An iterative substructuring method for the hp-version of the BEM on quasi-uniform triangular meshes

• Autores: Norbert Heuer , Florian Leydecker, Ernst P. Stephan
• Localización: Numerical Methods for Partial Differential Equations, ISSN 0749-159X, Vol. 23, Nº. 4, 2007, págs. 879-903
• Idioma: inglés
• DOI: 10.1002/num.20259
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• Resumen

  • We study an additive Schwarz based preconditioner for the hp-version of the boundary element method with quasi-uniform triangular meshes and for hypersingular integral operators. The model problem is Laplace's equation exterior to an open surface and is generic for elliptic boundary value problems of second order in bounded and unbounded domains with closed or open boundary. The preconditioner is based on a nonoverlapping subspace decomposition into a so-called wire basket space and interior functions for each element. We prove that the condition number of the preconditioned stiffness matrix has a bound, which is independent of the mesh size h and which grows only polylogarithmically in p, the maximum polynomial degree. Numerical experiments confirm this result. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 23: 879-903, 2007