VectorHelmholtz Boundary question

Numerical methods and mathematical models of Elmer
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PhysicsOptics
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VectorHelmholtz Boundary question

Post by PhysicsOptics »

Hi there,

I'm trying to model light coupling from a waveguide into a microresonator. My first step to get acquainted with Elmer has been to go through "Using VectorHelmholtz module to model wave propagation in bent waveguide." This I've successfully done, however now I'm trying to understand the example better and modify it towards what I'm trying to do and I'm having difficulty finding some information understanding the Inport boundary condition:

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Boundary Condition 2
  Target Boundaries(1) = 1 
  Name = "Inport"
  Magnetic Boundary Load 2 = Variable Coordinate 1;Real MATC "-2*beta0*k0/kc*sin(kc*(tx+a/2))"
  Electric Robin Coefficient im = $ beta0
End
I understand Variable Coordinate 1 defines whether tx is x, y, or z (or whatever's defined in Model > Setup...) and that MATC allows you to use functions like sin(), but that part I'm not getting is what's really going on with Magnetic Boundary Load 2. The MATC equation looks like the magnetic field in a waveguide, but I don't know which component nor what MBL2 is defining. I read the model manual section on VectorHelmholtz to no avail, but perhaps I don't understand Robin boundaries very well.

Could someone explain what Magnetic Boundary Load does and what field profile across the boundary I'd expect to see? e.g. sinusoidal field for Hy(x), but the period doesn't look normalized to the width of the waveguide.

Cheers,
annier
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Re: VectorHelmholtz Boundary question

Post by annier »

Hi PhysicsOptics,
I don't know much about this solver. So, i am just describing general words related to the Magnetic Boundary Load i
Magnetic Boundary Load i referes to the load in direction i, i =1,2,3.

Thus,
Magnetic Boundary Load 1 refers to the load in normal/radial direction to the boundary considered.
Magnetic Boundary Load 2 refers to the load in tangential direction to the boundary
Magnetic Boundary Load 3 refers to the load in remaining direction in 3D to the boundary

The word "load" in the above keyword refers to the nodal force.

Yours Sincerely
Anil Kunwar
Anil Kunwar
Faculty of Mechanical Engineering, Silesian University of Technology, Gliwice
kataja
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Re: VectorHelmholtz Boundary question

Post by kataja »

Hi PhysicsOptics,

it's great to hear someone experimenting with this solver.

The tutorial goes through a model fed with TE_10 waveguide mode where the incoming electric field is "u_y ik/k_c sin(k_c (x+a/2))e^(i beta z)". The port feed is modeled with the Robin boundary condition described around Eq. (15.11) in the documentation (ElmerModelsManual.pdf pg. 94). The Robin boundary condition (15.5) is used to model scattering of EM waves when there is only one propagating waveform at the input/output ports.

When alpha = 0 in Eq. (15.5), the boundary condition (15.5) becomes the pure Neumann condition for the electric field and the left-hand side of Eq. (15.5) becomes "i omega n x B". Hence the name "magnetic boundary load".

The line

Code: Select all

Magnetic Boundary Load 2 = Variable Coordinate ...
in your example defines the y component of "g" (Eq. (15.5)). So in general MBL1, 2, 3 defines x,y,z components of "g" in Eq. (15.5).

Cheers,
Juhani
kataja
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Re: VectorHelmholtz Boundary question

Post by kataja »

I forgot to add that I'm referring to elmer models manual at http://www.nic.funet.fi/pub/sci/physics ... Manual.pdf
PhysicsOptics
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Re: VectorHelmholtz Boundary question

Post by PhysicsOptics »

Thank you both for the help! I'll return to the models manual and tutorial to examine things more closely and see if I have more questions after working through things further.
Elanid
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Re: VectorHelmholtz Boundary question

Post by Elanid »

Hello,

I've tried the wave-guide tutorial and when I looked at the geometry file I've noticed that the size of the inlet and outlet is 100um by 50um rather than 10cm and 5cm (when you open the file in FreeCAD for instance). That concerned me, because I thought that the port sizes were associated with a=10cm and b=5cm. Could someone please clarify whether or not there is either a typo in manual, or there is something to do with scaling in this model? I'm new to microwave modelling so I'm not too strong with the theory but the sizes of the model and the wavelength for 2.5GHz (about 12cm) really confused me in this tutorial.

Thank you, Elanid.
raback
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Re: VectorHelmholtz Boundary question

Post by raback »

Hi Elanid

Many CAD software use "mm" as the base unit. However, the information of the unit is not passed over so when Elmer reads it in usually scaling by 0.001 is needed. Now if your initial CAD seems to be in um then that probably means that Elmer interprets them as mm. Yuo can verify the mesh size in visualization. There wouldn't be room for a wave if the case was in um:s.

-Peter
Elanid
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Re: VectorHelmholtz Boundary question

Post by Elanid »

Hello Peter,

Thank You for the clarification, it helps. Though, I do wonder why not keep the scales the same? Every time I make an .stp file in FreeCad, in [um], then mesh it in Gmsh and transfer it to Elmer, I would have to automatically assume that my new model 1000 times bigger? Looking at the Model Summary and the ParaView results I can see the discrepancy between my original CAD model, but I didn't think that such scaling would be applied to all the models :shock: . I've looked at the GUITutorial document again and noticed that this fact is actually mentioned in the "Capacitance of the Perforated Plate" but I really had no idea that this applies to all the models. I guess, I will have to keep this in mind until I find/learn how to make it easier.

Thanks nonetheless, Daniel.
raback
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Re: VectorHelmholtz Boundary question

Post by raback »

Hi Daniel

Well, I would blame the CAD software for using mm's as base unit. It is not really in accordance with SI standards ;-)

-Peter
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