Abstract




 
   

IJE TRANSACTIONS A: Basics Vol. 16, No. 4 (November 2003) 319-330   

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  SIGNIFICANT ERROR PROPAGATION IN THE FINITE DIFFERENCE SOLUTION OF NON-LINEAR MAGNETOSTATIC PROBLEMS UTILIZING BOUNDARY CONDITION OF THE THIRD KIND
 
 
E. Afjei

Department of Electrical and Computer Engineering, Shahid Beheshti University
Tehran, Iran, afjei@yahoo.com


J. Rashed-Mohassel

Department of Electrical and Computer Engineering, University of Tehran
Tehran, Iran, jrashed@ut.ac.ir


M. H. Arbab

Department of Electrical and Computer Engineering, Shahid Beheshti University
Tehran, Iran, h-arab@hotmail.com
 
 
( Received: May 10, 2003 – Accepted: November 05, 2003 )
 
 

Abstract    This paper poses two magnetostatic problems in cylindrical coordinates with different permeabilities for each region. In the first problem the boundary condition of the second kind is used while in the second one, the boundary condition of the third kind is utilized. These problems are solved using the finite element and finite difference methods. In second problem, the results of the finite difference method show low magnetic vector potential as well as the magnetic field density when compared to the finite element results and in the linear case, to the analytical solution. This paper investigates the reason behind the low magnetostatic field computation in cylindrical coordinates using the finite difference method when boundary condition of the third kind is used. It then, presents a technique to overcome the problem of low magnetic field calculation using the finite difference method. The results obtained by the new technique are in close agreement with the finite element method as well as the analytical solution. Finally, it analyzes the possible source of error in modeling magnetostatic boundary conditions in finite difference formulation of vector Poisson or Laplace’s equation in cylindrical coordinates.

 

Keywords    Nonlinear Magnetic Field, Finite Difference, Finite Element, Electromagnetics

 

References   

1. Afjei, E. and Rashed-Mohassel, J., “Inadequacies in Finite Difference Solution of Magnitostatic Problems”, Iranian Journal of Science and Technology, Transaction B, Vol. 25, No. B23, (2001), 533-541.

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3. Fuchs, E. F. and McNaughton, G. A., "Comparison of First-Order Finite Difference and Finite Element Algorithms for The Analysis of Magnetic Fields. Part II: Theoretical Analysis", IEEE Transaction on Power Apparatus and System, PAS-101, No. 5, (May 1982), 1027-1034.

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11. Jianming, J., “The Finite Element Method in Electromagnetics”, New York, NY:John Wiley and Sons,(1993).



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