Load Balancing Techniques for Asynchronous Spacetime Discontinuous Galerkin Methods
US National Congress on Computational Mechanics (USNCCM) 2009
Publication Type: Talk
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Summary
The spacetime discontinuous Galerkin (SDG) method for hyperbolic problems supports an advancing-front solution algorithm that interleaves unstructured spacetime meshing with a patch-wise-local finite element solution procedure. We exploit the local nature of the SDG algorithm to generate spacetime meshes that adapt continuously to capture the trajectories of moving features such as shocks and propagating cracks. Our implementation of the SDG method uses the Tent Pitcher meshing algorithm to generate a sequence of patches of spacetime finite elements such that the solution on each patch depends only on adjacent, previously-solved elements and boundary/initial data. We compute the local finite element solution on each new patch as soon as it is generated; therefore, parallelizing Tent Pitcher also parallelizes the SDG finite element solution. We describe here a highly asynchronous parallel implementation of the adaptive Tent Pitcher algorithm, in which each processor can initiate local adaptive operations at unpredictable points in space and time. We base our implementation on the ParFUM framework which in turn is based on the Charm++ runtime system. We associate subdomains of the spatial analysis domain with Charm++ objects whose methods can be invoked remotely. ParFUM manages the distributed data structures needed for parallel execution, with support for asynchronous local adaptive operations and dynamic load balancing.
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