Exploiting the flexibility of IDR(s) for grid computing

Exploiting the flexibility of IDR(s) for grid computing

Van Gijzen, M.B.
Collignon, T.P.

Electrical Engineering, Mathematics and Computer Science

2010-03-29

The IDR(s) method that is proposed in [26] is an efficient limited memory method for solving large nonsymmetric systems of linear equations. In [11] an IDR(s) variant is described that has a single synchronisation point per iteration step, which makes this variant well-suited for parallel and grid computing. In this paper, we combine this IDR(s) variant with an a-synchronous preconditioning iteration to further improve the performance of IDR(s) on a grid computer. A-synchronous preconditioners do not require expensive synchronisation and adapt to volatile computational resources, and are therefore well-suited for such a computational environment. However, an a-synchronous preconditioning operation is also non-constant by nature: the preconditioner changes in every iteration. The success of the combination of IDR(s) with an a-synchronous preconditioner therefore depends on the flexibility of IDR(s). We will explain why IDR(s) can be used as a flexible method, and we will successfully use the combination of IDR(s) with an a-synchronous preconditioner for solving large convection-diffusion problems. The numerical experiments are performed on the DAS-3 grid computer, which is composed of five geographically separated parallel clusters.

iterative methods
IDR(s)
Krylov-subspace methods
grid computing
flexible
methods
a-synchronous preconditioning

http://resolver.tudelft.nl/uuid:0f9b12f3-2e1e-49ab-9423-f1aac526604f

Delft University of Technology, Faculty of Electrical Engineering, Mathematics and Computer Science, Delft Institute of Applied Mathematics

1389-6520

Reports of the Department of Applied Mathematical Analysis, 10-11

Institutional Repository

report

(c)2010 Van Gijzen, M.B., Collignon, T.P.