Domain decomposition algorithms for fourth-order nonlinear elliptic eigenvalue problems

We study domain decomposition methods for fourth-order plate problems. The well-known von Kلrmلn 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 Kلrmلn 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 Kلrmلn equations.