Robust iterative methods for elliptic problems
with highly varying coefficients in thin substructures |
| |
Authors: | BN Khoromskij G Wittum |
| |
Institution: | Institut für Computeranwendungen, Universit?t Stuttgart,
Pfaffenwaldring 27, D-70569 Stuttgart, Germany, DE
|
| |
Abstract: | Summary.
In this paper we introduce a class of robust multilevel
interface solvers for two-dimensional
finite element discrete elliptic problems with highly
varying coefficients corresponding to geometric decompositions by a
tensor product of strongly non-uniform meshes.
The global iterations convergence rate is shown to be of
the order
with respect to the number of degrees
of freedom on the single subdomain boundaries, uniformly upon the
coarse and fine mesh sizes, jumps in the coefficients
and aspect ratios of substructures.
As the first approach, we adapt the frequency filtering techniques
28] to construct robust smoothers
on the highly non-uniform coarse grid. As an alternative, a multilevel
averaging procedure for successive coarse grid correction is
proposed and analyzed.
The resultant multilevel coarse grid
preconditioner is shown to have (in a two level case) the condition
number independent
of the coarse mesh grading and
jumps in the coefficients related to the coarsest refinement level.
The proposed technique exhibited high serial and parallel
performance in the skin diffusion processes modelling 20]
where the high dimensional coarse mesh problem inherits a strong geometrical
and coefficients anisotropy.
The approach may be also applied to magnetostatics problems
as well as in some composite materials simulation.
Received December 27, 1994 |
| |
Keywords: | Mathematics Subject Classification (1991):65F10 65N20 65N30 |
本文献已被 SpringerLink 等数据库收录! |
|