
Open access
Date
1995-09Type
- Report
ETH Bibliography
yes
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Abstract
We analyze multiscale Galerkin methods for strongly elliptic boundary integral equations of order zero on closed surfaces in $R^3$. Piecewise polynomial, discontinuous multiwavelet bases of any polynomial degree are constructed explicitly. We show that optimal convergence rates in the boundary energy norm and in certain negative norms can be achieved with "compressed" stiffness matrices containing $O(N({\log N})^2)$ nonvanishing entries where $N$ denotes the number of degrees of freedom on the boundary manifold. We analyze a quadrature scheme giving rise to fully discrete methods. We show that the fully discrete scheme preserves the asymptotic accuracy of the scheme and that its overall computational complexity is $O(N({\log N})^4)$ kernel evaluations. The implications of the results for the numerical solution of elliptic boundary value problems in or exterior to bounded, three-dimensional domains are discussed. Show more
Permanent link
https://doi.org/10.3929/ethz-a-004289236Publication 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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