Additive Schwarz Methods for Semilinear Elliptic Problems with Convex Energy Functionals: Convergence Rate Independent of Nonlinearity

• DOI: 10.1137/23m159545x
• Publication Date: 2024-05-02T08:02:33Z
• Authors: Jongho Park
• Keywords: Schwarz alternating method; Additive Schwarz method

.We investigate additive Schwarz methods for semilinear elliptic problems with convex energy functionals, which have wide scientific applications. A key observation is that the convergence rates of both one- and two-level bounds independent nonlinear term in problem. That is, do not deteriorate by presence nonlinearity, so solving a problem requires no more iterations than linear Moreover, method scalable sense rate depends on \(H/h\) \(H/\delta\) only, where \(h\) \(H\) are typical diameters an element subdomain, respectively, \(\delta\) measures overlap among subdomains. Numerical results provided to support our theoretical findings.Keywordsadditive methodssemilinear problemsconvex optimizationconvergence analysisdomain decomposition methodsMSC codes65N5565J1535J6190C25