Two-level parallel Schwarz methods for singularly perturbed semilinear elliptic problems
Two-level domain decomposition methods based on the Schwarz alternating procedure are proposed for the numerical solution of singularly perturbed semilinear elliptic problems. The convergence rate estimates are established on differential level (independently of specific numerical realizations of the methods) and for regular rectangular domain decomposition. The author also describes a modified two-level Schwarz method with Newton's linearization. Numerical experiments for a test problem illustrate the behaviour of the methods with respect to the critical parameters, such as the perturbation parameter, the amount of overlapping and sizes of subdomains.. Application of one of the two-level Schwarz methods to a semiconductor model problem is also discussed.
scientific article; zbMATH DE number 1528525
scientific article