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Date
2002-06Type
- Report
ETH Bibliography
yes
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Abstract
Weakly singular boundary integral equations $(BIEs)$ of the first kind on polyhedral surfaces $\Gamma$ in $R^3$ are discretized by Galerkin BEM on shape-regular, but otherwise unstructured meshes of meshwidth $h$. Strong ellipticity of the integral operator is shown to give nonsingular stiffness matrices and, for piecewise constant approximations, up to $O(h^3)$ convergence of the farfield. The condition number of the stiffness matrix behaves like $O(h^-$$^1)$ in the standard basis. An $O(N)$ agglomeration algorithm for the construction of a multilevel wavelet basis on $\Gamma$ is introduced resulting in a preconditioner which reduces the condition number to $O(| log (h)|)$. A class of kernel-independent clustering algorithms (containing the fast multipole method as special case) is introduced for approximate matrix-vector multiplication in $O(N(log (N))^3)$ memory and operations. Iterative approximate solution of the linear system by $CG$ or $GMRES$ with wavelet preconditioning and clustering-acceleration of matrix-vector multiplication is shown to yield an approximate solution in log-linear complexity which preserves the $O(h^3)$ convergence of the potentials. Numerical experiments are given which confirm the theory. Show more
Permanent link
https://doi.org/10.3929/ethz-a-004363446Publication status
publishedExternal links
Journal / series
SAM Research ReportVolume
Publisher
Seminar for Applied Mathematics, ETH ZurichOrganisational unit
03435 - Schwab, Christoph / Schwab, Christoph
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ETH Bibliography
yes
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