Newton-Raphson Solver for Finite Element Methods Featuring Nonlinear Hysteresis Models

• Published in: IEEE transactions on magnetics 2018-01, Vol.54 (1), p.1-8
• Main Authors: Chama, Abdoulkadri, Gerber, Stiaan, Rong-Jie Wang
• Format: Article
• Language: English
• Subjects: Comparative analysis; Convergence; Finite element; Finite element analysis; Finite element method; Hysteresis; hysteresis curve; Iterative methods; Jacobian matrices; Magnetic hysteresis; Magnetism; Magnetization; Magnetization curves; Mathematical analysis; Mathematical model; Newton method; Newton methods; Newton-Raphson method; Nonlinear programming; Permeability; weak derivatives
• ISSN: 0018-9464; 1941-0069
• DOI: 10.1109/TMAG.2017.2761319

It is well known that the Newton-Raphson method is the most popular iterative method for nonlinear finite element problems. The method has a quadratic convergence. Under certain conditions on the Jacobian of the functional and the initial guess the Newton-Raphson method can converge very fast. However, standard evaluation of such Jacobian may not be possible for the solution of nonlinear hysteresis field problems. This is due to the nature of the magnetization curves that may not be differentiable or possess a very steep gradient. In this paper, an alternative finite element implementation using the Newton-Raphson method for hysteresis field problems is described in detail. To improve the convergence of the method, a method for evaluation of the initial guess is also proposed. It is shown that the Newton method can be reliably used for solving hysteresis field problems.