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 \cite{BLP94}. 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.
@article{arxiv.1202.6083,
title = {Convergence analysis of a multigrid algorithm for the acoustic single layer equation},
author = {Simon Gemmrich and Jay Gopalakrishnan and Nilima Nigam},
journal= {arXiv preprint arXiv:1202.6083},
year = {2012}
}