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This article presents the numerical eigensolver to find the resonantfrequencies of 3-D closed cavity resonators filled with both electric andmagnetic lossy, anisotropic media. By introducing a dummy variable with zerovalue in the 3-D linear vector Maxwell eigenvalue problem for the electricfield, we enforce the divergence-free condition for electric flux density in aweak sense. In addition, by introducing a dummy variable with constant value inthe 3-D linear vector Maxwell eigenvalue problem for the magnetic field, weenforce the divergence-free condition for magnetic flux density in a weaksense. Moreover, it is theoretically proved that the novel method ofintroducing dummy variables can be free of all the spurious modes in solvingeigenmodes of the 3-D closed cavity problem. Numerical experiments show thatthe numerical eigensolver supported by this article can eliminate all thespurious modes, including spurious dc modes.

Numerical Eigensolver for Solving Eigenmodes of Cavity Resonators Filled With both Electric and Magnetic Lossy, Anisotropic Media