Premium
An integral equation method for the solution of 3‐dimensional, non‐linear, magnetostatic problems
Author(s) -
Loines Janet,
Bernal Michael J. M.
Publication year - 1987
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620240811
Subject(s) - mathematics , finite element method , algebraic equation , mathematical analysis , integral equation , jacobian matrix and determinant , scalar (mathematics) , quadrature (astronomy) , magnetic field , collocation method , geometry , physics , nonlinear system , differential equation , ordinary differential equation , quantum mechanics , optics , thermodynamics
A finite element method for computing the resultant magnetic field arising from a given source field in the presence of a magnetic material of variable permeability is described; in this method finite element approximations to the scalar potential of the resulting field and the magnetic susceptibility, in the region occupied by the magnetic material, are determined from the non‐linear integral equation for the scalar potential and the constitutive susceptibility relation, using a collocation scheme. The method is used to compute the shielding effect of a thin rectangular plate of variable permeability on a given source field. The plate is subdivided uniformly into brick elements; the resulting translational invariance of the integrals required in the calculations is exploited to achieve major computational savings. A consequence of the thinness of the plate is that the calculation of the requisite integrals by analytic methods leads to considerable loss of accuracy by differencing; this difficulty is overcome by using a scheme which combines both analytic and quadrature techniques. The resulting system of non‐linear algebraic equations is solved by Powell's hybrid method; an efficient scheme for calculating an initial approximation to the Jacobian, which utilizes the structure of the equations, is presented. The results of the calculations are discussed.