Meshing wire antenna - optimal size and tradeoff

Altair Forum User

I would like to mesh a half wavelength dipole, and the user manual does give some meshing guidelines on setting radius and segment length. I have set my radius to lambda/2000. I was wondering what would happen if I make the segment length smaller and smaller. Does it give me some erroneous result or the finer meshing would give me better result. Why?  

 

On the other hand what if I make my segment length greater than 0.1*lambda? Is there an optimal tradeoff here? I would appreciate if someone can give a brief explanation here.  

 

Thanks

JIF

Hello Badheka,

 

Lets start with the effect of the segment radius. For the segment radius, I would suggest that you use the radius that you need to simulate - don't make the wire infinitely thin thinking the answer is more correct for some reason. If the ratio of the radius to length become to extreme, then it is time to use a cylinder (triangles) instead of segments. What I mean by 'extreme' is that the MoM segments uses a thin wire model and the approximation becomes better the longer the segment is relative to its radius (or rather, the smaller the radius for a given segment length). You can get good results even with relatively fat segments (5 to 1 ratio). FEKO will give a warning and eventually an error if the segments are too think compared to the segment length.

 

Your main question was about the effect of creating too long or too short segments. Obviously if you make the segments too short, the segment length to radius ratio will start violating the thin wire approximation and your results will become less accurate (see the comments in the previous paragraph). Also, increasing the number of segments by making them shorter increases the size of the model since more unknowns need to be taken into account.

 

The CEM model is solved by breaking the model into small pieces, associating basis functions on the elements and then solving the unknown coefficients associated with the basis functions. If you mesh too coarsely (coarser than lambda/10), the results would become less accurate and at some point it would simply be incorrect. FEKO will give a warning and later an error when elements are meshed too coarsely. If you mesh finer and finer, the answer generally becomes more and more accurate (converge to the exact answer). There is a point where meshing finer could start diverging again. The exact behaviour depends on the solution method (MoM, FEM, etc.) and the basis functions that are being used.

 

The comments above are very general and apply to various methods and elements (segments, triangles, tetrahedra, etc.). How do you know how fine to mesh a model? The best is to have a good starting point and the general rules are provided in the FEKO manual. It is good practice to do a mesh convergence test - the basic idea is to refine the mesh until the results converge (stop changing). Another approach is to calculate error estimates on the elements and instead of refining the entire mesh, only refine the mesh in the areas where the errors are estimated to be the largest and again continue this process until the results converge.

 

Using the suggestions for meshing (standard and fine) should give accurate results in most cases. The coarse mesh setting is expected to give less accurate results, but faster simulations due to the model begin smaller. The optimal point depends on your model and the accuracy that you need from the simulation.

Altair Forum User

Thank you for the explanation Jif. I understand that if we use less number of basis functions (higher segment length) then we won't be able to accurately represent current distribution on the wire. Thus leading to higher relative error in result. On the other hand, if we use more number of basis functions (the segment length is quite less- say comparable to radius), we will again have higher relative error - this one is due to thin-wire approximation. 

 

I know the user manual give you the range of segment length and radius (and hence the number of basis functions) to use for low relative error. However I am wondering if there is an optimal number of basis function (or optimal segment length) that one should use for say-lambda/2 dipole (of a given radius), to get the lowest possible error? 

 

Thanks