/// <summary>
/// Calculates a stable time step according to the time step constraints
/// The individual constraints are connected by a harmonic sum
/// </summary>
/// <param name="dt"></param>
/// <returns></returns>
virtual protected double CalculateTimeStep()
{
double dt;
if (TimeStepConstraints.First().dtMin != TimeStepConstraints.First().dtMax)
{
// Use "harmonic sum" of step - sizes, see
// WatkinsAsthanaJameson2016 for the reasoning
dt = 1.0 / TimeStepConstraints.Sum(
c => 1.0 / c.GetGloballyAdmissibleStepSize(SubGrid));
if (dt == 0.0)
{
throw new ArgumentException(
"Time-step size is exactly zero.");
}
else if (double.IsNaN(dt))
{
throw new ArgumentException(
"Could not determine stable time-step size. This indicates illegal values in some cells.");
}
dt = Math.Min(dt, TimeStepConstraints.First().Endtime - Time);
dt = Math.Min(Math.Max(dt, TimeStepConstraints.First().dtMin), TimeStepConstraints.First().dtMax);
}
else
{
dt = TimeStepConstraints.First().dtMin;
dt = Math.Min(dt, TimeStepConstraints.First().Endtime - Time);
}
return(dt);
}
/// <summary>
/// Caluclates the local time step sizes
/// </summary>
/// <returns>the largest stable timestep</returns>
protected override double CalculateTimeStep()
{
if (TimeStepConstraints.First().dtMin != TimeStepConstraints.First().dtMax)
{
var result = clusterer.GetPerCluster_dtHarmonicSum_SubSteps(CurrentClustering, Time, TimeStepConstraints, eps: 1.0e-1);
double[] localDts = result.Item1;
return(localDts[0]);
}
else
{
double dt = TimeStepConstraints.First().dtMin;
dt = Math.Min(dt, TimeStepConstraints.First().Endtime - Time);
return(dt);
}
}
/// <summary>
/// Performs a time step
/// </summary>
/// <param name="dt">Time step size that equals -1, if no fixed time step is prescribed</param>
public override double Perform(double dt)
{
using (var tr = new ilPSP.Tracing.FuncTrace()) {
if (ABevolver[0].HistoryChangeRate.Count >= order - 1)
{
// +++++++++++++++++++++++++++++++++++++++++++
// Standard case -- sufficiently large history
// +++++++++++++++++++++++++++++++++++++++++++
using (var bt = new BlockTrace("AB_LTS_standard", tr)) {
if (!reclusteredByGridRedist)
{
TryNewClustering(dt);
}
List <int> numberOfLocalTimeSteps = new List <int>();
double[] clusterDts = new double[CurrentClustering.NumberOfClusters];
// Set the number of sub steps (is calculated in every time step, regardless of whether a reclustering has been performed or not)
if (TimeStepConstraints != null)
{
//dt = CalculateTimeStep();
// If no dtFixed is set
if (TimeStepConstraints.First().dtMin != TimeStepConstraints.First().dtMax)
{
(clusterDts, numberOfLocalTimeSteps) = clusterer.GetPerCluster_dtHarmonicSum_SubSteps(CurrentClustering, Time, TimeStepConstraints, eps: 1.0e-1);
dt = clusterDts[0];
}
else // dtFixed is set
// Not nice, but working
{
dt = CalculateTimeStep();
numberOfLocalTimeSteps = CurrentClustering.SubStepsInitial;
for (int i = 0; i < numberOfLocalTimeSteps.Count; i++)
{
clusterDts[i] = dt / numberOfLocalTimeSteps[i];
}
}
}
// Log time info
if (Logging)
{
this.log_clusterDts = clusterDts;
this.log_clusterSubSteps = numberOfLocalTimeSteps.ToArray();
this.log_clusterElements = CurrentClustering.Clusters.Select(s => s.GlobalNoOfCells).ToArray();
}
if (ConsoleOutput)
{
for (int i = 0; i < numberOfLocalTimeSteps.Count; i++)
{
Console.WriteLine("Perform(dt):\t\t id={0} -> sub-steps={1}\telements={2}\tdt={3:0.#######E-00}", i, numberOfLocalTimeSteps[i], CurrentClustering.Clusters[i].GlobalNoOfCells, clusterDts[i]);
//Console.WriteLine("Perform(dt):\t\t id={0} -> sub-steps={1}\telements={2}\tdt={3}", i, numberOfLocalTimeSteps[i], CurrentClustering.Clusters[i].GlobalNoOfCells, clusterDts[i]);
}
if (numberOfLocalTimeSteps.Last() > (clusterer.MaxSubSteps + 1) && clusterer.Restrict)
{
throw new Exception(String.Format("Number of local time steps is larger than {0}! Restriction failed!", clusterer.MaxSubSteps));
}
}
double[,] CorrectionMatrix = new double[CurrentClustering.NumberOfClusters, CurrentClustering.NumberOfClusters];
// Test code
//double[] bla = new double[numberOfLocalTimeSteps.Count];
//for (int i = 0; i < bla.Length; i++) {
// bla[i] = dt / numberOfLocalTimeSteps[i];
// if (bla[i] != clusterDts[i]) {
// throw new Exception("clusterDts wrong");
// }
//}
// Saves the results at t_n
double[] y0 = new double[Mapping.LocalLength];
CurrentState.CopyTo(y0, 0);
double time0 = m_Time;
double time1 = m_Time + clusterDts[0];
// Evolves each sub-grid with its own time step (only one step)
// (The result is not written to m_DGCoordinates!)
for (int i = 0; i < ABevolver.Length; i++)
{
//localABevolve[i].completeBndFluxes.Clear();
//if (localABevolve[i].completeBndFluxes.Any(x => x != 0.0)) Console.WriteLine("Not all Bnd fluxes were used in correction step!!!");
ABevolver[i].Perform(clusterDts[i]);
}
// After evolving each cell update the time with dt_min
m_Time = m_Time + clusterDts.Last();
TimestepNumber subTimestep = new TimestepNumber(TimeInfo.TimeStepNumber - 1);
//if (saveToDBCallback != null) {
// subTimestep = subTimestep.NextIteration();
// saveToDBCallback(subTimestep, m_Time);
//}
// Saves the history of DG_Coordinates for each cluster
Queue <double[]>[] historyDGC_Q = new Queue <double[]> [CurrentClustering.NumberOfClusters];
for (int i = 0; i < historyDGC_Q.Length; i++)
{
historyDGC_Q[i] = ABevolver[i].HistoryDGCoordinate;
}
if (!adaptive)
{
// Saves DtHistory for each cluster
historyTime_Q = new Queue <double> [CurrentClustering.NumberOfClusters];
for (int i = 0; i < historyTime_Q.Length; i++)
{
historyTime_Q[i] = ABevolver[i].HistoryTime;
}
}
// Perform the local time steps
for (int localTS = 1; localTS < numberOfLocalTimeSteps.Last(); localTS++)
{
for (int id = 1; id < CurrentClustering.NumberOfClusters; id++)
{
//Evolve Condition: Is "ABevolve.Time" at "AB_LTS.Time"?
if ((ABevolver[id].Time - m_Time) < 1e-10)
{
foreach (Chunk chunk in CurrentClustering.Clusters[id].VolumeMask)
{
foreach (int cell in chunk.Elements)
{
// f == each field
// n == basis polynomial
foreach (DGField f in Mapping.Fields)
{
for (int n = 0; n < f.Basis.GetLength(cell); n++)
{
int coordinateIndex = Mapping.LocalUniqueCoordinateIndex(f, cell, n);
CurrentState[coordinateIndex] = historyDGC_Q[id].Last()[coordinateIndex];
}
}
}
}
Dictionary <int, double> myDic = InterpolateBoundaryValues(historyDGC_Q, id, ABevolver[id].Time);
foreach (KeyValuePair <int, double> kvp in myDic)
{
CurrentState[kvp.Key] = kvp.Value;
}
ABevolver[id].Perform(clusterDts[id]);
m_Time = ABevolver.Min(s => s.Time);
//if (saveToDBCallback != null) {
// subTimestep = subTimestep.NextIteration();
// saveToDBCallback(subTimestep, m_Time);
//}
}
// Are we at an (intermediate-) syncronization levels?
// For conservatvity, we have to correct the values of the larger cell cluster
if (fluxCorrection)
{
for (int idCoarse = 0; idCoarse < id; idCoarse++)
{
if (Math.Abs(ABevolver[id].Time - ABevolver[idCoarse].Time) < 1e-10 &&
!(Math.Abs(ABevolver[idCoarse].Time - CorrectionMatrix[idCoarse, id]) < 1e-10))
{
if (fluxCorrection)
{
CorrectFluxes(idCoarse, id, historyDGC_Q);
}
CorrectionMatrix[idCoarse, id] = ABevolver[idCoarse].Time;
}
}
}
}
}
// Finalize step
// Use unmodified values in history of DGCoordinates (DGCoordinates could have been modified by
// InterpolateBoundaryValues, should be resetted afterwards)
CurrentState.Clear();
for (int id = 0; id < historyDGC_Q.Length; id++)
{
CurrentState.axpy <double[]>(historyDGC_Q[id].Last(), 1);
}
// Update time
m_Time = time0 + clusterDts[0];
}
}
else
{
// +++++++++++++++++++++++++++++++++++++++++++++++++++++
// Startup - use Runge Rutta until history is sufficient
// +++++++++++++++++++++++++++++++++++++++++++++++++++++
using (var rkPhase = new BlockTrace("AB_LTS_Rkstartup", tr)) {
double[] currentChangeRate = new double[Mapping.LocalLength];
double[] upDGC = new double[Mapping.LocalLength];
// Save time history
if (adaptive)
{
for (int i = 0; i < ABevolver.Length; i++)
{
double[] currentTime = new double[ABevolver[i].ABSubGrid.LocalNoOfCells];
for (int j = 0; j < currentTime.Length; j++)
{
currentTime[j] = m_Time;
}
ABevolver[i].historyTimePerCell.Enqueue(currentTime);
}
}
else
{
if (ABevolver[0].HistoryTime.Count == 0)
{
for (int i = 0; i < ABevolver.Length; i++)
{
ABevolver[i].HistoryTime.Enqueue(m_Time);
}
}
}
// Needed for the history
for (int i = 0; i < CurrentClustering.NumberOfClusters; i++)
{
double[] localCurrentChangeRate = new double[currentChangeRate.Length];
double[] edgeFlux = new double[gridData.iGeomEdges.Count * Mapping.Fields.Count];
ABevolver[i].ComputeChangeRate(localCurrentChangeRate, m_Time, 0, edgeFlux);
ABevolver[i].HistoryChangeRate.Enqueue(localCurrentChangeRate);
ABevolver[i].HistoryBoundaryFluxes.Enqueue(edgeFlux);
}
dt = RungeKuttaScheme.Perform(dt);
CurrentState.CopyTo(upDGC, 0);
// Saves ChangeRateHistory for AB LTS
// Only entries for the specific cluster
for (int i = 0; i < CurrentClustering.NumberOfClusters; i++)
{
ABevolver[i].HistoryDGCoordinate.Enqueue(OrderValuesByCluster(CurrentClustering.Clusters[i], upDGC));
if (!adaptive)
{
ABevolver[i].HistoryTime.Enqueue(RungeKuttaScheme.Time);
}
}
// RK is a global timeStep
// -> time update for all other timeStepper with rk.Time
m_Time = RungeKuttaScheme.Time;
foreach (ABevolve ab in ABevolver)
{
ab.ResetTime(m_Time, TimeInfo.TimeStepNumber);
}
}
}
}
return(dt);
}
/// <summary>
/// Caluclates the local time step sizes
/// </summary>
/// <returns>the largest stable timestep</returns>
protected override double CalculateTimeStep()
{
if (TimeStepConstraints.First().dtMin != TimeStepConstraints.First().dtMax)
{
double[] localDts = new double[CurrentClustering.NumberOfClusters];
for (int i = 0; i < CurrentClustering.NumberOfClusters; i++)
{
// Use "harmonic sum" of step - sizes, see
// WatkinsAsthanaJameson2016 for the reasoning
double dt = 1.0 / TimeStepConstraints.Sum(
c => 1.0 / c.GetGloballyAdmissibleStepSize(CurrentClustering.Clusters[i]));
if (dt == 0.0)
{
throw new ArgumentException(
"Time-step size is exactly zero.");
}
else if (double.IsNaN(dt))
{
throw new ArgumentException(
"Could not determine stable time-step size in sub-grid " + i + ". This indicates illegal values in some cells.");
}
// restrict timesteps
dt = Math.Min(dt, TimeStepConstraints.First().Endtime - Time);
dt = Math.Min(Math.Max(dt, TimeStepConstraints.First().dtMin), TimeStepConstraints.First().dtMax);
localDts[i] = dt;
}
#if DEBUG
bool hasChanged = false;
#endif
for (int i = 0; i < CurrentClustering.NumberOfClusters; i++)
{
double fraction = localDts[0] / localDts[i];
//Accounting for roundoff errors
double eps = 1.0e-1;
int subSteps;
if (fraction > Math.Floor(fraction) + eps)
{
subSteps = (int)Math.Ceiling(fraction);
}
else
{
subSteps = (int)Math.Floor(fraction);
}
if (NumberOfLocalTimeSteps[i] != subSteps)
{
#if DEBUG
hasChanged = true;
#endif
NumberOfLocalTimeSteps[i] = subSteps;
}
}
#if DEBUG
if (hasChanged)
{
Console.WriteLine("CHANGE OF SUBSTEPS");
for (int i = 0; i < CurrentClustering.NumberOfClusters; i++)
{
Console.WriteLine("id=" + i + " -> sub-steps=" + NumberOfLocalTimeSteps[i] + " and elements=" + CurrentClustering.Clusters[i].GlobalNoOfCells);
}
}
#endif
return(localDts[0]);
}
else
{
double dt = TimeStepConstraints.First().dtMin;
dt = Math.Min(dt, TimeStepConstraints.First().Endtime - Time);
return(dt);
}
}