I'm trying to develop a 3D Cylindrical FDTD code with CPML boundary conditions regarding a simulation of a waveguide. So, CPML will be located at the far end of the waveguide along the z-axis (propagation axis). The Z coordinate should be stretched also and pml conductivity should be scaled according to a numeric profile. Usual FDTD equations include the term (2epsilon-sigma*dt)/(2epsilon+sigma*dt) regarding conductivity inside the medium. But CPML equations also use the term conductivity to describe the scaled quantity used in them. With only z stretching, only rho and phi components' PML equations use the scaled conductivity (in this case z-component of coductivity via the convolution terms). The question is, should I use the z-component of the scaled conductivity in the update equations of Ez component, or it should be used ONLY for the stretched components' equations (namely Erho and Ephi in this case)?
Thanks for the answers. I know these coefficients. But my question is a little bit different. Does conductivity used in PML (ie σi) be used in normal FDTD relations in CPML (not the Ψ components)
Your normal media conductivity has nothing to do with the PML one. Especially in a stretched space formulation this is much easier to see why. The PML "conductivity" is just a loss term that is used to attenuate the right components in the PML. For a correction based PML implementation you can try this http://dx.doi.org/10.1109/TAP.2011.2180344
but I have never used it in cylindrical coordinates and obviously as I have developed it I should not be the one to promote it ... Good luck.
Dear Antonios
I think you are right. But any of the books (such as Taflove's one) seperates the conductivities (pml and media) resulting in a confusion like mine
Dimitri, look at my 2000 SIAM paper on the unsplit PML in cylindrical coords. If you still have questions, send me an e-mail.
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