On adaptative GMRES(m) in the PETSc package
Resumen
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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