Grasedyck, LarsLarsGrasedyckKriemann, RonaldRonaldKriemannLe Borne, SabineSabineLe Borne2021-10-252021-10-252009-03-03Numerische Mathematik 112 (4): 565-600 (2009-06-01)http://hdl.handle.net/11420/10611Hierarchical matrices provide a data-sparse way to approximate fully populated matrices. The two basic steps in the construction of an H-matrix are (a) the hierarchical construction of a matrix block partition, and (b) the blockwise approximation of matrix data by low rank matrices. In this paper, we develop a new approach to construct the necessary partition based on domain decomposition. Compared to standard geometric bisection based H-matrices, this new approach yields H-LU factorizations of finite element stiffness matrices with significantly improved storage and computational complexity requirements. These rigorously proven and numerically verified improvements result from an H-matrix block structure which is naturally suited for parallelization and in which large subblocks of the stiffness matrix remain zero in an LU factorization. We provide numerical results in which a domain decomposition based H-LU factorization is used as a preconditioner in the iterative solution of the discrete (three-dimensional) convection-diffusion equation. © 2009 Springer-Verlag.en0029-599X20094565600MathematikJournal Article10.1007/s00211-009-0218-6Other