BackwardEulerIvpOdeSolver.cpp

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#include "BackwardEulerIvpOdeSolver.hpp"
#include <cmath>
 
void BackwardEulerIvpOdeSolver::ComputeResidual(AbstractOdeSystem* pAbstractOdeSystem,
                                                double timeStep,
                                                double time,
                                                std::vector<double>& rCurrentYValues,
                                                std::vector<double>& rCurrentGuess)
{
    std::vector<double> dy(mSizeOfOdeSystem); //For JC to optimize
    pAbstractOdeSystem->EvaluateYDerivatives(time+timeStep, rCurrentGuess, dy);
    for (unsigned i=0; i<mSizeOfOdeSystem; i++)
    {
        mResidual[i] = rCurrentGuess[i] - timeStep * dy[i] - rCurrentYValues[i];
    }
}
 
void BackwardEulerIvpOdeSolver::ComputeJacobian(AbstractOdeSystem* pAbstractOdeSystem,
                                                double timeStep,
                                                double time,
                                                std::vector<double>& rCurrentYValues,
                                                std::vector<double>& rCurrentGuess)
{
    for (unsigned i=0; i<mSizeOfOdeSystem; i++)
    {
        for (unsigned j=0; j<mSizeOfOdeSystem; j++)
        {
            mJacobian[i][j] = 0.0;
        }
    }
 
    if (pAbstractOdeSystem->GetUseAnalyticJacobian() && !mForceUseOfNumericalJacobian)
    {
        // The ODE system has an analytic jacobian, so use that
        auto* p_ode_system = static_cast<AbstractOdeSystemWithAnalyticJacobian*>(pAbstractOdeSystem);
        p_ode_system->AnalyticJacobian(rCurrentGuess, mJacobian, time, timeStep);
    }
    else
    {
        ComputeNumericalJacobian(pAbstractOdeSystem,
                                 timeStep,
                                 time,
                                 rCurrentYValues,
                                 rCurrentGuess);
    }
}
 
void BackwardEulerIvpOdeSolver::SolveLinearSystem()
{
    double fact;
    for (unsigned i=0; i<mSizeOfOdeSystem; i++)
    {
        for (unsigned ii=i+1; ii<mSizeOfOdeSystem; ii++)
        {
            fact = mJacobian[ii][i]/mJacobian[i][i];
            for (unsigned j=i; j<mSizeOfOdeSystem; j++)
            {
                mJacobian[ii][j] -= fact*mJacobian[i][j];
            }
            mResidual[ii] -= fact*mResidual[i];
        }
    }
    // This needs to int, since a downloop in unsigned won't terminate properly
    for (int i=mSizeOfOdeSystem-1; i>=0; i--)
    {
        mUpdate[i] = mResidual[i];
        for (unsigned j=i+1; j<mSizeOfOdeSystem; j++)
        {
            mUpdate[i] -= mJacobian[i][j]*mUpdate[j];
        }
        mUpdate[i] /= mJacobian[i][i];
    }
}
 
double BackwardEulerIvpOdeSolver::ComputeNorm(double* pVector)
{
    double norm = 0.0;
    for (unsigned i=0; i<mSizeOfOdeSystem; i++)
    {
        if (fabs(pVector[i]) > norm)
        {
            norm = fabs(pVector[i]);
        }
    }
    return norm;
}
 
void BackwardEulerIvpOdeSolver::ComputeNumericalJacobian(AbstractOdeSystem* pAbstractOdeSystem,
                                                         double timeStep,
                                                         double time,
                                                         std::vector<double>& rCurrentYValues,
                                                         std::vector<double>& rCurrentGuess)
{
    std::vector<double> residual(mSizeOfOdeSystem);
    std::vector<double> residual_perturbed(mSizeOfOdeSystem);
    std::vector<double> guess_perturbed(mSizeOfOdeSystem);
 
    double epsilon = mNumericalJacobianEpsilon;
 
    ComputeResidual(pAbstractOdeSystem, timeStep, time, rCurrentYValues, rCurrentGuess);
    for (unsigned i=0; i<mSizeOfOdeSystem; i++)
    {
        residual[i] = mResidual[i];
    }
 
    for (unsigned global_column=0; global_column<mSizeOfOdeSystem; global_column++)
    {
        for (unsigned i=0; i<mSizeOfOdeSystem; i++)
        {
            guess_perturbed[i] = rCurrentGuess[i];
        }
 
        guess_perturbed[global_column] += epsilon;
 
        ComputeResidual(pAbstractOdeSystem, timeStep, time, rCurrentYValues, guess_perturbed);
        for (unsigned i=0; i<mSizeOfOdeSystem; i++)
        {
            residual_perturbed[i] = mResidual[i];
        }
 
        // Compute residual_perturbed - residual
        double one_over_eps = 1.0/epsilon;
        for (unsigned i=0; i<mSizeOfOdeSystem; i++)
        {
            mJacobian[i][global_column] = one_over_eps*(residual_perturbed[i] - residual[i]);
        }
    }
}
 
void BackwardEulerIvpOdeSolver::CalculateNextYValue(AbstractOdeSystem* pAbstractOdeSystem,
                                                    double timeStep,
                                                    double time,
                                                    std::vector<double>& rCurrentYValues,
                                                    std::vector<double>& rNextYValues)
{
    // Check the size of the ODE system matches the solvers expected
    assert(mSizeOfOdeSystem == pAbstractOdeSystem->GetNumberOfStateVariables());
 
    const double eps = 1e-6; // JonW tolerance
    double norm = 2*eps;
 
    std::vector<double> current_guess(mSizeOfOdeSystem);
    current_guess.assign(rCurrentYValues.begin(), rCurrentYValues.end());
 
    // Ensure no infinite loops by keeping a counter
    // TODO should this limit of 20 be a function param?
    unsigned counter = 0u;
    const unsigned iter_limit = 20u;
    while (norm > eps && counter < iter_limit)
    {
        // Calculate Jacobian and mResidual for current guess
        ComputeResidual(pAbstractOdeSystem, timeStep, time, rCurrentYValues, current_guess);
        ComputeJacobian(pAbstractOdeSystem, timeStep, time, rCurrentYValues, current_guess);
 
        // Solve Newton linear system
        SolveLinearSystem();
 
        // Update norm (JonW style)
        norm = ComputeNorm(mUpdate);
 
        // Update current guess
        for (unsigned i=0; i<mSizeOfOdeSystem; i++)
        {
            current_guess[i] -= mUpdate[i];
        }
 
        counter++;
    }
    assert(counter < iter_limit); // avoid infinite loops
 
    rNextYValues.assign(current_guess.begin(), current_guess.end());
}
 
BackwardEulerIvpOdeSolver::BackwardEulerIvpOdeSolver(unsigned sizeOfOdeSystem)
{
    mSizeOfOdeSystem = sizeOfOdeSystem;
 
    // default epsilon
    mNumericalJacobianEpsilon = 1e-6;
    mForceUseOfNumericalJacobian = false;
 
    // allocate memory
    mResidual = new double[mSizeOfOdeSystem];
    mUpdate = new double[mSizeOfOdeSystem];
 
    mJacobian = new double*[mSizeOfOdeSystem];
    for (unsigned i=0; i<mSizeOfOdeSystem; i++)
    {
        mJacobian[i] = new double[mSizeOfOdeSystem];
    }
}
 
BackwardEulerIvpOdeSolver::~BackwardEulerIvpOdeSolver()
{
    // Delete pointers
    delete[] mResidual;
    delete[] mUpdate;
 
    for (unsigned i=0; i<mSizeOfOdeSystem; i++)
    {
        delete[] mJacobian[i];
    }
    delete[] mJacobian;
}
 
void BackwardEulerIvpOdeSolver::SetEpsilonForNumericalJacobian(double epsilon)
{
    assert(epsilon > 0);
    mNumericalJacobianEpsilon = epsilon;
}
 
void BackwardEulerIvpOdeSolver::ForceUseOfNumericalJacobian()
{
    mForceUseOfNumericalJacobian = true;
}
 
 
// Serialization for Boost >= 1.36
#include "SerializationExportWrapperForCpp.hpp"
CHASTE_CLASS_EXPORT(BackwardEulerIvpOdeSolver)