Preprint 85/2007

Approximation of solution operators of elliptic partial differential equations by H- and H2-matrices

Steffen Börm

Contact the author: Please use for correspondence this email.
Submission date: 06. Sep. 2007 (revised version: September 2007)
Pages: 27
published in: Numerische Mathematik, 115 (2010) 2, p. 165-193 
DOI number (of the published article): 10.1007/s00211-009-0278-7
MSC-Numbers: 65N22, 65N30, 65F05
Keywords and phrases: Hierarchical matrix, H^2-matrix, PDE
Download full preprint: PDF (243 kB), PS ziped (229 kB)

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 formula11- and formula13-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 formula11- and formula13-matrix approximations of the entire matrices.

20.11.2019, 02:13