Reformulation of nonlinear integral magnetostatic equations for rapid iterative convergence
The integral equations of magnetostatics, conventionally given in terms of the field variables M and H, are reformulated with M and B. Stability criteria and convergence rates of the eigenvectors of the linear iteration matrices are evaluated. The relaxation factor ..beta.. in the MH approach varies inversely with permeability ..mu.., and nonlinear problems with high permeability converge slowly. In contrast, MB iteration is stable for ..beta.. < 2, and nonlinear problems converge rapidly, at a rate essentially independent of ..mu... For a permeability of 10/sup 3/, the number of iterations is reduced by two orders of magnitude over the conventional method, and at higher permeabilities the reduction is proportionally greater. The dependence of MB convergence rate on ..beta.., degree of saturation, element aspect ratio, and problem size is found numerically. An analytical result for the MB convergence rate for small nonlinear problems is found to be accurate for ..beta..less than or equal to1.2. The results are generally valid for two- and three-dimensional integral methods and are independent of the particular discretization procedures used to compute the field matrix.
- Research Organization:
- Xerox Corporation, Palo Alto Research Center, Palo Alto, CA
- OSTI ID:
- 6193457
- Report Number(s):
- CONF-840937-
- Journal Information:
- IEEE Trans. Magn.; (United States), Vol. MAG-21:2; Conference: Applied superconductivity conference, San Diego, CA, USA, 9 Sep 1984
- Country of Publication:
- United States
- Language:
- English
Similar Records
Boundary parametric approximation to the linearized scalar potential magnetostatic field problem
Iterative spectral method for solving electrostatic or magnetostatic problems in complex and evolving heterostructures