电动力学电磁场边值问题的广义变分原理

Generalized Variational Principles for Boundary Value Problem of Electromagnetic Field in Electrodynamics

给出了线性各项异性电磁场边值问题的广义虚功原理表达式,运用钱伟长教授提出的方法建立了该问题的广义变分原理,可直接反映该问题的全部特征,即4个Maxwell方程、2个场强-位势方程、2个本构方程和8个边界条件.继而导出了一族有先决条件的广义变分原理.作为例证,导出了两个退化形式的广义变分原理,和已知的广义变分原理等价.此外还导出了两个修正的广义变分原理,可为该问题提供杂交有限元模型.建立的各广义变分原理可为电磁场边值问题的有限元应用提供更为完善的理论基础.

The expression of the generalized principle of virtual work for the boundary value problem of linear and anisotropic electromagnetic field was given. Using Prof. W. Z. Chien＇ s method, a pair of generalized variational principles （GVPs） were established, which could directly lead to all four Maxwell equations, two intensity-potential equations, two constitutive equa- tions and eight boundary conditions. A family of constrained variational principles was deduced sequentially. As the additional verifications, two degenerated forms were obtained, which were equivalent to two known variational principles. Two modified GVPs were given to provide the hybrid finite element models for the present problem. A more complete theoretical foundation for the finite element applications was provided for the discussed problem.