Implications of Discretization Choices for Mixed-Precision, Parallel-in-Time Methods for PDE’s (Hans Johansen)

22.09.2026 14:00 – 15:00

In this talk I will argue that numerical PDE codes need to evolve a new flexibility, that includes careful tradeoffs between spatial and temporal discretizations in mixed precisions. This is important because modern CPU and GPU hardware is increasingly evolving multi-precision capabilities, where precision is aggressively controlled to improve memory bandwidth and throughput for machine learning algorithms. Ominously, newer generations of chips are emulating double precision operations, so that scientific codes that rely on these will miss out on the 100x+ speedups being promised. We will present a structured analysis of a mixed-precision algorithm for cut-cell finite volume methods for PDEs, which combines regular grid operations with boundary discretizations that can be arbitrarily high order. We’ll show that naive conversion to lower precision, as is often done in linear algebra libraries, introduces low-frequency errors and effectively solves the wrong problem. Fixing this requires knowledge of the PDEs and a discrete optimization problem to recover the correct behavior. I demonstrate that this is particularly important for multi-resolution algorithms, such as adaptive mesh refinement (AMR), multigrid solvers, and parallel-in-time (PinT) methods. Several examples will show that codes can be adapted, but not blindly and without knowledge of the underlying PDEs and discretizations. This is joint work with Tallula Johansen (M.Eng. King’s College, London), who just graduated with first-class honors.

Lieu

Conseil Général 7-9, Room 1-05, Séminaire d'analyse numérique

entrée libre