Paper Info
Title
Smoothed aggregation for Helmholtz problems.
Abstract
We outline a smoothed aggregation algebraic multigrid method for ID and 2D scalar Helmholtz problems with exterior radiation boundary conditions. We consider standard ID finite difference discretizations and 2D discontinuous Galerkin discretizations. The scalar Helmholtz problem is particularly difficult for algebraic multigrid solvers. Not only can the discrete operator be complex-valued, indefinite, and non-self-adjoint, but it also allows for oscillatory error components that yield relatively small residuals. These oscillatory error components are not effectively handled by either standard relaxation or standard coarsening procedures. We address these difficulties through modifications of SA and by providing the SA setup phase with appropriate wave-like near null-space candidates. Much is known a priori about the character of the near null-space, and our method uses this knowledge in an adaptive fashion to find appropriate candidate vectors. Our results for GMRES preconditioned with the proposed SA method exhibit consistent performance for fixed points-per-wavelength and decreasing mesh size. Copyright (C) 2010 John Wiley & Sons, Ltd.
Year
DOI
Venue
2010
10.1002/nla.686
NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS
Keywords
Field
DocType
algebraic multigrid (AMG),smoothed aggregation (SA),Helmholtz,indefinite,non-symmetric,discontinuous Galerkin
Discontinuous Galerkin method,Mathematical optimization,Generalized minimal residual method,Mathematical analysis,Finite difference,A priori and a posteriori,Scalar (physics),Helmholtz free energy,Operator (computer programming),Mathematics,Multigrid method
Journal
Volume
Issue
ISSN
17
SP2-3
1070-5325
Citations 
PageRank 
References 
7
0.53
23
Authors
2
Name
Order
Citations
PageRank
Luke Olson123521.93
Jacob B. Schroder2607.93