# Polyline Refinement

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I would be grateful if you can explain in more detail how to use Polyline Refinement expanding what is already in the UserManual.pdf.

Consider the Yagi_Pattern_Optimisation.cfx example from the ExampleGuide. Let's say that I want to know how the Yagi performs when the elements have different shapes (bent, folded dipole, etc).

To start, I replace the straight Active Element with a Polyline. After recalculating, all results are the same as before as one would expect. Now insert two corners in the Active Element, for example, at N: L1*lambda/2 and N: -L1*lambda/2, so the Active Element has 3 sections with the Port in the middle. This doesn't change the physical problem, but recalculation shows a significant difference in the impedance magnitude compared to the original model using a standard mesh.

Ideally I would like to refine only the mesh of the Active Element. If I use Polyline Refinement do I have to copy the same Corners that I defined for the Active Element? What values should I set for the Radius and Mesh Size in this context? How can I guess what is a reasonable Mesh Size?

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Hello FEKOFan,

10 hours ago, FEKOFan said:

To start, I replace the straight Active Element with a Polyline. After recalculating, all results are the same as before as one would expect. Now insert two corners in the Active Element, for example, at N: L1*lambda/2 and N: -L1*lambda/2, so the Active Element has 3 sections with the Port in the middle. This doesn't change the physical problem, but recalculation shows a significant difference in the impedance magnitude compared to the original model using a standard mesh.

I'm not sure I understand and without seeing results or the model, appreciating the significant difference is difficult. I assume that you suspect that the change in the mesh is responsible for the change in the results. Since you are using a polyline for the wire, take into account that every node in the polyline will result in a mesh vertex. Thus, be careful to not place the nodes too close together (this can cause problems if your segments become "fat" and the thin line approximation is violated).

10 hours ago, FEKOFan said:

Ideally I would like to refine only the mesh of the Active Element. If I use Polyline Refinement do I have to copy the same Corners that I defined for the Active Element?

If you want to refine the active element, refine it. This is easily done by setting a local mesh size on the wires of the active element. I'm not sure why you want to use the polyline refinement.

10 hours ago, FEKOFan said:

What values should I set for the Radius and Mesh Size in this context?

If you do want to use polyline refinement instead of local mesh settings, you don't need to have the same "corners" for the refinement. The poly line refinement simply defines a region (tube) where the mesh will be refined. You would pick a radius that is big enough to enclose the elements that should be refined and exclude the elements that should not. You can use the automatic mesh settings as a guide (see the manual), but assuming that you want a fine mesh, start with lambda/20. The best would be to do a mesh convergence test - refine the mesh until the results stop changing much.

Note that since you are working with wires, you do have a lower limit for the mesh segment length that is determined by the radius of the segments. The segments use a thin wire formulation and thus the segment should be much longer than its diameter. I would use segments that are at least 5 times longer than its diameter, but 10 times or more would improve the approximation.

10 hours ago, FEKOFan said:

How can I guess what is a reasonable Mesh Size?

This is a strange question in my opinion. You seem to feel that the automatic meshing is not good enough, but you don't know what mesh settings to use. The only answer for this is to do a mesh convergence study.

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Thank you very much for your replies, they are very helpful. The attached files should make clear what I meant. The model files are as follows:

1. Yagi_Pattern_Optimisation-0.cfx is the same as the original example delivered with the software, but I converted the active element into a Polyline. This makes no difference to the results of the calculation.

2. In Yagi_Pattern_Optimisation.cfx, I inserted two corners into the Polyline that defines the active element. No change to the physical problem, but the Impedance magnitude is different to the previous case when using a Standard Mesh. I need these corners because my plan is to bend the active element, but first I want to double check that I don't get changes in results because of numerical issues.

3. In Yagi_Pattern_Optimisation-1.cfx I added local mesh size of lambda/20 to the three wires that form the active element polyline. Different results again as shown in the ImpMag.tif file.

If I use a Fine Mesh for the whole structure, the Impedance Magnitude of models in 1. and 2. is the same, but how can I be confident that convergence has been achieved? I tried Create Mesh > Mesh Size : Custom to define a mesh smaller than Fine, but meshing time seemed to take forever. Further advice would be much appreciated.

Yagi_Pattern_Optimisation-1.cfx

Yagi_Pattern_Optimisation.cfx

Yagi_Pattern_Optimisation-0.cfx

ImpMag.tif

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Looking at ImpMag.tif as a check for mesh convergence, there are a few things that I would do differently.

1. Firstly, run the simulation over a wider frequency range. Running the simulation at a single frequency can be very deceiving when the model is close to resonance and the imput impedance potentially changes fast. With a slight frequency shift (less than 2%), the difference in the impedance could be considerable, but still converged. Your simulation is at 1GHz with a bandwidth of 2 MHz or 0.2% (basically nothing).
2. When performing a mesh convergence study, start of by simply refining the entire model (if you can afford it). The alternative is to be selective about the refinement areas (at ports, where elements are close (small separation) or any other critical parts in the model).

Below is an image where I took your Yagi model (middle one in the comment above) and simulated it with a mesh of lambda/8 (FEKO coarse), lambda/12 (FEKO standard), lambda/16, lambda/20, lambda/24 (almost FEKO fine), lambda/28, lambda/32, lambda/36 and lambda/40.

As you can see,  the frequency shift is around 2% or less even for coarse and standard mesh (w.r.t. a very fine mesh of lambda/40). For most engineering problems, that would be considered good (probably better than you would be able to build or measure for this Yagi). The difference (frequency shift) for lamda/24 (close to FEKO fine of lambda/25) w.r.t. lambda/40 is very small. As you can see, a mesh of around lambda/16 would be considered to be converged for this model in my opinion.