2018/01/26 by Dominic Etienne Charrier, Charrier, Dominic E., Tobias Weinzierl +1 · 2 citations
Engineering · Mathematics · Physics and Astronomy · #Computational Fluid Dynamics and Aerodynamics #FOS: Computer and information sciences #FOS: Mathematics #Mathematical Software (cs.MS) #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.1801.08682
openalex publication_date 2018/01/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a communication- and data-sensitive formulation of ADER-DG for hyperbolic differential equation systems. Sensitive here has multiple flavours: First, the formulation reduces the persistent memory footprint. This reduces pressure on the memory subsystem. Second, the formulation realises the underlying predictor-corrector scheme with single-touch semantics, i.e., each degree of freedom is read on average only once per time step from the main memory. This reduces communication through the memory controllers. Third, the formulation breaks up the tight coupling of the explicit time stepping's algorithmic steps to mesh traversals. This averages out data access peaks. Different operations and algorithmic steps are ran on different grid entities. Finally, the formulation hides distributed memory data transfer behind the computation aligned with the mesh traversal. This reduces pressure on the machine interconnects. All techniques applied by our formulation are elaborated by means of a rigorous task formalism. They break up ADER-DG's tight causal coupling of compute steps and can be generalised to other predictor-corrector schemes.