Domain decomposition algorithms for fourth-order nonlinear elliptic eigenvalue problems

Authors:
S.-L. Chang;C.-S. Chien
Affiliations:
Center for General Education, Southern Taiwan University of Technology, Tainan 710, Taiwan, ROC;Department of Applied Mathematics, National Chung-Hsing University, Taichung 402, Taiwan, ROC
Venue:
Journal of Computational Physics
Year:
2003

Citing 9
Cited 0

Analysis of preconditioners for domain decomposition

SIAM Journal on Numerical Analysis
A comparison of domain decomposition techniques for elliptic partial differential equations and their parallel implementation

SIAM Journal on Scientific and Statistical Computing
Domain decomposition interface preconditioners for fourth-order elliptic problems

Applied Numerical Mathematics - II on Domain decomposition; Guest Editor: W. Proskurowski
The interface probing technique in domain decomposition

SIAM Journal on Matrix Analysis and Applications
Domain decomposition: parallel multilevel methods for elliptic partial differential equations

Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Multiple Bifurcation in the von Kármán Equations

SIAM Journal on Scientific Computing
Symmetry and scaling properties of the von Ka´rma´n equations

Zeitschrift für Angewandte Mathematik und Physik (ZAMP)
Mode Jumping In The Von Kármán Equations

SIAM Journal on Scientific Computing
Iterative Methods for Sparse Linear Systems

Iterative Methods for Sparse Linear Systems

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Abstract

We study domain decomposition methods for fourth-order plate problems. The well-known von Kármán equations are used as our model problem. By exploiting the symmetry of the domain, the solution of the original problem can be obtained by solving those associated reduced problems, which are defined on subdomains with appropriate boundary conditions. We show how nonoverlapping and overlapping domain decomposition methods can be used to solve the reduced problems. For the linearized von Kármán equation, we present preconditioners using both Fourier analysis and probing techniques for the interface systems, which are similar to those derived by Chan et al. Finally, we compare the efficiency of various domain decomposition preconditioners for solving the von Kármán equations.