Domain decomposition based -matrix preconditioners for the skin problem

Boris N. Khoromskij and Alexander Litvinenko

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Submission date: 05. Sep. 2006 (revised version: August 2008)
Pages: 10
published in: Domain decomposition methods in science and engineering : [Proceedings of the 17th International Conference on Domain Decomposition Methods, July 3-7, 2006, St. Wolfgang/Strobl, Austria] / U. Langer (ed.)
Berlin [u.a.] : Springer, 2008. - P. 175 - 182
(Lecture notes in computational science and engineering ; 60) 
DOI number (of the published article): 10.1007/978-3-540-75199-1_17
Bibtex
Keywords and phrases: skin problem, hierarchical Cholesky, preconditioner
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Abstract:
In this paper we propose and analyse a new preconditioner for the so-called skin problem (in 2D and 3D) based on a hierarchical Cholesky (-Cholesky) factorization. After a special reordering of indices and omitting the coupling between subdomains and the interface layer, we obtain a block diagonal matrix which is well suited for the -Cholesky factorization. We apply the -Cholesky factorization of this matrix as a preconditioner for the pcg method. We will show that the new preconditioner requires less memory and computational time than the -Cholesky preconditioner applied to the global stiffness matrix, which is also very cheap and fast.