Acceleration of a parallel BDDC solver by using graphics processing units on subdomains
Authors
Šístek, J.; Oberhuber, T.
Year
2023
Published
International Journal of High Performance Computing Applications. 2023, 37(2), 151-164. ISSN 1094-3420.
Type
Article
Departments
Annotation
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.
BDDC for MHFEM discretization of unsteady two-phase flow in porous media
Authors
Solovský, J.; Fučík, R.; Šístek, J.
Year
2022
Published
Computer Physics Communications. 2022, 271 ISSN 0010-4655.
Type
Article
Departments
Annotation
This work deals with the application of the Balancing Domain Decomposition by Constrains (BDDC) method to unsteady two-phase flow problems in porous media. We briefly describe the spatial discretization of the problem which is based on the mixed-hybrid finite element method (MHFEM) and semi-implicit time discretization. Then, we describe the BDDC method, in detail discuss the differences between the symmetric and nonsymmetric cases, and present the necessary modifications of the algorithm for the more complicated nonsymmetric case. We describe the parallel implementation of the method and highlight the critical steps of the algorithm that affect the performance and scalability. The parallel implementation is then tested on benchmark problems in 2D and 3D and its efficiency is investigated on various meshes. The numerical results indicate that the method preserves good computational efficiency for increasing number of processes and, therefore, allows solving problems on very fine meshes. In the case of unsteady problem, additional speed-up is achieved using the information from previous time steps for the solution in the current time step.
Adaptive BDDC in three dimensions
Authors
Mandel, J.; Sousedik, B.; Šístek, J.
Year
2012
Published
Mathematics and Computers in Simulation. 2012, 82(10), 1812-1831. ISSN 0378-4754.
Type
Article
Departments
Annotation
The adaptive BDDC method is extended to the selection of face constraints in three dimensions. A new implementation of the BDDC method is presented based on a global formulation without an explicit coarse problem, with massive parallelism provided by a multifrontal solver. Constraints are implemented by a projection and sparsity of the projected operator is preserved by a generalized change of variables. The effectiveness of the method is illustrated on several engineering problems. (c) 2011 IMACS. Published by Elsevier B.V. All rights reserved.