CPML or UPML in FDTD method for a waveguide simulation in high frequencies-questions

[peponas]

Since 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 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 know before simulation. So CPML comes to mind for a better and more robust solution.
What are, according your to your opinion, pros and cons about these two types of PML. In CPML is there nessecary to know ,before the simulation, the wave impendance. And how the conductivity is 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 many information about the wave that it will be grown and/or propagate inside the structure.

Too many questions, but thank you in advance!

 

[wavenology]

Your terms are confusing, Uni-axial PML (UPML) (By Stephen Gedney) should be compared against split-field PML (By JP Berenger), and it has been proved that the two are essentially equivalent (Forgot the paper here, sorry). Both Uniaxial PML and Split field PML can have original version and the Complex-Frequency shifted version. the PML and CFS-PML does have difference CFS did a much better job on absorbing evanescent waves. In waveguide case, this is very obvious. On PML parameters selection, it is based on experienced formula since such PML is artificially created thus there is no strict laws on how to choose params, but there are optimal choices, check the following paper or Allen's FDTD book, it talks very clear about how to determine PML parameters. basically, you can not choose conductivity too high since it will make FDTD cell properties jump too fast and will introduce error as reflection.


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**broken link removed**

 

[peponas]

Thank you for the answer. I have already read Taflove's chapter about PML but these characteristics confuse me. One more question...about kappa, in strech coordination formulation. What is the maximum value that can be assigned to it? Same question about alpha in CPML formulation. What is the maximum value? Any empirical relation?

 

[wavenology]

kappa is used to "squeeze the wave", kappa=1 means the wave will propagate inside the PML without any "squeezing" effect. Kappa can be as large as to 10 but this is related to other parameters, such as power scaling, sigma and others. General sense is if kappa is too large, you have to scale kappa from 1 to kappa_max this will cause stiff jump between FDTD cells and will cause reflection, thus kappa=1 but no larger than 10 is in my personal preference, however, again I need to emphasize its related to your choices of other parameters.

As to alpha, it should be a small number, the true meaning of alpha is still on-going research in my personal point of view.