280
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RWTH Publication No: 47215 2007   IGPM280.pdf |
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
|
DOI |
10.1007/s00211-009-0278-7 |
PUBLICATION |
Numerische Mathematik volume 115, pages165–193 (2010) |