Applied Numerical Mathematics
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.
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Published as: 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.