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A fast algorithm for nonlinear finite element analysis using equivalent magnetization current A parallel conjugate gradients algorithm for finite element analysis of electromagnetic fields New nonlinear algorithms are presented that use the given material B-H curve directly, rather than converting it to a reluctivity Y = (H/B) vs B2 curve as is common. In addition to full Newton-Raphson iteration, also discussed are modified Newton-Raphson iteration, quasi-Newton iteration, and line search algorithms. Full Newton-Raphson iteration with the new direct B-H algorithm is shown in most typical small 3D and 2D magnetostatic problems to achieve convergence in a much smaller number of iterations than the Y vs B2 algorithm.

New techniques are presented for finite element modeling of permanent magnets in magnetic devices such as motors and generators. These techniques extend a previous sheet-current permanent magnet model that applies only for straight line B-H loops and rectangular-shaped magnets. Here Maxwell’s equations are used to derive the model of a permanent magnet having a general curved B-H loop and any geometric shape. The model enables a nonlinear magnetic finite element program to use Newton–Raphson iteration to solve for saturable magnetic fields in a wide variety of devices containing permanent magnets and steels. The techniques are applied to a brushless dc motor with irregular-shaped permanent magnets. The calculated motor torque agrees well with measured torque.

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