280 IGPM280.pdf        October 2007
TITLE Approximation of Solution Operators of Elliptic Partial Differential Equations by H- and H2-Matrices
AUTHORS Steffen Börm
ABSTRACT We investigate the problem of computing the inverses of stiffness matrices resulting from the finite element discretization of elliptic partial differential equations. Since the solution operators are non-local, the inverse matrices will in general be dense, therefore they cannot be represented by standard techniques. In this paper, we prove that these matrices can be approximated by H- and H2-matrices. The key results are existence proofs for local low- rank approximations of the solution operator and its discrete counterpart, which give rise to error estimates for H- and H2-matrix approximations of the entire matrices.
KEYWORDS Hierarchical matrices, data-sparse approximation, finite element methods, elliptic partial differential equations