Inexact Newton solvers offer many attractive features for the solution of nonlinear problems in the field of electromagnetics. A critical point for the optimal setup of the solver is the choice of the best algorithm for the evaluation of the approximate solution of the linear systems at each Newton step and the most effective preconditioning strategy. In this paper, the Newton iterative solver method is proposed for the solution of a nonlinear magnetostatic problem. The problem is discretized by means of a finite-element approach. The generalized minimum residuals (GMRES) method is adopted as linear solver, and three preconditioners are tested. The performance of this procedure is evaluated for different magnetostatic problems and compared to the results obtained by means of a Newton–Raphson method.

An Application of the Inexact Newton Method to Nonlinear Magnetostatics

BORGHI, CARLO ANGELO;BRESCHI, MARCO;CRISTOFOLINI, ANDREA;CARRARO, MARIO ROBERTO
2004

Abstract

Inexact Newton solvers offer many attractive features for the solution of nonlinear problems in the field of electromagnetics. A critical point for the optimal setup of the solver is the choice of the best algorithm for the evaluation of the approximate solution of the linear systems at each Newton step and the most effective preconditioning strategy. In this paper, the Newton iterative solver method is proposed for the solution of a nonlinear magnetostatic problem. The problem is discretized by means of a finite-element approach. The generalized minimum residuals (GMRES) method is adopted as linear solver, and three preconditioners are tested. The performance of this procedure is evaluated for different magnetostatic problems and compared to the results obtained by means of a Newton–Raphson method.
C. Borghi; M. Breschi; A. Cristofolini; M. R. Carraro
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/8040
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