Summary: Computing and Visualization in Science manuscript No.
(will be inserted by the editor)
Burak Aksoylu · Ivan G. Graham · Hector Klie · Robert Scheichl
Towards a rigorously justified algebraic preconditioner for
high-contrast diffusion problems
Dedicated to Prof. Dr. Wolfgang Hackbusch on the occasion of his 60th birthday.
Abstract In this paper we present a new preconditioner
suitable for solving linear systems arising from finite ele-
ment approximations of elliptic PDEs with high-contrast
coefficients. The construction of the preconditioner con-
sists of two phases. The first phase is an algebraic one
which partitions the degrees of freedom into "high" and
"low" permeability regions which may be of arbitrary ge-
ometry. This partition yields a corresponding blocking of
the stiffness matrix and hence a formula for the action of
its inverse involving the inverses of both the high permeabil-
ity block and its Schur complement in the original matrix.
The structure of the required sub-block inverses in the high
contrast case is revealed by a singular perturbation analysis
(with the contrast playing the role of a large parameter).