Sponsored by the MFEM project, the FEM@LLNL Seminar Series focuses on finite element research and applications talks of interest to the MFEM community.
On March 11, 2025, Stefan Turek from Technical University Dortmund presented “Hardware-Oriented Numerics for Massively Parallel & Low Precision Accelerator Hardware and Application to ‘Large Scale’ CFD Problems.” The aim of this talk is to present and to discuss how modern High Performance Computing (HPC) facilities including massively parallel hardware with millions of cores together with very fast, but lower precision accelerator hardware can be exploited via techniques from hardware-oriented Numerics for PDEs so that a very high computational and numerical efficiency can be obtained. Here, as prototypical large scale PDE-based applications, we concentrate on nonstationary flow simulations with hundreds of millions or even billions of spatial unknowns in long-time computations with many thousands up to millions of time steps. For the expected huge computational resources in the coming exascale era, such spatially discretized problems which typically are treated sequentially in time, that means one time step after the other, are still too small to exploit adequately the huge number of compute nodes, resp., cores so that further parallelism, for instance with regard to time, might get necessary. In this context, we discuss how “parallel-in-space global-in-time” Newton-Krylov Multigrid approaches can be designed which allow a much higher degree of parallelism. Moreover, to exploit current accelerator hardware in lower precision (for instance, GPUs), that means mainly working in single or even half precision, we discuss the concept of “prehandling” (in contrast to “preconditioning”) of the corresponding ill-conditioned systems of equations, for instance arising from Poisson-like problems in incompressible flow simulations. Here, we assume a transformation into an equivalent linear system with similar sparsity but with much lower condition numbers so that the use of lower precision hardware might get feasible. In our talk, we provide for both aspects numerical results as “proof-of-concept” and discuss the challenges, particularly for large scale flow problems.
Learn more about MFEM at https://mfem.org/ and view the seminar speaker lineup at https://mfem.org/seminar/. LLNL-VIDEO-2004100