低频涡流电磁场非自伴变分问题的研究

利用伴随算子和伴随场函数,建立了低频涡流电磁场中非自伴算子问题的一般变分描述.还分别应用最小作用原理和拉格朗日乘子法(广义变分原理)建立了低频涡流电磁场中非自伴算子问题的变分描述.将这3种变分方法与迦辽金法进行了比较.结果显示,上述所有方法均可获得与迦辽金法完全一致的结果.最后讨论了拉格朗日乘子的意义及其与伴随场函数的关系.

Study of non-self-adjoint variational problem in low-frequency eddy current electromagnetic field

A system procedure is proposed to derive the variational principle for a non self adjoint low frequency eddy current problem through adjoint operator and adjoint function. The other two approaches are proposed to derive the variational principle through the principle of least action and lagrange multipliers(the general variational principle). These three variational methods are compared with the Galerkin method. It is shown that all these procedures can get the same results as the Galerkin method. At last, the meaning of Lagrange multiplier and its relationship to adjoint function is discussed.