Efficient parallel multirate time stepping for accelerating explicit discontinuous Galerkin computations.
(2011) 11th U.S. National Congress on Computational Mechanics — Location: Minneapolis, MN, USA (25.July.2011)
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- The development of suitable and fast time integration methods for ocean modeling con- stitutes an important challenge. No single time-discretisation works well for all physical processes in a complex marine model, as dierent subsystems have widely dierent charac- teristics in terms of time scales, dynamic behaviour, and accuracy requirements. We believe that building appropriate time stepping strategies for multi-scale computations will enable us to gain an order of magnitude. Indeed, unstructured-mesh generation processes are complex and, even though it is possible to control average element sizes in specic regions of the domain, it is not the case for each element size. The smallest element is usually much more smaller than the criterion that was prescribed a priori and it determines the stable time step for the entire model. Therefore, the computational eciency of explicit time-stepping methods may be drastically low. Multirate schemes represent a class of methods that use various time steps on dierent grid cells. The strategy consists in splitting the domain in a smart way. Grid cells are gathered in dierent groups that satisfy the local CFL stability conditions for a certain range of time steps. Standard explicit Runge- Kutta methods are applied on independent partitions while buer groups have to be introduced between them, with adapted methods, in order to accommodate the transitions between them. These methods are especially suited for the Discontinuous Galerkin spatial discretization. Nevertheless, development of such methods is still challenging. Both, stability requirements and conservation properties should be satised. Two approaches are explored. Constantinescu introduced a conservative 2nd order scheme while Schlegel proposed a 3rd method that is, unfortunately, not conservative. Large-scale applications like the Great Barrier Reef require the use of parallel computers. Some kind of load balancing strategy has to be supplied to accomodate multirate schemes: indeed, small elements have a higher cost than large elements in such a strategy. Moreover, small elements at inter-processor interfaces will require more frequent updates. The key idea consists in creating an optimized mesh partition in a way that the amount of grid cells of the dierent multirate groups is ideally the same on each computer core. However, a compromise should also be found between the eective work on each processor and the amount of communications between them.
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Seny, B., Lambrechts, J., Legat, V., & Remacle, J.-F. (2011). Efficient parallel multirate time stepping for accelerating explicit discontinuous Galerkin computations. 11th U.S. National Congress on Computational Mechanics, Minneapolis, MN, USA. https://hdl.handle.net/2078.5/229007