Fmg Cycle With the Preconditioned Explicit Group-2 Linear System

Abstract

In [1] incomplete matrix decompositions are presented for the block matrix associated with the linear system generated from the discretization of elliptic partial differential equations by the explicit group-2 method which has been introduced by [2].

In this paper we presented the practical application and comparison of the performance of the smoothing methods successive displacement iterative method and preconditioning conjugate gradient method in the full multigrid scheme (cycle) with specific mesh ratio related to the characteristic of the explicit group-2 discretization approach.

Keywords:

• Explicit group-2 finite difference
• incomplete matrix decomposition
• linear elliptic partial differential equation
• preconditioning conjugate gradient method
• multigrid technique

C.R.Categories:

• G.1.3
• G1.8