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MiS Preprint
95/2006
Domain decomposition based $\mathcal{H}$-matrix preconditioners for the skin problem
Boris N. Khoromskij and Alexander Litvinenko
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 ($\mathcal{H}$-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.
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)
