Schwarz Method with Two-sided Transmission Conditions for the Gravity Equations on Graphics Processing Unit

In this paper, we solve the gravity equations on hybrid multi-CPU/GPU using high order finite elements. Domain decomposition methods are inherently parallel algorithms making them excellent candidates for implementation on hybrid architectures. Here, we propose a new stochastic-based optimization procedure for the optimized Schwarz domain decomposition method, which is implemented and tuned to graphics processors unit. To obtain high speed-up, several implementation optimizations should be carrefully performed, such as data transfert between CPU and GPU, matrix data storage, etc. We investigate, describe and present the optimizations we have developed for finite elements analysis, leading to better efficiency. Numerical experiments carried out on a reallistic test case, namely the Chicxulub crater, demonstrates the efficiency and robustness of the proposed method on massive hybrid multi-CPU/GPU platforms.