Direct Domain Decomposition using the Hierarchical Matrix Technique

• inside of the subdomains, L∞-coefficients are allowed (i.e., jumping coefficients, oscillatory coefficients, etc.). There is no need to place the skeleton along jump lines. A proof concerning robustness against rough boundaries and non-smooth coefficients is given in [1]. If, however, it happens that the coefficients are piecewise constant or analytic in the subdomains, a further improvement is possible using a new technique of Khoromskij and Melenk [7] (see Subsection 3.2).