Stochastic Optimized Schwarz Methods for the Gravity Equations on Graphics Processing Unit

TL;DR

This paper introduces a stochastic optimization approach for Schwarz methods applied to gravity equations, leveraging high-order finite elements on hybrid CPU/GPU systems to improve solution accuracy and computational efficiency.

Contribution

It presents a novel stochastic-based optimization procedure for Schwarz methods tailored for high-order finite element discretizations on hybrid CPU/GPU architectures.

Findings

Demonstrates robustness of the method on realistic test cases

Shows efficiency gains on multi-CPU/GPU clusters

Achieves improved gravity anomaly solutions in heterogeneous media

Abstract

Low order, sequential or non-massively parallel finite elements are generaly used for three-dimensional gravity modelling. In this paper, in order to obtain better gravity anomaly solutions in heterogeneous media, we solve the gravimetry problem using massively parallel high order finite elements on hybrid multi-CPU/GPU clusters. Parallel algorithms well suited for such hybrid architectures have to be designed. A new stochastic-based optimization procedure for the optimized Schwarz method is here presented, implemented and tuned to graphical cards processors units. Numerical experiments performed on a reallistic test case, demonstrates the robustness and efficiency of the proposed method and of its implementation on massive multi-CPU/GPU architectures.