THE FINITE DIFFERENCE METHOD IN MAGNETIC FIELD PROBLEMS

摘要

Finite difference techniques are widely used in the solution of electromagnetic boundary value problems, but seldom employed with static or quasi-static field problems. Historically this departure was warranted by (1) the relative ease by which problem geometries can be modeled using the finit element counterpart, and (2) the lack of symmetrical properties and large banding in the governing matrices. Presented here are some methods for generalizing the finite difference approach so that problem definition is easily modeled and Hermitian matrices result. The technique uses a conventional finite difference grid placed in the work area irrespective of the problem geometry. Finite difference equations are written in their simplest form across the problem work space. Boundary conditions are then introduced after the bulk equations are in place. The problem is solved using a non square governing matrix in a least square sense. This is accomplished most easily by premultiplying the matrix equation by its transpose. An alternative to the preconditioned conjugate gradient technique for solving the resultant matrix equation is to seek the eigenvalues for the system and express the answer as a sum of the eigenvectors. Results are shown for a salient pole motor. The technique is very useful in handling rotating or translating problems where considerable attention must be given to the proper connection and re-connection of the grid points. [Vol. 9, No. 2 (1994), Special Issue on The Numerical Computation of Low Frequency Electromagnetic Fields, pp 93-97]