Mixed and Variable Precision for an Exascale Hyperbolic PDE Engine

• Applicant: Professor Dr. Michael Bader
• Subject Area: Computer Architecture, Embedded and Massively Parallel Systems
• Term: since 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 462423388

The goal of the project ExaHyPE-MVP is to systematically explore and exploit the use of mixed and variable floating point precision in the ExaHyPE engine.ExaHyPE allows to solve a wide range of models (i.e., hyperbolic systems of partial differential equations, as they often stem from conservation laws) on supercomputers, using a fixed mesh and parallelisation infrastructure and discretisation method, but allowing flexibility with respect to the solved equations. ExaHyPE is based on high-order ADER-DG (discontinuous Galerkin with Arbitrary High-order DERivative time stepping) discretisation, which consists of a multitude of kernels with different performance characteristics. We will extend ExaHyPE's code generation utilities to allow engine users and developers to specify the precision used for each kernel. In addition, we will extend ExaHyPE to support variable target precision, for example in areas of higher or lower accuracy demands. For both mixed and variable precision, we will explore criteria for adaptively selecting the precision, thus introducing "epsilon"-adaptivity (i.e., adaptive variable precision) as an HPC-motivated counterpart to the concepts of adaptivity w.r.t. mesh refinement or discretisation order (“h- “or “p-adaptivity”).We will systematically evaluate possible gains in overall time to solution and impact in terms of accuracy on benchmark scenarios from a range of widely relevant hyperbolic PDE systems, and we will demonstrate the impact on real use cases on scenarios that stem from two projects on earthquake simulation and modelling rupture propagation. A key challenge will be how to manage the resulting software complexity via expanding ExaHyPE's code generation facilities.

• DFG Programme: Research Grants