Zou, Jun; Huang, Hongci Algebraic subproblem decomposition methods and parallel algorithms with monotone convergence. (English) Zbl 0793.65040 J. Comput. Math. 10, Suppl., 47-59 (1992). Summary: We discuss the solution of a kind of systems of algebraic equations which arise from the discretization of symmetric or nonsymmetric elliptic boundary value problems including the related problems of parabolic type, weakly nonlinear elliptic problems, and linear or nonlinear network problems. A class of algebraic subproblem decomposition methods and parallel algorithms with their iterative sequences possessing monotone convergence componentwise are proposed for these discrete systems. These methods are suitable for arbitrary domain decomposition cases with many subdomains overlapping one another. Cited in 3 Documents MSC: 65H10 Numerical computation of solutions to systems of equations 65Y05 Parallel numerical computation 65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs 35J65 Nonlinear boundary value problems for linear elliptic equations Keywords:systems of algebraic equations; weakly nonlinear; parallel algorithms; monotone convergence; domain decomposition PDFBibTeX XMLCite \textit{J. Zou} and \textit{H. Huang}, J. Comput. Math. 10, 47--59 (1992; Zbl 0793.65040)