Acceleration of a parallel BDDC solver by using graphics processing units on subdomains

0575122 - MÚ 2024 RIV GB eng J - Journal Article
Šístek, Jakub - Oberhuber, T.
Acceleration of a parallel BDDC solver by using graphics processing units on subdomains.
International Journal of High Performance Computing Applications. Roč. 37, č. 2 (2023), s. 151-164. ISSN 1094-3420. E-ISSN 1741-2846
R&D Projects: GA ČR(CZ) GA20-01074S
Institutional support: RVO:67985840
Keywords : balancing domain decomposition method by constraints * domain decomposition * graphics processing units
OECD category: Applied mathematics
Impact factor: 3.1, year: 2022
Method of publishing: Limited access
https://doi.org/10.1177/10943420221136873

An approach to accelerating a parallel domain decomposition (DD) solver by graphics processing units (GPUs) is investigated. The solver is based on the Balancing Domain Decomposition Method by Constraints (BDDC), which is a nonoverlapping DD technique. Two kinds of local matrices are required by BDDC. First, dense matrices corresponding to local Schur complements of interior unknowns are constructed by the sparse direct solver. These are further used as part of the local saddle-point problems within BDDC. In the next step, the local matrices are copied to GPUs. Repeated multiplications of local vectors with the dense matrix of the Schur complement are performed for each subdomain. In addition, factorizations and backsubstitutions with the dense saddle-point subdomain matrices are also performed on GPUs. Detailed times of main components of the algorithm are measured on a benchmark Poisson problem. The method is also applied to an unsteady problem of incompressible flow, where the Krylov subspace iterations are performed repeatedly in each time step. The results demonstrate the potential of the approach to speed up realistic simulations up to 5 times with a preference towards large subdomains.
Permanent Link: https://hdl.handle.net/11104/0344979