DiscreteSystemForceCalculator.cpp

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*/
 
#include "DiscreteSystemForceCalculator.hpp"
 
DiscreteSystemForceCalculator::DiscreteSystemForceCalculator(MeshBasedCellPopulation<2>& rCellPopulation,
                                                             std::vector<boost::shared_ptr<AbstractTwoBodyInteractionForce<2> > > forceCollection)
    : mrCellPopulation(rCellPopulation),
      mForceCollection(forceCollection),
      mEpsilon(0.01)
{
}
 
std::vector< std::vector<double> > DiscreteSystemForceCalculator::CalculateExtremalNormalForces()
{
    unsigned num_nodes = mrCellPopulation.GetNumNodes();
 
    std::vector< std::vector<double> > extremal_normal_forces;
    std::vector<double> minimum_normal_forces(num_nodes);
    std::vector<double> maximum_normal_forces(num_nodes);
 
    for (unsigned i=0; i<num_nodes; i++)
    {
        std::vector<double> sampling_angles = GetSamplingAngles(i);
        std::vector<double> extremal_angles = GetExtremalAngles(i, sampling_angles);
 
        double minimum_normal_force_for_node_i = DBL_MAX;
        double maximum_normal_force_for_node_i = -DBL_MAX;
 
        for (unsigned j=0; j<extremal_angles.size(); j++)
        {
            double current_normal_force = CalculateFtAndFn(i, extremal_angles[j])[1];
 
            if (current_normal_force > maximum_normal_force_for_node_i)
            {
                maximum_normal_force_for_node_i = current_normal_force;
            }
            if (current_normal_force < minimum_normal_force_for_node_i)
            {
                minimum_normal_force_for_node_i = current_normal_force;
            }
        }
 
        assert( minimum_normal_force_for_node_i <= maximum_normal_force_for_node_i);
 
        minimum_normal_forces[i] = minimum_normal_force_for_node_i;
        maximum_normal_forces[i] = maximum_normal_force_for_node_i;
    }
 
    extremal_normal_forces.push_back(minimum_normal_forces);
    extremal_normal_forces.push_back(maximum_normal_forces);
 
    return extremal_normal_forces;
}
 
void DiscreteSystemForceCalculator::WriteResultsToFile(std::string simulationOutputDirectory)
{
    double time = SimulationTime::Instance()->GetTime();
    std::ostringstream time_string;
    time_string << time;
    std::string results_directory = simulationOutputDirectory + "/results_from_time_" + time_string.str();
 
    OutputFileHandler output_file_handler2(results_directory+"/", false);
    mpVizStressResultsFile = output_file_handler2.OpenOutputFile("results.vizstress");
 
    (*mpVizStressResultsFile) <<  time << "\t";
 
    double global_index;
    double x;
    double y;
    double minimum;
    double maximum;
 
    TetrahedralMesh<2,2>& r_mesh = mrCellPopulation.rGetMesh();
 
    std::vector< std::vector<double> > extremal_normal_forces = CalculateExtremalNormalForces();
 
    for (unsigned i=0; i<r_mesh.GetNumNodes(); i++)
    {
        global_index = (double) i;
 
        x = r_mesh.GetNode(i)->rGetLocation()[0];
        y = r_mesh.GetNode(i)->rGetLocation()[1];
 
        minimum = extremal_normal_forces[0][i];
        maximum = extremal_normal_forces[1][i];
 
        (*mpVizStressResultsFile) << global_index << " " << x << " " << y << " " << minimum << " " << maximum << " ";
    }
 
    (*mpVizStressResultsFile) << "\n";
    mpVizStressResultsFile->close();
}
 
std::vector<double> DiscreteSystemForceCalculator::CalculateFtAndFn(unsigned index, double theta)
{
    TetrahedralMesh<2,2>& r_mesh = mrCellPopulation.rGetMesh();
 
    std::set<unsigned> neighbouring_node_indices = mrCellPopulation.GetNeighbouringNodeIndices(index);
 
    double tangential_force = 0.0;
    double normal_force = 0.0;
    double alpha;
 
    c_vector<double,2> unit_vec_between_nodes(2);
 
    for (std::set<unsigned>::iterator iter = neighbouring_node_indices.begin();
         iter != neighbouring_node_indices.end();
         ++iter)
    {
        // The method GetAngleBetweenNodes() returns an angle in the range (-pi,pi]
        alpha = r_mesh.GetAngleBetweenNodes(index, *iter);
 
        assert(alpha <= M_PI);
        assert(alpha > -M_PI);
 
        if (sin(alpha-theta) > DBL_EPSILON)
        {
            // Initialise a zero force vector between neighbouring nodes
            c_vector<double,2> force_between_nodes = zero_vector<double>(2);
 
            // Iterate over vector of forces present and add up forces between nodes
            for (std::vector<boost::shared_ptr<AbstractTwoBodyInteractionForce<2> > >::iterator force_iter = mForceCollection.begin();
                 force_iter != mForceCollection.end();
                 ++force_iter)
            {
               force_between_nodes += (*force_iter)->CalculateForceBetweenNodes(index, *iter, mrCellPopulation);
            }
 
            unit_vec_between_nodes[0] = cos(alpha);
            unit_vec_between_nodes[1] = sin(alpha);
 
            double plusminus_norm_force = inner_prod(force_between_nodes,unit_vec_between_nodes);
            tangential_force += plusminus_norm_force * cos(alpha-theta);
            normal_force += plusminus_norm_force * sin(alpha-theta);
        }
    }
 
    std::vector<double> ret(2);
    ret[0] = tangential_force;
    ret[1] = normal_force;
 
    return ret;
}
 
std::vector<double> DiscreteSystemForceCalculator::GetSamplingAngles(unsigned index)
{
    TetrahedralMesh<2,2>& r_mesh = mrCellPopulation.rGetMesh();
 
    std::set<unsigned> neighbouring_node_indices = mrCellPopulation.GetNeighbouringNodeIndices(index);
 
    std::vector<double> sampling_angles(4*neighbouring_node_indices.size());
 
    unsigned i=0;
 
    for (std::set<unsigned>::iterator iter = neighbouring_node_indices.begin();
         iter != neighbouring_node_indices.end();
         ++iter)
    {
        // The method GetAngleBetweenNodes() returns an angle in the range (-pi,pi]
        double alpha = r_mesh.GetAngleBetweenNodes(index, *iter);
 
        double alpha_minus_epsilon = alpha - mEpsilon;
        double alpha_plus_epsilon = alpha + mEpsilon;
        double alpha_plus_pi_minus_epsilon = alpha + M_PI - mEpsilon;
        double alpha_plus_pi_plus_epsilon = alpha + M_PI + mEpsilon;
 
        // Calculate sampling angles in the range (-pi,pi]
        if (alpha_minus_epsilon <= -M_PI)
        {
            alpha_minus_epsilon += 2*M_PI;
        }
        sampling_angles[i] = alpha_minus_epsilon;
 
        assert(sampling_angles[i] <= M_PI);
        assert(sampling_angles[i] > -M_PI);
        i++;
 
        if (alpha_plus_epsilon > M_PI)
        {
            alpha_plus_epsilon -= 2*M_PI;
        }
        sampling_angles[i] = alpha_plus_epsilon;
 
        assert(sampling_angles[i] <= M_PI);
        assert(sampling_angles[i] > -M_PI);
        i++;
 
        if (alpha_plus_pi_minus_epsilon > M_PI)
        {
            alpha_plus_pi_minus_epsilon -= 2*M_PI;
        }
        sampling_angles[i] = alpha_plus_pi_minus_epsilon;
 
        assert(sampling_angles[i] <= M_PI);
        assert(sampling_angles[i] > -M_PI);
        i++;
 
        if (alpha_plus_pi_plus_epsilon > M_PI)
        {
            alpha_plus_pi_plus_epsilon -= 2*M_PI;
        }
        sampling_angles[i] = alpha_plus_pi_plus_epsilon;
 
        assert(sampling_angles[i] <= M_PI);
        assert(sampling_angles[i] > -M_PI);
        i++;
    }
 
    sort(sampling_angles.begin(), sampling_angles.end());
    return sampling_angles;
}
 
double DiscreteSystemForceCalculator::GetLocalExtremum(unsigned index, double angle1, double angle2)
{
    // We always pass in angle1 and angle2 such that angle1<angle2,
    // but note that angle1 may be <M_PI
    assert(angle1 < angle2);
 
    double tolerance = 1e-5;
    unsigned counter = 0;
 
    double previous_angle;
    double current_error;
    double current_angle = angle1;
 
    current_error = angle2 - angle1;
    std::vector<double> current_ft_and_fn(2);
 
    while (current_error > tolerance)
    {
        previous_angle = current_angle;
        current_ft_and_fn = CalculateFtAndFn(index, current_angle);
        current_angle -= current_ft_and_fn[0]/current_ft_and_fn[1];
        current_error = fabs(current_angle - previous_angle);
        counter++;
    }
 
    assert(current_angle>angle1 && current_angle<angle2);
    assert(current_error < tolerance);
 
    return current_angle;
}
 
std::vector<double> DiscreteSystemForceCalculator::GetExtremalAngles(unsigned index, std::vector<double> samplingAngles)
{
    std::vector<double> extremal_angles;
    std::vector<double> ft_and_fn(2);
    std::vector<double> tangential_force(samplingAngles.size());
 
    for (unsigned i=0; i<samplingAngles.size(); i++)
    {
        ft_and_fn = CalculateFtAndFn(index, samplingAngles[i]);
        tangential_force[i] = ft_and_fn[0];
    }
 
    unsigned n = samplingAngles.size()-1;
 
    for (unsigned i=0; i<n; i++)
    {
        if ((tangential_force[i%n]>0 && tangential_force[(i+1)%n]<0)
            || (tangential_force[i%n]<0 && tangential_force[(i+1)%n]>0))
        {
            double next_extremal_angle;
 
            // If we are in the interval that crosses the branch line at pi,
            // then subtract 2*pi from the positive angle
            if (i==n-1)
            {
                samplingAngles[i%n] -= 2*M_PI;
            }
 
            if (samplingAngles[(i+1)%n] - samplingAngles[i%n] < 2*mEpsilon + 1e-6 )
            {
                // If we find a jump through zero, then the local extremum is
                // simply at the mid-point of the interval
                next_extremal_angle = 0.5*(samplingAngles[(i+1)%n] + samplingAngles[i%n]);
            }
            else
            {
                // Otherwise we need to find it using Newton's method
                next_extremal_angle = GetLocalExtremum(index, samplingAngles[i%n], samplingAngles[(i+1)%n]);
            }
 
            if (next_extremal_angle <= -M_PI)
            {
                next_extremal_angle += 2*M_PI;
            }
            assert(next_extremal_angle>-M_PI && next_extremal_angle<=M_PI);
            extremal_angles.push_back(next_extremal_angle);
        }
    }
 
    return extremal_angles;
}
 
void DiscreteSystemForceCalculator::SetEpsilon(double epsilon)
{
    mEpsilon = epsilon;
}