariables.push_back(1);
 
    // Define the normal velocity fields
    if (m_fields[0]->GetTrace())
    {
        m_traceVn = Array<OneD, NekDouble>(GetTraceNpoints());
    }
 
    std::string advName;
    std::string riemName;
    m_session->LoadSolverInfo("AdvectionType", advName, "WeakDG");
    m_advObject =
        SolverUtils::GetAdvectionFactory().CreateInstance(advName, advName);
    m_advObject->SetFluxVector(&ImageWarpingSystem::GetFluxVector, this);
    m_session->LoadSolverInfo("UpwindType", riemName, "Upwind");
    m_riemannSolver = SolverUtils::GetRiemannSolverFactory().CreateInstance(
        riemName, m_session);
    m_riemannSolver->SetScalar("Vn", &ImageWarpingSystem::GetNormalVelocity,
                               this);
 
    m_advObject->SetRiemannSolver(m_riemannSolver);
    m_advObject->InitObject(m_session, m_fields);
 
    if (m_explicitAdvection)
    {
        m_ode.DefineOdeRhs(&ImageWarpingSystem::DoOdeRhs, this);
        m_ode.DefineProjection(&ImageWarpingSystem::DoOdeProjection, this);
    }
    else
    {
        ASSERTL0(false, "Implicit unsteady Advection not set up.");
    }
}
 
/**
 *
 */
void ImageWarpingSystem::DoOdeRhs(
    const Array<OneD, const Array<OneD, NekDouble>> &inarray,
    Array<OneD, Array<OneD, NekDouble>> &outarray,
    [[maybe_unused]] const NekDouble time)
{
    int npoints = GetNpoints();
    int ncoeffs = inarray[0].size();
    StdRegions::ConstFactorMap factors;
 
    // Load parameter alpha.
    m_session->LoadParameter("Alpha", m_alpha);
 
    ASSERTL0(m_projectionType == MultiRegions::eDiscontinuous,
             "CG not implemented yet.");
 
    // Set up storage arrays.
    Array<OneD, NekDouble> tmp(npoints);
    Array<OneD, NekDouble> alloc(3 * npoints);
    Array<OneD, NekDouble> dIdx1(alloc);
    Array<OneD, NekDouble> dIdx2(alloc + npoints);
    Array<OneD, NekDouble> dIdx3(alloc + 2 * npoints);
 
    // Calculate grad I.
    m_fields[0]->PhysDeriv(inarray[0], dIdx1, dIdx2);
 
    // Set factors.
    // TODO: Check - should be -1?
    factors[StdRegions::eFactorLambda] = 1.0 / m_alpha / m_alpha;
 
    // Multiply by phi, and perform Helmholtz solve to calculate the
    // advection velocity field.
    for (int i = 0; i < 2; ++i)
    {
        Vmath::Vmul(npoints, &alloc[i * npoints], 1, inarray[1].data(), 1,
                    m_fields[i + 2]->UpdatePhys().data(), 1);
        Vmath::Smul(npoints, 1 / m_alpha / m_alpha,
                    m_fields[i + 2]->GetPhys().data(), 1,
                    m_fields[i + 2]->UpdatePhys().data(), 1);
        m_fields[i + 2]->HelmSolve(m_fields[i + 2]->GetPhys(),
                                   m_fields[i + 2]->UpdateCoeffs(), factors);
        m_fields[i + 2]->BwdTrans(m_fields[i + 2]->GetCoeffs(), m_velocity[i]);
    }
 
    // Calculate the weak advection operator for I and phi - result is put
    // in WeakAdv and is in physical space.
    m_advObject->Advect(2, m_fields, m_velocity, inarray, outarray, 0.0);
    for (int i = 0; i < 2; ++i)
    {
        Vmath::Neg(npoints, outarray[i], 1);
    }
 
    // Calculate du/dx -> dIdx1, dv/dy -> dIdx2.
    m_fields[2]->PhysDeriv(m_velocity[0], dIdx1, dIdx3);
    m_fields[3]->PhysDeriv(m_velocity[1], dIdx3, dIdx2);
 
    // Calculate RHS = I*div(u) = I*du/dx + I*dv/dy -> dIdx1.
    Vmath::Vvtvvtp(npoints, dIdx1.data(), 1, inarray[0].data(), 1, dIdx2.data(),
                   1, inarray[0].data(), 1, dIdx1.data(), 1);
 
    // Take inner product to get to coefficient space.
    Array<OneD, NekDouble> tmp2(ncoeffs);
    m_fields[0]->IProductWRTBase(dIdx1, tmp2);
 
    // Multiply by elemental inverse mass matrix, backwards transform
    m_fields[0]->MultiplyByElmtInvMass(tmp2, tmp2);
    m_fields[0]->BwdTrans(tmp2, tmp);
    Vmath::Vadd(npoints, outarray[0], 1, tmp, 1, outarray[0], 1);
}
 
/**
 *
 */
void ImageWarpingSystem::DoOdeProjection(
    const Array<OneD, const Array<OneD, NekDouble>> &inarray,
    Array<OneD, Array<OneD, NekDouble>> &outarray, const NekDouble time)
{
    int nvariables = inarray.size();
    SetBoundaryConditions(time);
 
    switch (m_projectionType)
    {
        case MultiRegions::eDiscontinuous:
        {
            // Just copy over array
            if (inarray != outarray)
            {
                int npoints = GetNpoints();
 
                for (int i = 0; i < nvariables; ++i)
                {
                    Vmath::Vcopy(npoints, inarray[i], 1, outarray[i], 1);
                }
            }
        }
        break;
        default:
            ASSERTL0(false, "Unknown projection scheme");
            break;
    }
}
 
/**
 * @brief Get the normal velocity
 */
Array<OneD, NekDouble> &ImageWarpingSystem::GetNormalVelocity()
{
    // Number of trace (interface) points
    int nTracePts = GetTraceNpoints();
 
    // Auxiliary variable to compute the normal velocity
    Array<OneD, NekDouble> tmp(nTracePts);
 
    // Reset the normal velocity
    Vmath::Zero(nTracePts, m_traceVn, 1);
 
    for (int i = 0; i < m_velocity.size(); ++i)
    {
        m_fields[0]->ExtractTracePhys(m_velocity[i], tmp);
 
        Vmath::Vvtvp(nTracePts, m_traceNormals[i], 1, tmp, 1, m_traceVn, 1,
                     m_traceVn, 1);
    }
 
    return m_traceVn;
}
 
/**
 *
 */
void ImageWarpingSystem::GetFluxVector(
    const Array<OneD, Array<OneD, NekDouble>> &physfield,
    Array<OneD, Array<OneD, Array<OneD, NekDouble>>> &flux)
{
    ASSERTL1(flux[0].size() == m_velocity.size(),
             "Dimension of flux array and velocity array do not match");
 
    int nq = physfield[0].size();
 
    for (int i = 0; i < flux.size(); ++i)
    {
        for (int j = 0; j < flux[0].size(); ++j)
        {
            Vmath::Vmul(nq, physfield[i], 1, m_velocity[j], 1, flux[i][j], 1);
        }
    }
}
 
/**
 *
 */
void ImageWarpingSystem::v_GenerateSummary(SolverUtils::SummaryList &s)
{
    AdvectionSystem::v_GenerateSummary(s);
}
} // namespace Nektar