On adaptative GMRES(m) in the PETSc package

Autores

  • Eduardo Gómez
  • Lucas Vega
  • Verónica Domiguez
  • Juan Carlos Cabral
  • Christian E. Schaerer

Resumo

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. [...]

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Biografia do Autor

Eduardo Gómez

Polytechnic School, National University of Asuncion, San Lorenzo, Paraguay

Lucas Vega

Polytechnic School, National University of Asuncion, San Lorenzo, Paraguay

Verónica Domiguez

Polytechnic School, National University of Asuncion, San Lorenzo, Paraguay

Juan Carlos Cabral

Polytechnic School, National University of Asuncion, San Lorenzo, Paraguay

Christian E. Schaerer

Polytechnic School, National University of Asuncion, San Lorenzo, Paraguay

Referências

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.

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Publicado

2023-12-18

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