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