Convergence Analysis of a Multigrid Algorithm for the Acoustic Single Layer Equation

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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.

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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. doi:10.1016/j.apnum.2012.02.003