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Hello Sunny Liu

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Hi,
I want to use COMSOL 4.3a to simulate the reflection and transmission spectra of a free standing Ag film with periodic hole arrays. There is an error " Failed to find a solution for the initial parameter. Singular matrix. ....."(Please find the detail as the attachment).
I have attached the paper I want to simulated, and the .mph file. Could you help me check about it?
Thank you very much!

Hi,
Have you solved your problem?
I have taken a look at your model, and could hardly find a problem in your model setting. The error must be subtle.
If you have understood the reason of errors, hope you can share the experience with me.

--
good enough.

Happy 2014, Sunny!

Here are several things I would do to modify your model:

First, the error given stems from Port 2. You have listed no propagation constant. I'm guessing you want it as abs(k3z). You should not be getting the error for emw.S2x after that.

Second, you want to simulate a periodic structure at normal incidence, but your BCs are ALL PECs. With a field as you have that goes as H[x,z] = Hy = H0[x]e^(-j*abs(kz)*z), then your setup has symmetric BCs on all boundaries. Instead, you want a PMC on the boundaries parallel to your H-field (x) and PEC on boundaries normal to the field (y). Reverse for an electric field.

Third, you list "dielectric loss" as your wave equation model, yet you list ni_Ag and nr_Ag as your material inputs, rather than the permittivities. And if you have n/k for all materials, why not just use one wave equation?

Fourth, you might want to adjust your mesh. The port probably does not need to be 10*lambda0 long, nor does the mesh probably need to be as fine uniformly along the port. The mesh should be fine near the air/Ag boundaries, then expand to larger meshes farther away from the port, where the fields are not evanescent and not rapidly varying.

Last, although it seems you want to go to off-normal eventually, for this initial verification of the model, why don't you reduce it to a 1/4 model and use symmetry? At normal incidence, you have both geometrical AND electromagnetic symmetries; however, at off-normal, there are no EM symmetries, so you'd have to use the full model. Should save you some time.

Hope this helps--happy COMSOLing!

-Bryan