High-Order Finite Elements for Exascale Applications

In this talk we review our experience with porting the MFEM finite element library (https://mfem.org) to GPU-based exascale architectures. This development included both software and algorithmic changes, as well as co-design with hardware vendors and large-scale multi-physics applications as part of the US Exascale Computing Project (ECP). Modern architectures favor algorithms, such as high-order finite elements, that expose fine-grain parallelism and maximize the ratio of floating-point operations to energy intensive data movement. These methods are particularly well-suited for exascale architectures with GPU accelerators, where their efficiency and scalability rely on the adoption of partially assembled algorithms that reduce memory data motion. The matrix-free nature of partial assembly algorithms enables higher efficiency, but also motivates new research in areas such as meshing, discretizations and solvers. We will present some of the recent work on GPU-oriented algorithms and software in MFEM, and also report on developments in related projects, including high-order ALE compressible hydrodynamics in LLNL's BLAST code; GPU benchmarks from the Center for Efficient Exascale Discretizations in the ECP; and the Cascadia project for acoustic–gravity waves in tsunami modeling.