三维非线性恒定磁场的有限元法计算(上)

Calculating the Three-dimensional Nonlinear Constant Field with Finite Element Method

本文对用向量磁位描述的三维非线性恒定磁场的有限元解法进行了分析研究。文中首先对与三维恒定非线性磁场边值问题等价的泛函及变分问题进行了讨论。然后对变分问题的离散化分析进行了推导和论证,并得出了有关的计算公式。对于非线性问题的求解,本文采用了牛顿—拉夫逊法,并就三维情况下如何形成系数矩阵[J]和右端向量[△P]进行了研究和推导。本文将波阵解技术应用于求解大型、稀疏有限元代数方程组,编制了三维网格自动形成子程序。在以上工作的基础上,编制了有限元计算主程序,进行了实例计算,计算与实验结果的较好吻合充分证明了算法和程序的正确性。

In this paper, a nonlinear three-dimensional magnetostatic field analysis by the finite-element method is presented based on vector potential. The functional and variational problem equivalent to the boundary value problem of three-dimen sional nonlinear magnetostatic field are discussed first. Then, the discrete analysis of the variational probleim is investigated and correspondent formulation are yielded The Neuton-Laphson method is used in solving nonlinear problem. The coefficient matrix [J] and right matrix [p] are yielded. The front solusion technique is applied to solving large, sparse finite-element algebraic equasions. A sub-program for three-dimensional automatic mesh generation is programmed Based on all above, the program for finite-element calculation is given and practical calculation is carried out. Comparison between the calculation and experiment results is satisfactory.