A High-Order 2-D CPITD Method for Electrically Large Waveguide Analysis

Based on the fourth-order finite difference (FD) scheme, a modified compact two dimensional precise integration time domain (CPITD) method, called CPITD(4), is proposed to mitigate the numerical dispersion errors of the CPITD algorithm when modeling electrically large and longitudinally invariant wave-guiding structures. Both the stability condition and the dispersion equation of the CPITD(4) method are derived analytically. It is found that the dispersion error of the CPITD(4) method is much smaller than that of the CPITD method. In particular, it should be pointed out that the CPITD(4) method can improve the performance of the CPITD method when
$\beta_{z}/\beta$
leaves away from 1. Numerical experiments of typical waveguide structures validate and verify that the CPITD(4) method can decrease the calculated error without increasing the memory requirement and the execution time for all the cases.