SimpleNewtonNonlinearSolver.cpp

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#include "SimpleNewtonNonlinearSolver.hpp"
#include <iostream>
#include <cassert>
#include "Exception.hpp"

SimpleNewtonNonlinearSolver::SimpleNewtonNonlinearSolver(double linearSolverRelativeTolerance)
        : mLinearSolverRelativeTolerance(linearSolverRelativeTolerance),
        mTolerance(1e-5),
        mWriteStats(false)
{
    mTestDampingValues.push_back(-0.1);
    mTestDampingValues.push_back(0.05);
    for (unsigned i=1; i<=12; i++)
    {
        double val = double(i)/10;
        mTestDampingValues.push_back(val);
    }
}

SimpleNewtonNonlinearSolver::~SimpleNewtonNonlinearSolver()
{}

Vec SimpleNewtonNonlinearSolver::Solve(PetscErrorCode (*pComputeResidual)(SNES,Vec,Vec,void*),
                                       PetscErrorCode (*pComputeJacobian)(SNES,Vec,Mat*,Mat*,MatStructure*,void*),
                                       Vec initialGuess,
                                       unsigned fill,
                                       void* pContext)
{
    PetscInt size;
    VecGetSize(initialGuess, &size);

    Vec current_solution;
    VecDuplicate(initialGuess, &current_solution);
    VecCopy(initialGuess, current_solution);

    LinearSystem linear_system(current_solution, fill);

    (*pComputeResidual)(NULL, current_solution, linear_system.rGetRhsVector(), pContext);


    double residual_norm;
    VecNorm(linear_system.rGetRhsVector(), NORM_2, &residual_norm);
    double scaled_residual_norm = residual_norm/size;

    if (mWriteStats)
    {
        std::cout << "Newton's method:\n  Initial ||residual||/N = " << scaled_residual_norm
                  << "\n  Attempting to solve to tolerance " << mTolerance << "..\n";
    }

    double old_scaled_residual_norm;
    unsigned counter = 0;
    while (scaled_residual_norm > mTolerance)
    {
        counter++;

        // Store the old norm to check with the new later
        old_scaled_residual_norm = scaled_residual_norm;

        // Compute Jacobian and solve J dx = f for the (negative) update dx, (J the jacobian, f the residual)
        (*pComputeJacobian)(NULL, current_solution, &(linear_system.rGetLhsMatrix()), NULL, NULL, pContext);

        Vec negative_update = linear_system.Solve();


        Vec test_vec;
        VecDuplicate(initialGuess, &test_vec);

        double best_damping_factor = 1.0;
        double best_scaled_residual = 1e20; // large

        // Loop over all the possible damping value and determine which gives smallest residual
        for (unsigned i=0; i<mTestDampingValues.size(); i++)
        {
            // Note: WAXPY calls VecWAXPY(w,a,x,y) which computes w = ax+y
            PetscVecTools::WAXPY(test_vec,-mTestDampingValues[i],negative_update,current_solution);

            // Compute new residual
            linear_system.ZeroLinearSystem();
            (*pComputeResidual)(NULL, test_vec, linear_system.rGetRhsVector(), pContext);
            VecNorm(linear_system.rGetRhsVector(), NORM_2, &residual_norm);
            scaled_residual_norm = residual_norm/size;

            if (scaled_residual_norm < best_scaled_residual)
            {
                best_scaled_residual = scaled_residual_norm;
                best_damping_factor = mTestDampingValues[i];
            }
        }
        PetscTools::Destroy(test_vec);

        // Check the smallest residual was actually smaller than the previous; if not, quit
        if (best_scaled_residual > old_scaled_residual_norm)
        {
            // Free memory
            PetscTools::Destroy(current_solution);
            PetscTools::Destroy(negative_update);

            // Raise error
            EXCEPTION("Iteration " << counter << ", unable to find damping factor such that residual decreases in update direction");
        }

        if (mWriteStats)
        {
            std::cout << "    Best damping factor = " << best_damping_factor << "\n";
        }

        // Update solution: current_guess = current_solution - best_damping_factor*negative_update
        PetscVecTools::AddScaledVector(current_solution, negative_update, -best_damping_factor);
        scaled_residual_norm = best_scaled_residual;
        PetscTools::Destroy(negative_update);

        // Compute best residual vector again and store in linear_system for next Solve()
        linear_system.ZeroLinearSystem();
        (*pComputeResidual)(NULL, current_solution, linear_system.rGetRhsVector(), pContext);

        if (mWriteStats)
        {
            std::cout << "    Iteration " << counter << ": ||residual||/N = " << scaled_residual_norm << "\n";
        }
    }

    if (mWriteStats)
    {
        std::cout << "  ..solved!\n\n";
    }

    return current_solution;
}

void SimpleNewtonNonlinearSolver::SetTolerance(double tolerance)
{
    assert(tolerance > 0);
    mTolerance = tolerance;
}