## BEM with linear complexity for the classical boundary integral operators

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- by Steffen Börm and Stefan A. Sauter PDF
- Math. Comp.
**74**(2005), 1139-1177 Request permission

## 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.## References

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## Additional Information

**Steffen Börm**- Affiliation: Max-Planck-Institut für Mathematik in den Naturwissenschaften, Inselstraße 22–26, 04103 Leipzig, Germany
- MR Author ID: 678579
- Email: sbo@mis.mpg.de
**Stefan A. Sauter**- Affiliation: Institut für Mathematik, Universität Zürich, Winterthurerstr. 190, CH-8057 Zürich, Switzerland
- MR Author ID: 313335
- Email: stas@amath.unizh.ch
- 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.
- © Copyright 2004 American Mathematical Society
- Journal: Math. Comp.
**74**(2005), 1139-1177 - MSC (2000): Primary 65N38, 65D05
- DOI: https://doi.org/10.1090/S0025-5718-04-01733-8
- MathSciNet review: 2136997