Now I am using UPML for waveguide termination due to the simplicity and uniformity in the equations that describe it. But there is some cost, namely a larger number of operations and double the number of field components (main and auxillary). Moreover, there is a limitation regarding the wave impendance that has to be known before simulation. So CPML comes to mind for a better and more robust solution.
What are, according your to your opinion, the pros and cons about these two types of PML? In CPML is it necessary to know, before the simulation, the wave impendance? How is the conductivity scaled inside the absorbing layer? Moreover, in UPML we have to know wave impendance before simulation (in order to be used in the conductivity scaling). But what if the excitation can't tell us much information about the wave that it will grow and/or propagate inside the structure?
I have written a home-made FDTD code which first included UPML, but later it was expanded by adding CPML to terminate dispersive materials inside the boundary conditions. I based the code on this paper by Roden and Gedney: Microwave and Optical Technology Letters 27, 334 (2000). While it has been a while and I dont remember exactly everything, I looked into my code and found that I needed used twice the arrays to store CPML data than the UPML data. And I remember that indeed, my CPML simulations used more memory than the equivalent UPML, obviously without dispersive materials inside the PML layer.
For UPML you basically need, in additon to material data, to store one auxillary component per field component, which you calculate from the fields of the other component, follwed by an update of the main component (e.g. H->D->E). My code was a body-of-revolution approach so the number may vary, but to calculate Er in the UPML i neede to make 6 multiplications, 5 additions/subtractions, and one division. (both Er and Dr).
For CPML, as far as I read in that paper and my notebook, one needs two auxillary components for each field and to update e.g. Er I needed 7 multiplications, 8 additions/subtractions, and 2 divisions.
The divisions are because of the body-of-revolution scheme.
Regarding the conductivity, I dont see a large difference in how I treated the two absorbers, except that, of course, CPML was used to terminate dispersive materials so its parameters (sigma and kappa) both had to be adjusted to compensate for the dispersive permittivity inside the CPML. Used the same grading scheme for UPML and CPML and it worked fine.
The CPML is generally accepted to be better and more efficient. I am not sure it is better, but perhaps more efficient. You can implement the UPML without the auxilliary parameters. I describe that in my lecture series that you get to here:
http://emlab.utep.edu/ee5390fdtd.htm
Thank you all for the answers. I don't think, till now, to need double the number of arrays for CPML, because additional matrices are needed only inside the PML region, unlike UPML where auxiliary fields are needed throughout the simulation
One does not need auxiliary equations inside the simulation volume. One can do that to have "a single set of equations" for the whole simulation volume, but outside of the "true" UPML the sigma/kappa parameters are (should be) such that no absorption takes place. Another approach is to split the domain into one where only the E/H fields are updated and the auxiliary fields are not (simulation volume) and the border where the UPML is - there both E/H and auxiliary D/B fields are updated. That is how I coded my soft and it works.
- Badges
- Science topic
- Similar topics
- Physical Sciences
- Waves