On parallel multisplitting block iterative methods for linear systems arising in the numerical solution of Euler equations

TL;DR

This paper analyzes the convergence of various parallel multisplitting block iterative methods for solving linear systems from Euler equations, providing conditions for convergence and demonstrating their effectiveness through examples.

Contribution

It introduces new convergence conditions for parallel multisplitting block iterative methods applied to Euler equations, including special cases and specific matrix structures.

Findings

Convergence conditions for parallel multisplitting methods are established.

The methods are effective for block tridiagonal matrices in Euler equations.

Numerical examples confirm theoretical results.

Abstract

The paper studies the convergence of some parallel multisplitting block iterative methods for the solution of linear systems arising in the numerical solution of Euler equations. Some sufficient conditions for convergence are proposed. As special cases the convergence of the parallel block generalized AOR (BGAOR), the parallel block AOR (BAOR), the parallel block generalized SOR (BGSOR), the parallel block SOR (BSOR), the extrapolated parallel BAOR and the extrapolated parallel BSOR methods are presented. Furthermore, the convergence of the parallel block iterative methods for linear systems with special block tridiagonal matrices arising in the numerical solution of Euler equations are discussed. Finally, some examples are given to demonstrate the convergence results obtained in this paper.