This article presents the numerical eigensolver to find the resonant frequencies of 3-D closed cavity resonators filled with both electric and magnetic lossy, anisotropic media. By introducing a dummy variable with zero value in the 3-D linear vector Maxwell eigenvalue problem for the electric field, we enforce the divergence-free condition for electric flux density in a weak sense. In addition, by introducing a dummy variable with constant value in the 3-D linear vector Maxwell eigenvalue problem for the magnetic field, we enforce the divergence-free condition for magnetic flux density in a weak sense. Moreover, it is theoretically proved that the novel method of introducing dummy variables can be free of all the spurious modes in solving eigenmodes of the 3-D closed cavity problem. Numerical experiments show that the numerical eigensolver supported by this article can eliminate all the spurious modes, including spurious dc modes.

翻译：此篇文章展示了数字 egensolt 以查找 3 - D 闭闭腔共振频率 3 - D 闭闭闭腔共振频率, 填充电磁失落的电磁介质 。 通过引入电场3 - D 线性矢量 Maxwell 双向二次数值问题中零值的模拟变量, 我们强制实施电磁通量密度的无差异状态 。 此外, 在理论上证明引入假变量的新方法可以在解决 3 - D 闭闭闭闭腔问题的双向模式中排除所有虚假模式 。 数值实验显示, 本条支持的数字 egensoster 能够消除所有虚假模式, 包括虚假的 dc 模式 。