Treffer: A highly parallel Schwarz-chaotic relaxation method and its convergence proof

Title:
A highly parallel Schwarz-chaotic relaxation method and its convergence proof
Authors:
Zhou, Shuquan, Fang, Jinglong
Publisher Information:
Nanjing University of Aeronautics \& Astronautics, Nanjing
Subject Terms:
Finite difference methods for boundary value problems involving PDEs, Iterative numerical methods for linear systems, domain-decomposition method, Multigrid methods, domain decomposition for boundary value problems involving PDEs, convergence, parallel processing, Numerical computation of solutions to systems of equations, Parallel numerical computation, chaotic relaxation, MIMD parallel algorithms, Boundary value problems for second-order elliptic equations, maximum principle, Nonlinear boundary value problems for linear elliptic equations, Schwarz alternating procedure, Schwarz-chaotic relaxation method, Dirichlet problem
Document Type:
Fachzeitschrift Article
File Description:
application/xml
Access URL:
https://zbmath.org/465375
Accession Number:
edsair.c2b0b933574d..ed890a89140ff012a39abdbf8f181b4e
Database:
OpenAIRE

Weitere Informationen

\textit{L. Kang, Y. Chen, L. Sun} and \textit{H. Quan} [Int. J. Comput. Math. 18, No. 2, 163-172 (1985; Zbl 0653.65078)] introduced the chaotic relaxation idea into the Schwarz alternating procedure and obtained the Schwarz-chaotic relaxation method. The method uses the \(n\)-step iterative result on a pseudo-boundary when it calculates the \((n+1)\)-step iterative result. So the parallelism of this method vanishes, and neither a synchronous nor an asynchronous MIMD parallel algorithm is obtained. In this paper the authors give a highly parallel Schwarz-chaotic relaxation method. The method involves the Schwarz alternating procedure and the relevant (synchronous and asynchronous) MIMD parallel algorithms. Using the maximum principle for differential equations they prove the convergence of this method for the Dirichlet problem of second order linear and nonlinear differential equations.