General formulation of an efficient implicit BOR-FDTD method based on the locally one-dimensional scheme

A complete set of equations of the LOD-BOR-FDTD has been derived for the analysis of not only fundamental but also higher-order modes with respect to the rotational direction. The number of arithmetic operation is significantly reduced in comparison with the ADI counterpart. Numerical results of a circular cavity resonator show that the resonance frequency is efficiently obtained particularly for higher-order modes, while maintaining the accuracy comparable to the ADI-BOR-FDTD. The application of the LOD scheme to cylindrical coordinates is under investigation.