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BEM with linear complexity for the classical boundary integral operators

Authors: Steffen Börm and Stefan A. Sauter
Journal: Math. Comp. 74 (2005), 1139-1177
MSC (2000): Primary 65N38, 65D05
Published electronically: December 8, 2004
MathSciNet review: 2136997
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Abstract: Alternative representations of boundary integral operators corresponding to elliptic boundary value problems are developed as a starting point for numerical approximations as, e.g., Galerkin boundary elements including numerical quadrature and panel-clustering. These representations have the advantage that the integrands of the integral operators have a reduced singular behaviour allowing one to choose the order of the numerical approximations much lower than for the classical formulations. Low-order discretisations for the single layer integral equations as well as for the classical double layer potential and the hypersingular integral equation are considered. We will present fully discrete Galerkin boundary element methods where the storage amount and the CPU time grow only linearly with respect to the number of unknowns.

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Additional Information

Steffen Börm
Affiliation: Max-Planck-Institut für Mathematik in den Naturwissenschaften, Inselstraße 22–26, 04103 Leipzig, Germany

Stefan A. Sauter
Affiliation: Institut für Mathematik, Universität Zürich, Winterthurerstr. 190, CH-8057 Zürich, Switzerland

Keywords: BEM, data-sparse approximation, ${\mathcal H}^2$-matrices
Received by editor(s): September 9, 2003
Received by editor(s) in revised form: March 29, 2004
Published electronically: December 8, 2004
Additional Notes: This work was supported by the Swiss National Science Foundation, Grant 21-6176400.
Article copyright: © Copyright 2004 American Mathematical Society

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