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

[Ningfeng HUANG]

Hi Michael.

Thanks so much. It works!

I stuck at this issue for about one month.

Regards,

Peter

On Mon, Jul 27, 2015 at 9:32 AM, <michael.asam at infineon.com> wrote:

>  Hi Peter,
>
>
>
> the different result accuracy is due to the different polynomial order of
> the basis functions.
>
> Let’s look at the lowest order basis functions:
>
>
>
> Form 1P represents a field which is pointing only in z-direction. This (E)
> field
>
> is interpolated linearly between the nodes -> 1st order basis function.
>
>
>
> In contrast form 1 represents a field in the x-y plane for 2D-problems.
> The lowest order basis function
>
> has a constant tangential vector component along each edge (order: 0)
> which is interpolated
>
> linearly to the element interior (order: 1). Therefore it is usually said
> to be of “order 0.5”.
>
> To have the same polynomial order along each edge as in form 1P, you need
> a form 1 basis function
>
> which is one order higher.
>
> The same is true in your case. So just add one additional order to your
> form 1 function space (BF_Edge_3F):
>
>
>
>
>
> FunctionSpace {
>
>     { Name eSpace ; Type Form1 ;
>
>       BasisFunction {
>
>         { Name sn  ; NameOfCoef en  ; Function BF_Edge     ; Support
> TotAll ; Entity EdgesOf[All] ; }
>
>         { Name sn2 ; NameOfCoef en2 ; Function BF_Edge_2E  ; Support
> TotAll ; Entity EdgesOf[All] ; }
>
>         { Name sn3a; NameOfCoef en3a; Function BF_Edge_3F_a; Support
> TotAll ; Entity FacetsOf[All] ; }
>
>         { Name sn3b; NameOfCoef en3b; Function BF_Edge_3F_b; Support
> TotAll ; Entity FacetsOf[All] ; }
>
>         { Name sn3c; NameOfCoef en3c; Function BF_Edge_3F_c; Support
> TotAll ; Entity FacetsOf[All] ; }
>
>       }
>
>       Constraint {
>
>         { NameOfCoef en   ; EntityType EdgesOf  ; NameOfConstraint
> eConstraint ; }
>
>         { NameOfCoef en2  ; EntityType EdgesOf  ; NameOfConstraint
> eConstraint ; }
>
>         { NameOfCoef en3a ; EntityType FacetsOf ; NameOfConstraint
> eConstraint ; }
>
>         { NameOfCoef en3b ; EntityType FacetsOf ; NameOfConstraint
> eConstraint ; }
>
>         { NameOfCoef en3c ; EntityType FacetsOf ; NameOfConstraint
> eConstraint ; }
>
>       }
>
>     }
>
> }
>
>
>
>
>
> Cheers,
>
> Michael
>
>
>
>
>
>
>
> *From:* getdp [mailto:getdp-bounces at ace20.montefiore.ulg.ac.be] *On
> Behalf Of *Ningfeng HUANG
> *Sent:* Friday, July 24, 2015 1:50 AM
> *To:* getdp at geuz.org
> *Subject:* [Getdp] Why does Form 1 converge much slower than Form 1P on
> this problem?
>
>
>
> 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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