Research

Research interests

The main focus of my work is the development of high order numerical schemes, particularly the discontinuous Galerkin (DG) method, and application of these methods to the simulation of circulation and transport in coastal and global ocean.

A number of very interesting though difficult issues have to be addressed in order to fully exploit the potential of DG methods and still achieve competitive computational performance for this type of application.

The problems of interest in deep and coastal ocean studies tend to be very large; the time scales being simulated can lie anywhere between minutes (as in fast moving flooding and storm fronts) and centuries — the latter typically found in climate applications. Highly complex bottom topography and coast lines call for algorithms that can efficiently utilize unstructured grids. Computational domains change with time in the vertical direction (free surface) and may also have moving lateral boundaries (flooding), thus dynamic meshes must be supported by the numerical algorithm.

The DG methods possess many desirable properties that make them an attractive choice for a new generation of ocean models. These include

  • robust treatment of shocks and discontinuities;
  • local conservation of all variables;
  • choice of high or low order approximation spaces;
  • support for non-conforming meshes and hanging nodes;
  • approximation spaces easily accomodating h- and p-refinement;
  • locality of approximation stencil.

A much higher computational cost of DG algorithms even compared to other unstructured methods such as the classical finite elements makes the task of formulating and implementing DG methods for ocean applications quite challenging. Several strategies that build on the strengths of the method appear to hold promise with regard to increasing method’s efficiency for realistic problems. My research concerns all of these strategies:

  • using adaptivity to efficiently utilize computational resources in order to obtain an accurate solution in the areas of interest;
  • exploiting locality of the DG approximation stencil to achieve good scalability on parallel clusters and hybrid computational architectures;
  • improving accuracy and resolution of the numerical solution by means of dynamic mesh and approximation space optimization — all this without violating the local conservation properties of the scheme.

Publications

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Projects

Term: 01.01.2017 - 30.09.2020
Funding source: DFG-Einzelförderung / Sachbeihilfe (EIN-SBH)
Acronym: OCEAN
Project leader: , ,

Um akkurate Ozean, Atmosphären oder Klima Simulationen durchzuführen werden sehr effiziente numerische Verfahren und große Rechenkapazitäten benötigt, die in vielen Teilen der Welt und bei vielen Forschungsgruppen in diesen Anwendungsfeldern nicht verfügbar sind. Solche Beschränkungen führen auch dazu, dass Modelle und Softwarepakete basierend auf strukturierten Gittern derzeit in der Ozeanwissenschaft immer noch vorherrschend sind.In diesem Projekt soll zum einen die Rechenzeit für Modelle, die…

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