Towards high-performance unstructured-mesh computations

Physics-based simulations often involve irregularly shaped solution domains, thus the need for unstructured computational meshes. The curse of "the memory wall" is particularly hurtful for such unstructured-mesh computations, due to the resulting irregular memory accesses. The mesh partitioning problem associated with parallelizing unstructured-mesh computations is also challenging. In this talk, we will look at several techniques that can contribute to achieving high performance for these computations. Specifically, we will study the impact of mesh entity reordering, physics-accommodating mesh partitioning, automated generation of GPU-accelerated finite element code, as well as re-purposing AI accelerators for unstructured-mesh computations. Examples from computational electrocardiology and geoscience will be used to illuminate the inherent difficulties and the obtainable performance improvements.