Overlapping additive Schwarz preconditioners for boundary element methods
Thanh Tran
Abstract:
We study overlapping additive Schwarz preconditioners for the
Galerkin boundary element method when used to solve Neumann
problems for the Laplacian. Both the $h$ and $p$ versions of the
Galerkin scheme are considered. We prove that the condition number
of the additive Schwarz operator is bounded by
$O(1+\log^2\frac{H}{\delta})$ for the $h$ version, where $H$ is the
size of the coarse mesh and $\delta$ is the size of the overlap,
and bounded independently of the mesh size and the polynomial order
for the $p$ version.
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