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Applied Numerical Mathematics

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Algorithms, Equations -- Numerical solutions, Dimensional analysis, Numerical analysis


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.


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).



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