Article
Convergence Analysis of a Multigrid Algorithm for the Acoustic Single Layer Equation
Applied Numerical Mathematics
Document Type
Post-Print
Publication Date
2-1-2012
Subjects
- Algorithms,
- Equations -- Numerical solutions,
- Dimensional analysis,
- Numerical analysis
Disciplines
Abstract
We present and analyze a multigrid algorithm for the acoustic single layer equation in two dimensions. The boundary element formulation of the equation is based on piecewise constant test functions and we make use of a weak inner product in the multigrid scheme as proposed in Bramble et al. (1994) . A full error analysis of the algorithm is presented. We also conduct a numerical study of the effect of the weak inner product on the oscillatory behavior of the eigenfunctions for the Laplace single layer operator.
Rights
Crown copyright © 2012 Published by Elsevier B.V. All rights reserved.
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
DOI
10.1016/j.apnum.2012.02.003
Persistent Identifier
http://archives.pdx.edu/ds/psu/10609
Citation Information
Published as: Gemmrich, S., Gopalakrishnan, J., & Nigam, N. (2012). Convergence analysis of a multigrid algorithm for the acoustic single layer equation. Applied Numerical Mathematics, 62(6), 767-786.
NOTICE: this is the author’s version of a work that was accepted for publication in Applied Numerical Mathematics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Applied Numerical Mathematics, Vol. 62, Issue 6, p.767-786 (2012).