MiS Preprint Repository

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.