First and Second order Field Estimation Using Multi- Grid Algorithm

This paper poses a magnetic field problem in cylindrical coordinate for two regions with different permeabilities for each one. The linear partial differential equation governing this problem is in the form of Helm-Holtz equation. This problem is then solved using classical Gauss-Seidel Algorithm for the Finite difference (FD) solution of linear partial differential equation. In order to obtain adequate solution for a reasonable number of grid points for the regions under consideration a considerable amount of time will take for the program to converge. The paper presents a different technique known as Multi-Grid which will speed up the convergence process In this method, the solution to the differential equation between two grid points for obtaining the initial condition is considered to be linear at firs t and then of the second order in nature. The main contribution is made by regarding the effect of the initial values of the variable vector in the convergence time of the Gauss- Seidel algorithm

کلیدواژه ها:

Multi-Grid ، Finite Difference ، Electromagnetics