Double sweep preconditioner for optimized Schwarz methods applied to the Helmholtz problem

Journal Article · Sun Jun 01 00:00:00 EDT 2014 · Journal of Computational Physics

DOI:https://doi.org/10.1016/J.JCP.2014.02.015· OSTI ID:22314867

Vion, A., E-mail: [e-mail]; Geuzaine, C., E-mail: [e-mail]

This paper presents a preconditioner for non-overlapping Schwarz methods applied to the Helmholtz problem. Starting from a simple analytic example, we show how such a preconditioner can be designed by approximating the inverse of the iteration operator for a layered partitioning of the domain. The preconditioner works by propagating information globally by concurrently sweeping in both directions over the subdomains, and can be interpreted as a coarse grid for the domain decomposition method. The resulting algorithm is shown to converge very fast, independently of the number of subdomains and frequency. The preconditioner has the advantage that, like the original Schwarz algorithm, it can be implemented as a matrix-free routine, with no additional preprocessing.

• OSTI ID: 22314867
• Journal Information: Journal of Computational Physics, Vol. 266; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGORITHMS
APPROXIMATIONS
FINITE ELEMENT METHOD
ITERATIVE METHODS
MATHEMATICAL OPERATORS
MATRICES
PARTITION
SCATTERING