scholarly journals Krylov subspace recycling for sequences of shifted linear systems

2014 ◽  
Vol 81 ◽  
pp. 105-118 ◽  
Author(s):  
Kirk M. Soodhalter ◽  
Daniel B. Szyld ◽  
Fei Xue
Keyword(s):  
Linear Systems ◽  
Krylov Subspace ◽  
Shifted Linear Systems ◽  
Subspace Recycling

scholarly journals A Flexible Global GCRO-DR Method for Shifted Linear Systems and General Coupled Matrix Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Jing Meng ◽  
Xian-Ming Gu ◽  
Wei-Hua Luo ◽  
Liang Fang
Keyword(s):  
Linear Systems ◽  
Numerical Experiments ◽  
Matrix Equations ◽  
The Novel ◽  
Dr Method ◽  
Shifted Linear Systems ◽  
Novel Method ◽  
General Coupled Matrix Equations ◽  
Subspace Recycling ◽  
The Right

In this paper, we mainly focus on the development and study of a new global GCRO-DR method that allows both the flexible preconditioning and the subspace recycling for sequences of shifted linear systems. The novel method presented here has two main advantages: firstly, it does not require the right-hand sides to be related, and, secondly, it can also be compatible with the general preconditioning. Meanwhile, we apply the new algorithm to solve the general coupled matrix equations. Moreover, by performing an error analysis, we deduce that a much looser tolerance can be applied to save computation by limiting the flexible preconditioned work without sacrificing the closeness of the computed and the true residuals. Finally, numerical experiments demonstrate that the proposed method illustrated can be more competitive than some other global GMRES-type methods.

Preconditioning Techniques for Nonsymmetric Linear Systems in the Computation of Incompressible Flows

2009 ◽  
Vol 76 (2) ◽  
Author(s):  
Murat Manguoglu ◽  
Ahmed H. Sameh ◽  
Faisal Saied ◽  
Tayfun E. Tezduyar ◽  
Sunil Sathe
Keyword(s):  
Linear Systems ◽  
Krylov Subspace ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Handling Time ◽  
Navier Stokes ◽  
Preconditioning Techniques ◽  
Navier Stokes Equations ◽  
Nonsymmetric Linear Systems ◽  
Steady State Solutions

In this paper we present effective preconditioning techniques for solving the nonsymmetric systems that arise from the discretization of the Navier–Stokes equations. These linear systems are solved using either Krylov subspace methods or the Richardson scheme. We demonstrate the effectiveness of our techniques in handling time-accurate as well as steady-state solutions. We also compare our solvers with those published previously.

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