解非线性方程组的一类多重分裂加性Schwarz算法

A Kind of Multisplitting Schwarz Algorithms for Solving System of Nonlinear Equations

讨论求解一类非线性方程组的多重分裂加性Schwarz算法和两水平多重分裂加性Schwarz算法,分析其收敛性和收敛速度并建立了收敛性理论.这类算法结合多重分裂和加性Schwarz算法,具有很好的并行性能,因而特别适合于并行计算.数值算例证实了算法的有效性.

A multisplitting additive Schwarz algorithm and a two-level multisplitting additive Schwarz algorithm were presented to solve a system of nonlinear equation sets. The convergence and the convergent rate were analyzed and some convergent theories were established. These kind of algorithms, combining multisplitting and additive Schwarz algorithms, could be easily applied to parallel computation. Several numerical examples were given to verify the effectiveness of the proposed method.