On adaptative GMRES(m) in the PETSc package
Abstract
The Restarted Generalized Minimal Residual method (GMRES(m)) is a standard method for solving non-symmetric indefinite large linear systems of equations of the form Ax = b [1, 2]. It has the limitation that if the restating parameter m is not adequately chosen can present either a slow convergence or stagnation [3]. This problem has been faced in several previous works [4–6]. However, to be useful for solving practical engineering and simulation problems, it is necessary to have the method in a computationally appropriate platform, allowing the simultaneous implementation in parallel and distributed architectures, and the implementation of several preconditioners. This work introduces a PETSc (Portable, Extensible Toolkit for Scientific Computation) routine that enforces the adaptation in the restarted parameter of the restarted-GMRES method of the solver in the PETSc. [...]
Downloads
References
Yousef Saad. Iterative Methods for Sparse Linear Systems. SIAM, 2003. isbn: 978-0-89871-534-7.
Christian E. Schaerer, Eugenius Kaszkurewicz, and Norberto Mangiavacchi. “A multilevel Schwarz shooting method for the solution of the Poisson equation in two dimensional incompressible flow simulations”. In: Applied Mathematics and Computation 153.3 (2004), pp. 803–831. doi: https://doi.org/10.1016/S0096-3003(03)00679-9.
Rolando Cuevas Nuñez, Christian E. Schaerer, and Amit Bhaya. “A proportional-derivative control strategy for restarting the GMRES(m) algorithm”. In: Journal of Computational and Applied Mathematics 337 (2018), pp. 209–224. doi: https://doi.org/10.1016/j.cam.2018.01.009.
Ed Bueler. PETSc for Partial Differential Equations: Numerical Solutions in C and Python. Software, environments and tools. SIAM, 2020. isbn: 978-1-611976-30-4.
“A simple strategy for varying the restart parameter in GMRES(m)”. In: Journal of Computational and Applied Mathematics 230.2 (2009), pp. 751–761. issn: 0377-0427. doi: https://doi.org/10.1016/j.cam.2009.01.009. url: https://www.sciencedirect.com/science/article/pii/S0377042709000132.
Juan C. Cabral, Christian E. Schaerer, and Amit Bhaya. “Improving GMRES(m) using an adaptive switching controller”. In: Numerical Linear Algebra with Applications (2020). doi: https://doi.org/10.1002/nla.2305.
