UPML implementation. Write a code to implement the UPML in a 2D TE FDTD simulation, using the same parameters as Problem 9.3 above.
(a) Excite the simulation at a frequency of 600 MHz, and compare the propagating waves along the x and y axes as in Figure 9.5. How do the reflections here compare to those in the split-field method? How do the simulation times compare?
(b) Excite a sinusoidal wave with f0 = 100 MHz. The PML is now in the near field of the source; How well does the PML perform?
Problem 9.3
Comparing the PML grading. Write a 2D FDTD simulation with the split- field PML, similar to the example in Section 9.2.3. Use the same parameters as the example, i.e., ?x = ?y = 5 cm in a space of 6 × 3 m. Excite a sinusoidal source at the center of the space with f0 = 600 MHz, and grade the PML with a polynomial of order 4 and R(0) = 10-6. Measure the reflections by comparing the field amplitude at a particular snapshot in time at a location just inside the PML.
(a) Modify the parameters of the polynomial grading, in particular the order m, between 3 and 4 (it need not be an integer). How does this affect the reflections? What m gives the lowest reflections?
(b) Now implement the PML with a geometric grading, choosing appropriate parameters g and σx,0 according to Equations (9.35). Compare the results to the polynomial grading. Experiment with the effect of the parameter g on the PML performance.
