A proof of concept for very fast finite element Poisson solvers on accelerator hardware

Abstract

It is demonstrated that modern accelerator hardware specialized in AI, e.g., “next gen GPUs” equipped with Tensor Cores, can be profitably used in finite element simulations by means of a new hardware-oriented method to solve linear systems arising from Poisson's equation in 2D. We consider the NVIDIA Tesla V100 Tensor Core GPU with a peak performance of 125 TFLOP/s, that is only achievable in half precision and if operations with high arithmetic intensity, such as dense matrix multiplications, are executed, though. Its computing power can be exploited to a great extent by the new method based on “prehandling” without loss of accuracy. We obtain a significant reduction of computing time compared to a standard geometric multigrid solver on standard x64 hardware.