Similarities between Implicit Multigrid Method and A-phi Formulation in Electromagnetic Field Analysis

摘要

This paper introduces a new multigrid type iterative method: the implicit multigrid method that the authors have recently proposed. In this method, linear systems of equations on all levels in a multigrid method are integrated into a large linear system of equations. When this integrated linear system is solved by using preconditioned iterative solvers, coarse grid correction is expected to be implicitly involved. Since any preconditioning techniques are applicable to the integrated linear system, the proposed method can extend the areas for application of conventional multigrid solvers. Numerical tests confirm that the proposed method involves coarse grid correction effects and attains a convergence rate independent of the grid-size. The basic concept of the new method has a strong relationship with the convergence behavior of the ICCG method in the A-phi method (formulation) for electromagnetic field analysis. This abstract describes the outline and the way to implement the implicit multigrid method. In a full paper version, we will discuss the similarity between the implicit multigrid method and the A-phi method in an electromagnetic field analysis.