Numerical Solution of the Nonlinear Magnetostatic-Field Equation in Two Dimensions
Numerical Solution of the Nonlinear Magnetostatic-Field Equation in Two Dimensions
复制标题
二维非线性静磁场方程的数值解
DOI：
10.1016/0021-9991(67)90043-5
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发表时间：
1967
期刊：
影响因子：
--
通讯作者：
P. Concus
中科院分区：
文献类型：
--
作者：
P. Concus
本文讨论了导磁率随磁场变化的二维静磁场问题中二阶椭圆型准线性偏微分方程的数值解。一组非线性差分方程近似的原始微分方程的推导，并在解决一个测试问题，非线性逐次超松弛的方法相比，毫不逊色牛顿的方法和常用的方法的基础上的小磁场近似。第一种方法，如这里提出的，也可以用来数值求解类似的方程，如高原的问题或无旋可压缩流体流动。
The numerical solution of the second-order, elliptic, quasi-linear, partial differential equation arising in a two-dimensional magnetostatic-field problem, where the magnetic permeability varies with the field, is considered. A set of nonlinear difference equations approximating the original differential equation is derived, and in solving a test problem, the method of nonlinear successive overrelaxation compares favorably both to Newton's method and to a commonly used method based on a small-magnetic-field approximation. The first method, as here presented, could also be used to numerically solve similar equations, such as those for Plateau's problem or for irrotational compressible fluid flow.