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MiS Preprint

Domain decomposition based $\mathcal{H}$-matrix preconditioners for the skin problem

Boris N. Khoromskij and Alexander Litvinenko


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 ($\mathcal{H}$-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 $\mathcal{H}$-Cholesky factorization. We apply the $\mathcal{H}$-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 $\mathcal{H}$-Cholesky preconditioner applied to the global stiffness matrix, which is also very cheap and fast.

skin problem, hierarchical Cholesky, preconditioner

Related publications

2008 Repository Open Access
Alexander Litvinenko and Boris N. Khoromskij

Domain decomposition based \(\mathscr {H}\)-matrix preconditioners for the skin problem

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] / Ulrich Langer (ed.)
Berlin [u.a.] : Springer, 2008. - pp. 175-182
(Lecture notes in computational science and engineering ; 60)