Frequency response of UPML and CPML. Implement the UPML and CPML separately in the simple square 2D simulation of Problem 4.5. Excite the simulations with the derivative of a Gaussian source five time steps wide. Measure the reflection coefficient as a function of frequency at locations on the PML boundary corresponding to incident angles of 0, 15, 30, and 45 degrees. Compare the UPML and CPML reflections. Which PML performs better at low frequencies, and why?
Problem 4.5
D rectangular resonator. Write a 3D FDTD algorithm using Equations (4.18) and (4.19) in a 100 × 50 × 20 m box with perfectly conducting walls. Use
(a) Excite this resonator with a sinusoidal z line source at the bottom center of the space with a frequency of 1.5 MHz. Make this source 10 grid cells long in z. Plot the magnitude of the field in the plane perpendicular to the source excitation, and in a plane parallel to the excitation. What do you notice about the field evolution with time?
(b) Repeat part (a), but at frequencies of 3 MHz and 10 MHz. Compare to part (a).
(c) This time, excite the box with the derivative of a Gaussian source that has a pulsewidth τ equal to five time steps. Add the source to the update equations as a current source so that it does not interfere with reflected waves. Find the resonance frequencies for this resonator and compare to the theoretical resonances, which for the TEmnp and TMmnp modes are given by [3]:
for a resonator with dimensions a, b, and d.