Optimal fixed-point method for solving 3D nonlinear periodic eddy current problems
Optimal fixed-point method for solving 3D nonlinear periodic eddy current problems
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DOI：
10.1108/03321640910959107
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发表时间：
2009-01-01
影响因子：
0.7
通讯作者：
Preis, Kurt
中科院分区：
文献类型：
--
作者：
Koczka, Gergely;Ausserhofer, Stefan;Preis, Kurt
目的 - 本文的目的是提出一种在非线性材料特性和周期性激励的情况下有效获得准静态麦克斯韦方程组稳态解的方法。设计/方法/途径 - 使用定点方法来考虑材料特性的非线性。谐波平衡原理和时间周期技术给出了所有非线性迭代的周期解。由于定点技术的应用，谐波被解耦。确定定点法的最优参数以加快其收敛速度。显示了该算法如何与迭代线性方程求解器配合使用。发现 - 确定了定点方法的最佳参数，并且还显示了在迭代求解方程系统的情况下该方法如何工作。原创性/价值 - 确定了迭代线性方程求解器的收敛标准。该方法用于解决三维问题。
Purpose - The purpose of the paper is to present a method for efficiently obtaining the steady-state solution of the quasi-static Maxwell's equations in case of nonlinear material properties and periodic excitations.Design/methodology/approach - The fixed-point method is used to take account of the nonlinearity of the material properties. The harmonic balance principle and a time periodic technique give the periodic solution in all nonlinear iterations. Owing to the application of the fixed-point technique the harmonics are decoupled. The optimal parameter of the fixed-point method is determined to accelerate its convergence speed. It is shown how this algorithm works with iterative linear equation solvers.Findings - The optimal parameter of the fixed-point method is determined and it is also shown how this method works if the equation systems are solved iteratively.Originality/value - The convergence criterion of the iterative linear equation solver is determined. The method is used to solve three-dimensional problems.