A Proof of Concept for Very Fast Finite Element Poisson Solvers on Accelerator Hardware. Issue 1 (14th December 2021)

• Record Type: Journal Article
• Authors: Ruda, Dustin; Turek, Stefan; Ribbrock, Dirk; Zajac, Peter
• Editors: Kaliske, M.
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 21:Issue 1(2021)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2021-12-14
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.202100091
• Languages: English
• ISSNs: 1617-7061

Abstract

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.