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.
Gemmrich, Simon; Gopalakrishnan, Jay; and Nigam, Nilima, "Convergence Analysis of a Multigrid Algorithm for the Acoustic Single Layer Equation" (2012). Mathematics and Statistics Faculty Publications and Presentations. 41.