A fast spectral element solver combining static condensation and multigrid techniques

We propose a spectral element multigrid method for the two-dimensional Helmholtz equation discretized on regular grids. Combining p-multigrid with static condensation the method achieves nearly linear complexity with an order-independent convergence rate for solving the condensed equations. For smoo...

Full description

Saved in:
Bibliographic Details
Published inJournal of computational physics Vol. 255; pp. 384 - 395
Main Authors Haupt, L., Stiller, J., Nagel, W.E.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.12.2013
Subjects
Condensing
Convergence
Degrees of freedom
Elliptic equations
Mathematical analysis
Multigrid method
Multigrid methods
Robustness
Solvers
Spectra
Spectral element method
Static condensation
Static condensation
Spectral element method
Multigrid method
Elliptic equations
Online AccessGet full text

Cover

More Information
Summary:We propose a spectral element multigrid method for the two-dimensional Helmholtz equation discretized on regular grids. Combining p-multigrid with static condensation the method achieves nearly linear complexity with an order-independent convergence rate for solving the condensed equations. For smoothing we consider two groups of edge-based relaxation schemes, the best of which attains a multigrid convergence rate of ρ≈0.014 to 0.028. Numerical experiments have been carried out that demonstrate the robustness of the approach for orders up to 32 and a total of 109 degrees of freedom. In comparison with a fast finite difference solver, the latter is clearly outperformed already for errors of one percent or lower.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2013.07.035