Hierarchical matrix preconditioners for the Oseen equations

Abstract

Hierarchical matrices provide a technique for the data-sparse approximation and matrix arithmetic of large, fully populated matrices. In particular, approximate inverses as well as approximate LU factorizations of finite element stiffness matrices may be computed and stored in nearly optimal complexity. In this paper, we develop efficient ℋ-matrix preconditioners for the Oseen equations. In particular, H-matrices will provide efficient preconditioners for the auxiliary (scalar) discrete convection-diffusion and pressure Schur complement problems. We will provide various numerical tests comparing the resulting preconditioners with each other. © 2007 Springer-Verlag.