Accuracy of results / microwave waveguide

[Tom]

Dear all,

I would like to use elmer for the simulation of passive HF components. To check the accuracy of elmers‘s results, I compared the calculated return loss (S11) of different solvers for a bandpass filter design published by Zhai et al. The same meshes were used for all solvers having a maximum element length of a/8 or a/16, respectively, with a being the waveguide width of 7.112 mm.

From figure 1 it can be seen that the obtained results, using linear elements, are similar regardless which solver was used. But in relation to the reference solution, the pass band is shifted towards higher frequencies. Using quadratic or cubic elements with the commercial solver yielded much better results (figure 2).

So, my question is: Are higher-order elements are supported by elmer and if yes, how do I have to modify my sif file accordingly?

Tom

[mzenker]

Hi,

I have never used higher order elements myself. However, you can have a look at Appendix E of the Solver Manual to get information on how they are supported in Elmer. AFAIK you will first have to build your mesh with higher order elements, so depending on the mesher you use you will have to find out how to do it. Both Salomé and gmsh should be able to build higher order meshes.

HTH,
Matthias

[raback]

Hi Tom

I guess you're using a solver with Hcurl conforming elements? Luckily they are available also as quadratic (for all element shapes). Say "Quadratic Approximation = Logical True" in solver section.

-Peter

[Tom]

Dear Matthias, dear Peter!

Thanks a lot for your hints. I added the lines "Quadratic Approximation = Logical True" and "Use Piola Transform = Logical True" to my sif file. Then I changed the element order by creating quadratic elements a) in Salome, b) in Gmsh, and c) with elmergrid during the conversation. For all three cases I got the error message

Code: Select all

ERROR:: PElementBase::TetraNodalPBasis: Unknown node for tetrahedron

The solver I used is the VectorHelmholtzSolver.

Tom

[raback]

Hi Tom

The VectorHelmholtz solver does not use nodal finite element. Hence there is no use in defining quadratic nodal elemenets. The Hcurl conforming elements automatically apply sufficient number of dofs on each edge, face and inside element to obtain the the appropriate basis function (the number of dofs is 12 for tets, 31 for pyramid, 36 for prisms, and 54 for hexahedrons). Because the creation is fully internal there is an additional keyword.

Now for the AVsolver the V uses the nodal basis function and therefore the background mesh has an effect to the solution. You can there basically combine quadratic Hcurl elements with either linear or quadratic nodal elements.

All this being said, I don't know what the problem. Perhaps you can try out with linear background mesh. At least the VectorHelmholtzWaveguide test case runs without problems with quadratic elements taking ~30 times more time than the linear elements. So the quadratic elements are rather expensive but may still provide better accuracy with the same cost using a coarser mesh.

-Peter

[Tom]

Hi Peter,

I can confirm that the waveguide test cases run using quadratic elements (and it seems also my model does) with a current version of Elmer. Unfortunately the 8.2 windows version is outdated; will there be current binaries in the (near) future?

Tom

[mzenker]

Hi,

you can find version 8.3 and nightly builds for windows here: http://www.nic.funet.fi/pub/sci/physics ... n/windows/

@Elmer team: The link at https://www.csc.fi/web/elmer/binaries would deserve an update...

HTH,
Matthias

[Tom]

Hi Matthias!

Great -- thanks for the link ...

Tom

[Tom]

Dear all,

For the sake of completeness a comparison between linear and quadratic elements is shown in the figure below. The computation times were:

• a/8 linear: 10.6 mins

• a/8 quadratic: 5.8 days

• a/16 linear: 1.1 days

• a/20 linear: 5.6 days

For my application I would prefer a finer mesh and linear elements than a coarser and quadratic elements ...

Tom

[raback]

Hi

The 2nd order results do not look too good. Are you sure it converged well?

Maybe you could share your case. It would be interesting to study the convergence behavior in more detail.

-Peter