Convergence analysis of a multigrid algorithm for the acoustic single layer equation

Authors:
S. Gemmrich;J. Gopalakrishnan;N. Nigam
Affiliations:
Dept. of Mathematics and Statistics, McGill University, Canada;Dept. of Mathematics, Portland State University, United States;Dept. of Mathematics, Simon Fraser University, Canada
Venue:
Applied Numerical Mathematics
Year:
2012

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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) [4]. 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.