Adaptive Galerkin Boundary Element Methods with Panel Clustering

Wolfgang Hackbusch, Boris N. Khoromskij, and Stefan A. Sauter

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Submission date: 03. Nov. 2004 (revised version: November 2006)
Pages: 21
published in: Numerische Mathematik, 105 (2007) 4, p. 603-631 
DOI number (of the published article): 10.1007/s00211-006-0047-9
Bibtex
MSC-Numbers: 65F50, 65F30
Keywords and phrases: hierarchical matrices, panel clustering, boundary element method
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Abstract:
The present paper introduces an hp-version of BEM for the Laplace equation in polyhedral domains based on meshes which are concentrated to zones on the surface (wire-basket zones), where the regularity of the solution is expected to be low. For the classical boundary integral equations, we prove the optimal approximation results and discuss the stability aspects. Then, we construct the panel-clustering and -matrix approximations to the corresponding Galerkin BEM stiffness matrix and prove their linear-logarithmic cost. The method is shown to have an almost linear complexity with respect to the number of degrees of freedom located on the wire basket.