Local Time Stepping Plan

We could rather quickly implement a local time steppging version a la SeisSol where we store the full space-time face data only for faces of coarse grid cells along mesh resolution transitions.

Steps (in German):

• Aufbrechen des Extrapolations-Operators (Cell Boundary -> Single Face)
• Aufbrechen der Face Data Felder. We need one pointer/index per face.
• Mithilfe meiner Marker fuer gewisse Faces space-time Face Data speichern
• Den space Prolongationsoperator mit einem space-time Operator ersetzen (Face Prolongation -> "Volume" Prolongation (vorhanden))
• Counter im State einfuehren und dann entsprechend des Wertes nur bestimmte Levels an* [ ] und ausschalten, ginge mit Hilfe Deiner level Information in den MappingSpecifications
• Nur am Anfang eines Batches die alte Loesung sichern (implementiert)
• Batchgroesse entsprechend des aktuellen tiefsten Verfeinerungslevels berechnen
• Rollback zu Anfang des Batches, falls das Gitter nicht gepasst hat.

Some implementational aspects

Some preparational work has already been done.

• No changes to the current faceIntegral procedure need to be performed as we already skip the integral where a Leaf cell shares an interface with a Refined ("Parent") cell.

  const int dofsPerFace = getBndFluxSize();
      for (int direction=0; direction<DIMENSIONS; direction++) {
        for (int orientation=0; orientation<2; orientation++) {
          const int faceIndex=2*direction+orientation;
          if ( cellDescription.getFacewiseAugmentationStatus(faceIndex)<MaximumAugmentationStatus ) { // ignore Ancestors
            double* const lFhbnd = static_cast<double*>(cellDescription.getFluctuation()) + dofsPerFace * faceIndex;
            faceIntegral(output,lFhbnd,direction,orientation,0/*implicit conversion*/,0,cellDescription.getSize(),
                         cellDescription.getTimeStepSize(),addToUpdate);
          }
        }
      }