Utilizing Sparsity in the GPU-accelerated Assembly of Schur Complement Matrices in Domain Decomposition Methods
Journal article
EUPEX partner ET4Innovations had a research paper accepted in Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis (SC 25, St-Louis, USA)
Abstract
Schur complement matrices emerge in many domain decomposition methods that can utilize supercomputers to solve complex engineering problems. As most of today’s high-performance clusters’ performance lies in GPUs, these methods should also be accelerated.
Typically, the offloaded components are the explicitly assembled dense Schur complement matrices used later in the iterative solver for multiplication with a vector. As the explicit assembly is expensive, it adds a significant overhead to this approach of acceleration. It has already been shown that the overhead can be minimized by assembling the Schur complements directly on the GPU.
This paper shows that the GPU assembly can be further improved by wisely utilizing the matrix sparsity. In the context of FETI, we achieved a speedup of 5.1 in the GPU section of the code and 3.3 for the whole assembly, making the acceleration beneficial from as few as 10 iterations for subdomains with 1,000-70,000 unknowns.
Authors
Jakub Homola, Ondřej Meca, Lubomír Říha, and Tomáš Brzobohatý
DOI: 10.1145/3712285.3759904
