CardiacNewtonSolver.hpp

/*

Copyright (C) University of Oxford, 2005-2010

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University of Oxford, having an administrative office at Wellington
Square, Oxford OX1 2JD, UK.

This file is part of Chaste.

Chaste is free software: you can redistribute it and/or modify it
under the terms of the GNU Lesser General Public License as published
by the Free Software Foundation, either version 2.1 of the License, or
(at your option) any later version.

Chaste is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
License for more details. The offer of Chaste under the terms of the
License is subject to the License being interpreted in accordance with
English Law and subject to any action against the University of Oxford
being under the jurisdiction of the English Courts.

You should have received a copy of the GNU Lesser General Public License
along with Chaste. If not, see <http://www.gnu.org/licenses/>.

*/
#ifndef CARDIACNEWTONSOLVER_HPP_
#define CARDIACNEWTONSOLVER_HPP_

#include <cmath>

#include "AbstractBackwardEulerCardiacCell.hpp"

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

    void Solve(AbstractBackwardEulerCardiacCell<SIZE> &rCell,
               double time,
               double rCurrentGuess[SIZE])
    {
        unsigned counter = 0;
//        const double eps = 1e-6 * rCurrentGuess[0]; // Our tolerance (should use min(guess) perhaps?)
        const double eps = 1e-6; // JonW tolerance
        double norm = 2*eps;

        // check that the initial guess that was given gives a valid residual
        rCell.ComputeResidual(time, rCurrentGuess, mResidual);
        for (unsigned i=0; i<SIZE; i++)
        {
            assert(!std::isnan(mResidual[i]));
        }

        while (norm > eps)
        {
            // Calculate Jacobian for current guess
            rCell.ComputeJacobian(time, rCurrentGuess, mJacobian);

//            // Update norm (our style)
//            norm = ComputeNorm(mResidual);

            // Solve Newton linear system
            SolveLinearSystem();

            // Update norm (JonW style)
            norm = ComputeNorm(mUpdate);

            // Update current guess and recalculate residual
            for (unsigned i=0; i<SIZE; i++)
            {
                rCurrentGuess[i] -= mUpdate[i];
            }
            rCell.ComputeResidual(time, rCurrentGuess, mResidual);

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



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

    double ComputeNorm(double vector[SIZE])
    {
        double norm = 0.0;
        for (unsigned i=0; i<SIZE; i++)
        {
            if (fabs(vector[i]) > norm)
            {
                norm = fabs(vector[i]);
            }
        }
        return norm;
    }

    void SolveLinearSystem()
    {
        double fact;
        for (unsigned i=0; i<SIZE; i++)
        {
            for (unsigned ii=i+1; ii<SIZE; ii++)
            {
                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];
            }
        }
        /*This must be int, since an unsigned down-loop wouldn't terminate*/
        for (int i=SIZE-1; i>=0; i--)
        {
            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:
    double mResidual[SIZE];
    double mJacobian[SIZE][SIZE];
    double mUpdate[SIZE];
};

#endif /*CARDIACNEWTONSOLVER_HPP_*/