The parallel local modified SOR for nonsymmetric linear systems

In this paper we introduce the local Modified Successive Overrelaxation (MSOR) method and apply Fourier analysis to study its convergence. Parallelism is introduced by decoupling the mesh points with the use of red-black ordering for the 5-point stencil. The optimum set of values for the parameters involved, when the Jacobi iteration operator possesses imaginary eigenvalues, is determined. The performance of the local MSOR method is illustrated by its application to the numerical solution of the convection diffusion equation. It is found that the proposed method is significantly more efficient than local SOR when the absolute value of the smallest eigenvalue of the Jacobi operator is larger than unity. Finally, the parallel implementation of the local MSOR method is discussed and results are presented for distributed memory processors with a mesh topology