[Getdp] Why does Form 1 converge much slower than Form 1P on this problem?

[Ningfeng HUANG]

Dear all,

Currently I am trying to solve a very simple 2D electromagnetic problem
with GetDP, which is the transmission of plane wave through a dielectric
slab. I attached the simulation configuration and the result as a PDF
document with this mail.

It is a slight modification from the waveguide example on OneLab website. A
high index slab (n=3.5) with thickness T is inserted in the middle of the
simulation region. The upper and lower boundaries are changed from PEC to
periodic to represent the infinity slab structure. The mode on port 1 is
changed to plane wave. I simulated this structure to get the transmission
spectra (S21) in two different ways with different polarizations:

1.s-polarization: the electric field is perpendicular to the 2D plane (Ez).
The simulation is in Form 1P.

2.p-polarization: the electric field is parallel to the 2D plane (Ey). The
simulation is in Form 1.

In principle, these two approaches represent the same configuration, which
is the infinitely extended slab with the normal incident light. However,
Form 1P converges much better than the Form 1. The result is shown in the
PDF document. The analytical result from transfer-matrix method is also
shown for reference. For s-polarization and Form 1P, all curves with
different resolutions are overlap with each other and match well with the
analytical result even with only 3 grid points per wavelength. However, for
p-polarization and Form 1, there is a systematic shift to the higher
frequency (lower wavelength) when the resolution is reduced. Even with 7
grids per wavelength, there is a large discrepancy to the analytical
result.


I wonder why there is a huge difference between Form 1P and Form 1 and
whether I can modify my code in Form 1 to have the similar accuracy as Form
1P. It would be nice that I have similar accuracy with Form 1. My final
goal is to simulate 3D structures (in Form 1P) and this shift is also
observed in my 3D simulations.

Here is some thoughts from my intuition. The blue shift of the spectra can
be caused by the effectively thinning of the high index material. I suspect
that I missed defining the proper basis for the surface such that the grid
at the interface is not considered as the high index material. The lower
the resolution, the larger the surface grid, thus the thinner the effective
slab thickness.

I attached my code for both Form 1 and Form 1P with this mail and matlab
(octave) scripts to run the batch simulation and plot the result. I
appreciate any kind of comments. I really want to know whether this is the
bug in my (OneLab) code, or bug in GetDP or just fundamental limitation in
the finite-element method.

Regards,

Peter
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