TimeStepper.cpp

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*/

#include <cassert>
#include <cmath>

#include "TimeStepper.hpp"
#include "Exception.hpp"
#include "MathsCustomFunctions.hpp"

TimeStepper::TimeStepper(double startTime, double endTime, double dt, bool enforceConstantTimeStep, std::vector<double> additionalTimes)
    : mStart(startTime),
      mEnd(endTime),
      mDt(dt),
      mTotalTimeStepsTaken(0),
      mAdditionalTimesReached(0),
      mTime(startTime),
      mEpsilon(DBL_EPSILON)
{
    if (startTime > endTime)
    {
        EXCEPTION("The simulation duration must be positive, not " << endTime-startTime);
    }

    // Remove any additionalTimes entries which fall too close to a time when the stepper would stop anyway
    for (unsigned i=0; i<additionalTimes.size(); i++)
    {
        if (i > 0)
        {
            if (additionalTimes[i-1] >= additionalTimes[i])
            {
                EXCEPTION("The additional times vector should be in ascending numerical order; "
                          "entry " << i << " is less than or equal to entry " << i-1 << ".");
            }
        }

        double time_interval = additionalTimes[i] - startTime;

        // When mDt divides this interval (and the interval is positive) then we are going there anyway
        if (!Divides(mDt, time_interval) && (time_interval > DBL_EPSILON))
        {
            mAdditionalTimes.push_back(additionalTimes[i]);
        }
    }

    /*
     * Note that when mEnd is large then the error of subtracting two numbers of
     * that magnitude is about DBL_EPSILON*mEnd (1e-16*mEnd). When mEnd is small
     * then the error should be around DBL_EPSILON.
     */
    if (mEnd > 1.0)
    {
        mEpsilon = DBL_EPSILON*mEnd;
    }

    // If enforceConstantTimeStep check whether the times are such that we won't have a variable dt
    if (enforceConstantTimeStep)
    {
        double expected_end_time = mStart + mDt*EstimateTimeSteps();

        if (fabs( mEnd - expected_end_time ) > mEpsilon)
        {
            EXCEPTION("TimeStepper estimates non-constant timesteps will need to be used: check timestep "
                      "divides (end_time-start_time) (or divides printing timestep). "
                      "[End time=" << mEnd << "; start=" << mStart << "; dt=" << mDt << "; error="
                      << fabs(mEnd-expected_end_time) << "]");
        }
    }

    mNextTime = CalculateNextTime();
}

double TimeStepper::CalculateNextTime()
{
    double next_time = mStart + (mTotalTimeStepsTaken - mAdditionalTimesReached + 1)*mDt;

    // Does the next time bring us very close to the end time?
    // Note that the inequality in this guard matches the inversion of the guard in the enforceConstantTimeStep
    // calculation of the constructor
    if (mEnd - next_time <= mEpsilon)
    {
        next_time = mEnd;
    }

    if (!mAdditionalTimes.empty())
    {
        if (mAdditionalTimesReached < mAdditionalTimes.size())
        {
            // Does this next step take us very close to, or over, an additional time?
            double next_additional_time = mAdditionalTimes[mAdditionalTimesReached];
            double epsilon = next_additional_time > 1 ? next_additional_time*DBL_EPSILON : DBL_EPSILON;
            if (next_additional_time - next_time <= epsilon)
            {
                next_time = next_additional_time;
                mAdditionalTimesReached++;
            }
        }
    }
    return next_time;
}

void TimeStepper::AdvanceOneTimeStep()
{
    mTotalTimeStepsTaken++;
    if (mTotalTimeStepsTaken == 0)
    {
        EXCEPTION("Time step counter has overflowed.");
    }
    if (mTime == mNextTime)
    {
        EXCEPTION("TimeStepper incremented beyond end time.");
    }
    mTime = mNextTime;

    mNextTime = CalculateNextTime();
}

double TimeStepper::GetTime() const
{
    return mTime;
}

double TimeStepper::GetNextTime() const
{
    return mNextTime;
}

double TimeStepper::GetNextTimeStep()
{
    double dt = mDt;

    if (mNextTime == mEnd)
    {
        dt = mEnd - mTime;
    }

    // If the next time or the current time is one of the additional times, the timestep will not be mDt
    if (mAdditionalTimesReached > 0)
    {
        if ((mNextTime == mAdditionalTimes[mAdditionalTimesReached-1]) || (mTime == mAdditionalTimes[mAdditionalTimesReached-1]))
        {
            dt = mNextTime - mTime;
            assert(dt > 0);
        }
    }

    return dt;
}
double TimeStepper::GetIdealTimeStep()
{
    return(mDt);
}

bool TimeStepper::IsTimeAtEnd() const
{
    return (mTime >= mEnd);
}

unsigned TimeStepper::EstimateTimeSteps() const
{
    return (unsigned) floor((mEnd - mStart)/mDt + 0.5) + mAdditionalTimes.size();
}

unsigned TimeStepper::GetTotalTimeStepsTaken() const
{
    return mTotalTimeStepsTaken;
}

void TimeStepper::ResetTimeStep(double dt)
{
    assert(dt > 0);
    /*
     * The error in subtracting two numbers of the same magnitude is about
     * DBL_EPSILON times that magnitude (we use the sum of the two numbers
     * here as a conservative estimate of their maximum). When both mDt and
     * dt are small then the error should be around DBL_EPSILON.
     */
    double scale = DBL_EPSILON*(mDt + dt);
    if (mDt + dt < 1.0)
    {
        scale = DBL_EPSILON;
    }
    if (fabs(mDt-dt) > scale)
    {
        mDt = dt;
        mStart = mTime;
        mTotalTimeStepsTaken = 0;

        mNextTime = CalculateNextTime();
    }
}