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Wavelet Galerkin BEM on unstructured meshes by aggregation

by G. Schmidlin and Ch. Schwab

(Report number 2000-15)

Abstract
We investigate the numerical solution of strongly elliptic boundary integral equations on unstructured surface meshes $\Gamma$ in $\IR^3$ by Wavelet-Galerkin boundary element methods (BEM). They allow complexity-reduction for matrix setup and solution from quadratic to polylogarithmic (i.e. from $O(N^2)$ to $O(N(\log N)^a)$ for some small $a\geq 0$, see, e.g. [2,3,9,10] and the references there). We introduce an agglomeration algorithm to coarsen arbitrary surface triangulations on boundaries $\Gamma$ with possibly complicated topology and to construct stable wavelet bases on the coarsened triangulations in linear complexity. We describe an algorithm to generate the BEM stiffness matrix in standard form in polylogarithmic complexity. The compression achieved by the agglomerated wavelet basis appears robust with respect to the complexity of $\Gamma$. We present here only the main results and ideas - full details will be reported elsewhere.

Keywords:

@Techreport{SS00_274,
  author = {G. Schmidlin and Ch. Schwab},
  title = {Wavelet Galerkin BEM on unstructured meshes by aggregation},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2000-15},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2000/2000-15.pdf },
  year = {2000}
}

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