Le Borne, SabineSabineLe BorneGrasedyck, LarsLarsGrasedyck2021-10-252021-10-252006-07-31SIAM Journal on Matrix Analysis and Applications 27 (4): 1172-1183 (2006-10-25)http://hdl.handle.net/11420/10607Hierarchical matrices provide a data-sparse way to approximate fully populated matrices. In this paper we exploit ℋ-matrix techniques to approximate the LU-decompositions of stiffness matrices as they appear in (finite element or finite difference) discretizations of convectiondominated elliptic partial differential equations. These sparse ℋ-matrix approximations may then be used as preconditioners in iterative methods. Whereas the approximation of the matrix inverse by an ℋ-matrix requires some modification in the underlying index clustering when applied to convectiondominant problems, the ℋ-LU-decomposition works well in the standard ℋ-matrix setting even in the convection dominant case. We will complement our theoretical analysis with some numerical examples. © 2006 Society for Industrial and Applied Mathematics.en0895-47982006411721183Convectiondominant problemsData-sparse approximationHierarchical matricesPreconditioningMathematikConference Paper10.1137/040615845Other