HETEROGENEOUS DOMAIN DECOMPOSITION FOR SINGULARLY PERTURBED ELLIPTIC BOUNDARY-VALUE-PROBLEMS

A heterogeneous domain-decomposition method is presented for the numer ical solution of singularly perturbed elliptic boundary value problems . The method, which is parallelizable at various levels, uses several ideas of asymptotic analysis. The subdomains match the domains of vali dity of the local (inner and outer) asymptotic expansions, and cut-off functions are used to match solutions in neighboring subdomains. The positions of the interfaces, as well as the mesh widths, depend on the small parameter epsilon. On the subdomains, iterative solution techni ques are used, which may vary from one subdomain to another. The globa l convergence rate depends on epsilon; it generally increases like som e power of (log(epsilon(-1)))(-1) as epsilon down arrow 0. The method is illustrated on several two-dimensional singular perturbation proble ms.