电磁场的一阶方程组表述及其最小二乘有限元法

The First Order Systen of Pateial Differential Equations for Electro—Magnetic Fields and It's Least—Squares Finite Element Method

本文讨论了电磁场最小二乘有限元系统。将磁场强度H和电流密度做为未知量,我们描述了依赖时间的三维麦克斯韦方程,然后将它们简化为三维和二维稳态问题。基于一阶偏微分方程体系,将最小二乘法应用于有限元法。H和两者的收敛速度实现同阶优化。该方法为发展计算机程序提供了一种易行途径。

Aleaxt—squares finite element approximation scheme for electro—magnetic fields in two and three dimensional doain is discussed. Considering the maguetic field strength H and the vector of the current density (?) as unknowns, we describe the Maxwell's equation as a time—deoent form in three dimensions, then reduce it into three and two dimensional steady problems. Based on the first order system of partial differential equations, the least—square method is applied to the fintie element method. The rates of convergence for both H and (?) and achieve optimal order. This method creates an easy way to develop computer software.