CardiacNewtonSolver.hpp

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*/
#ifndef CARDIACNEWTONSOLVER_HPP_
#define CARDIACNEWTONSOLVER_HPP_

#include <cmath>
#include "IsNan.hpp"
#include "UblasCustomFunctions.hpp"
#include "AbstractBackwardEulerCardiacCell.hpp"
#include "Warnings.hpp"

template<unsigned SIZE, typename CELLTYPE>
class CardiacNewtonSolver
{
public:
    static CardiacNewtonSolver<SIZE, CELLTYPE>* Instance()
    {
        static CardiacNewtonSolver<SIZE, CELLTYPE> inst;
        return &inst;
    }

    void Solve(CELLTYPE &rCell,
               double time,
               double rCurrentGuess[SIZE])
    {
        unsigned counter = 0;
        const double eps = 1e-6; // JonW tolerance

        // check that the initial guess that was given gives a valid residual
        rCell.ComputeResidual(time, rCurrentGuess, mResidual.data());
        double norm_of_residual = norm_inf(mResidual);
        assert(!std::isnan(norm_of_residual));
        double norm_of_update = 0.0; //Properly initialised in the loop
        do
        {
            // Calculate Jacobian for current guess
            rCell.ComputeJacobian(time, rCurrentGuess, mJacobian);

            // Solve Newton linear system for mUpdate, given mJacobian and mResidual
            SolveLinearSystem();

            // Update norm (JonW style)
            norm_of_update = norm_inf(mUpdate);

            // Update current guess and recalculate residual
            for (unsigned i=0; i<SIZE; i++)
            {
                rCurrentGuess[i] -= mUpdate[i];
            }
            double norm_of_previous_residual = norm_of_residual;
            rCell.ComputeResidual(time, rCurrentGuess, mResidual.data());
            norm_of_residual = norm_inf(mResidual);
            if (norm_of_residual > norm_of_previous_residual && norm_of_update > eps)
            {
                //Second part of guard:
                //Note that if norm_of_update < eps (converged) then it's
                //likely that both the residual and the previous residual were
                //close to the root.

                //Work out where the biggest change in the guess has happened.
                double relative_change_max = 0.0;
                unsigned relative_change_direction = 0;
                for (unsigned i=0; i<SIZE; i++)
                {
                    double relative_change = fabs(mUpdate[i]/rCurrentGuess[i]);
                    if (relative_change > relative_change_max)
                    {
                        relative_change_max = relative_change;
                        relative_change_direction = i;
                    }
                }

                if (relative_change_max > 1.0)
                {
                    //Only walk 0.2 of the way in that direction (put back 0.8)
                    rCurrentGuess[relative_change_direction] += 0.8*mUpdate[relative_change_direction];
                    rCell.ComputeResidual(time, rCurrentGuess, mResidual.data());
                    norm_of_residual = norm_inf(mResidual);
                    WARNING("Residual increasing and one direction changing radically - back tracking in that direction");
                }
            }
            counter++;

            // avoid infinite loops
            if (counter > 15)
            {
#define COVERAGE_IGNORE
                EXCEPTION("Newton method diverged in CardiacNewtonSolver::Solve()");
#undef COVERAGE_IGNORE
            }
        }
        while (norm_of_update > eps);

#define COVERAGE_IGNORE
#ifndef NDEBUG
        if (norm_of_residual > 2e-10)
        { //This line is for correlation - in case we use norm_of_residual as convergence criterion
            WARN_ONCE_ONLY("Newton iteration terminated because update vector norm is small, but residual norm is not small.");
        }
#endif // NDEBUG
#undef COVERAGE_IGNORE
    }

protected:
    CardiacNewtonSolver()
    {}
    CardiacNewtonSolver(const CardiacNewtonSolver<SIZE, CELLTYPE>&);
    CardiacNewtonSolver<SIZE, CELLTYPE>& operator= (const CardiacNewtonSolver<SIZE, CELLTYPE>&);

    void SolveLinearSystem()
    {
        for (unsigned i=0; i<SIZE; i++)
        {
            for (unsigned ii=i+1; ii<SIZE; ii++)
            {
                double fact = mJacobian[ii][i]/mJacobian[i][i];
                for (unsigned j=i; j<SIZE; j++)
                {
                    mJacobian[ii][j] -= fact*mJacobian[i][j];
                }
                mResidual[ii] -= fact*mResidual[i];
            }
        }
        for (unsigned i=SIZE; i-- > 0; )
        {
            mUpdate[i] = mResidual[i];
            for (unsigned j=i+1; j<SIZE; j++)
            {
                mUpdate[i] -= mJacobian[i][j]*mUpdate[j];
            }
            mUpdate[i] /= mJacobian[i][i];
        }
    }

private:
    c_vector<double, SIZE> mResidual;
    double mJacobian[SIZE][SIZE];
    c_vector<double, SIZE> mUpdate;
};

#endif /*CARDIACNEWTONSOLVER_HPP_*/