Uniform Domain Decomposition Methods
by
Igor Boglaev
Institute of Fundamental Sciences, Massey University

Our purpose is to study the multidomain decomposition algorithms for solving singularly perturbed problems with convection-dominated terms. We show that the algorithms converge uniformly on uniform and piecewise equidistant meshes. These meshes allow us to decompose the computational domain into subdomains outside boundary layers and inside them as well, and possess load balancing. This property is very important for implementation of the iterative algorithms on parallel computers, since it avoids loss of efficiency due to one processor being idle.

Numerical results confirm effectiveness of the proposed algorithms: these results indicate robustness of the algorithms; sufficiently small interfacial subdomains are needed to essentially reduce the number of iterations.

Date received: October 17, 2000