Discussion Forum

Hi,

As for your first question, I think the whole matrix equation system solved at last comes from both weak forms of Maxwell's equation and boundary conditions. As you may have noted the original weak form of Maxwell's equation corresponds to the one with negative sign, so if the one without negative sign is used, it's not consistent with the weak form of boundary conditions. I'm not sure, but this could be the reason.

The second one, you said the problem doesn't appear for 2D case, but I don't know how you introduce the coupling for 2D case. I suppose 3D case is the same.

Best
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Pu, ZHANG ??
Departamento de Física Teórica de la Materia Condensada,
Universidad Autónoma de Madrid,
Madrid, Spain.

Thanks Pu. You may be right, I will check the boundary constraints. For the 2D coupling case, you just need to consider the in-plane E, and as you mentioned, it has the same formulation expect that some terms reduce to zero.

Cordially,
Tony

I think the second question is about the coupling between the two equations. How do you do that for 2D case? I'm sorry I don't get it.

--
Pu, ZHANG ??
Departamento de Física Teórica de la Materia Condensada,
Universidad Autónoma de Madrid,
Madrid, Spain.

Hello Pu, for the coupling between two nano wires (2D case), you can use the following weak form for J,
beta^2*Jh1x+Jh2y)*test(Jh1x)-(omega0^2-1i*omega0*gamma)*Jh1*test(Jh1)-1i*omega0*epsilon0_const*omegap^2*emw.Ex*test(Jh1)
beta^2*Jh1x+Jh2y)*test(Jh2y)-(omega0^2-1i*omega0*gamma)*Jh2*test(Jh2)-1i*omega0*epsilon0_const*omegap^2*emw.Ey*test(Jh2)
and the boundary condition reduces to
nx*Jh1+ny*Jh2=0

And, for the Electric field, the user-defined weak form reduces to
-emw.curlEz*test(curlEz)+epsinf*emw.k0)^2*emw.Ex*test(emw.relEx)+emw.Ey*test(emw.relEy))-emw.iomega*mu0_const*(Jh1*test(emw.relEx)+Jh2*test(emw.relEy))

It works good for me.

Cordially,
Tony

Then the 3D should be the same way, just introduce Jh into the weak form of Maxwell's equation.

Yes, it should work. I'll double-check the configurations, there must be something wrong. Thanks anyway.

Good luck!

Oh, I just noticed that I was reading your recent paper a few days back which was just accepted by The Journal of Physical Chemistry. What a small world! And I appropriate that you guys cited our paper. Thanks. ^o^

Yes... That's why I'm somewhat familiar with this particular problem. Your paper is closely related to our work. Good to meet you here. Hope everything goes well!

Haha, you guys gave us a very interesting paper. Nice to meet you as well. Enjoy your day.

I checked the configurations and the coupled equations are good. It seem to me that the problem is the solver. The default iterative solver do not work since the two PDEs are highly coupled compared to the 2D one. If we use direct solvers, e.g., PARDISO, which requires much larger memory, we can get the desired results. Anyway, I believe there could be some iterative solvers suitable for this problem.

Cordially,
Tony