Synchronous Multi-splitting Two-stage TOR Methods for Systems of Weakly Nonlinear Equations

TL;DR

This paper introduces a class of synchronous parallel multi-splitting two-stage two-parameter over-relaxation methods designed for efficiently solving large sparse systems of weakly nonlinear equations on multiprocessor systems, with proven convergence properties.

Contribution

The paper proposes a novel class of synchronous multi-splitting two-stage TOR methods tailored for large sparse weakly nonlinear systems, including convergence analysis.

Findings

Methods are effective for large sparse systems

Global convergence is established under certain assumptions

Suitable for high-speed multiprocessor systems

Abstract

For the large sparse systems of weakly nonlinear equations arising in the discretizations of many classical differential and integral equations, this paper presents a class of synchronous parallel multi-splitting two-stage two-parameter over-relaxation (TOR) methods for getting their solutions by the high-speed multiprocessor systems. Under suitable assumptions, we study the global convergence properties of these synchronous multi-splitting two-stage TOR methods.