Supercomputing and Computation

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Scalable stencil-based solver algorithms


This research concentrates on developing highly scalable algorithms and modular software in support of numerical methods for solving partial differential equations with stencil-based discretization approaches. Stencil codes require only nearest neighbor information in order to perform a numerical update and are thereby amenable to efficient and hybrid parallelization. Focussing on structured patch-based kernels, presently considered disretizations include finite difference, shock-capturing finite volume and Lattice Boltzmann methods. Explicit as well as implicit matrix-free schemes are investigated. A current primary emphasis lies on increasing the scalability of multi-level techniques like multigrid and patch-based adaptive mesh refinement by reducing communication steps and volume, for instance, by incorporating asynchronous iteration ideas. Further on, we develop embedded boundary and level set algorithms that allow the application of scalable and dynamically adaptive stencil codes in geometrically complex energy-related multi-physics scenarios.

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