FEM Vs MoM -- a discussion

[arunkumar]

fem compared to mom planar

FEM and MoM are the two major numerical techniques that todays EM Modeling rely on. I know that the time taken by both of these numerical techniques is high & consumes considerable memory as well. By and large, the results produced by FEM are much better when compared experimentally than the those produced by MoM. I need a couple of real time facts/reasons that prove FEM (finite element modeling) performs better than MoM (method of moments).

 

[rautio]

advantages of numerical electromagnetic code

Hi Arunkumar -- FEM is a volume meshing approach. MoM is usually a surface meshing approach. Volume meshing is more appropriate for most 3-D arbitrary geometries. MoM is often specialized to planar geometries and is more appropriate for most planar geometries.

In most (but not quite all) cases, I consider application of any volume meshing technique to planar circuits to be an out-and-out mistake, a serious error in engineering judgement.

The exact same thing is true (for many cases) in reverse, if you apply a planar MoM tool to 3-D arbitrary structures. (You don't say what kind of structure you are trying to analyze.)

It is OK to be skeptical about my statements above. However, I also hope you will choose to be skeptical about whomever made the blanket statement that FEM is better than MoM.

Which is better is easy to test for yourself. To see that MoM is better, choose a simple planar structure, for example, a length of transmission line. If you use stripline (ground-dielectric-transmission line-dielectric-ground), there is even an exact answer. Analyze it in any volume mesher, and in any surface mesher (you can get a free surface mesher from my company www.sonnetsoftware.com, just download it, there is no time-out). Set roughly the same size meshing in both tools. The MoM tool will require, for typical mesh sizes, well under one second for such a simple problem. Depending on your selected geometry, the volume mesher will take 100x or even 1000x longer to analyze for the same meshing density.

Now, look at the current distribution. The MoM current distribution will typically be smooth, with strong current on all sharp edges, and have a healthy physical appearance. Then check the volume meshing current distribution. If it looks ragged and lacks strong high current on sharp edges (required by Maxwell's equations), you need to refine the solution and/or meshing even further. This makes the analysis go even longer.

If you want to prove that volume meshing is better, just do the same thing as above, only select a 3-D arbitrary structure (say, a coax to waveguide adapter).

Every now and then I run across this idea that volume meshing (FEM in particular) is better than MoM. This is true if the problem is appropriate for volume meshing and is not appropriate for MoM. But for planar circuits, and for planar MoM, MoM (any MoM!) is by far (orders of magnitude) better than volume meshing in both accuracy and in speed. (Beacuse each approach has both advantages and disadvantages for various kinds of problems, I often recommend that one should get both, if budget allows.)

 

[irfan1]

fem mom source code

Dear rautio,
Which tool would be better for metallic only structures? FDTD? FEM? MOM? To be specific, lets say we have a metallic grating with a hole on it and we want to simulate this structure. The metal has a certain thickness.

 

[rautio]

mom in sonnet software

Hi Irfan1 -- I think you mean metalic + empty space (i.e., no dielectric). If it is a wire mesh, I would seriously consider one of the NEC (numerical electromagnetic code), designed for wire antennas. Just treat your grid as a wire antenna. NEC code prices range from free to several thousand dollars, much cheaper than commercial EM codes (like our own Sonnet).

If you need broad band results, I would recommend FDTD (Finite Difference Time Domain), or, esp. its close relative FIT (Finite Integration Technique). In my opinion, FIT is usually superior (that is why we represent the leading commercial tool, CST, in North America), but certainly there is room for different opinions on this matter, and it is also problem dependent.

I would need more information about your specific problem and what kind of results you need to make a better recommendation. Additional information could completely change my recomendation.

 

[adel_48]

mom vs fem

Hi,

concerning MoM and FEM, I have programmed both methods, I agree with Mr rautio that MoM is better, but the number of mesh cells is not the only factor, since FEM cells are large and its matrix is very large but it is generally a sparse matrix and can easily be solved using iterative solvers unlike the dense and ill-conditioned matrices that generally result from MoM, also there are not any time consuming singular and normal integrations such as the MoM. Also, in MoM the excitation modelling is generally a problem and we have to model the exact excitation (e.g. a waveguide excited with TE10 or a coaxial excited with TEM wave would be too difficult to model in MoM) Also for Microstrip structures MoM requires de-embedding schemes which are in some cases proprietary.

However, I think that for large open structures that doesn't require too many surface meshcells MoM should be the method (both concerning accuracy and time), for small closed structures (e.g cavities or w.g filters) I would recommend FEM. For inhomogeneous media and/or too many interfaces FEM or FDTD should be used according to the frequency band of the structure.

Best Regards,
Adel

 

[rautio]

wg slot modeling mom code

Hi Adel_48 -- I agree with most of your comments. However, for planar structures in a shielded environment, the Green's function is a sum of sines and cosines. There are no nasty integrations (as there are in unshielded environment). In addition, planar MoM requires a 4-D integration (2-D over the source subsection and 2-D over the field subsection). In unshielded, this must be done numerically. In shielded MoM, the sines in the Green's function just go to cosines, etc. All the field/source integration is done analytically. All that is left to do is to sum the sines and cosines, and that is done with the FFT.

You are correct that most of the de-embedding done in planar MoM is proprietary. Sonnet (my company) is an exception, with all de-embedding completely published. FEM, and other volume meshing tools can indeed launch a plane wave or a TEM mode, etc., and then no de-embedding is needed. This is indeed an advantage when it can be done. However, in launching waves in inhomogeous media (with loss or with more than one dielectric constant), Zo is not known. They have to calculate it, assuming you want to know to what Zo your S-parameters are normalized. This roughly corresponds to planar MoM de-embedding. The problem is the definition of Zo is fuzzy for these cases, differences of over 10% are possible without much difficulty. These differences contribute directly to uncertainty in the resulting data.

In contrast, the Sonnet de-embedding does not make use of Zo to de-embed. This may seem like a very strange statement if you are used to only the traveling wave concept for de-embedding. Sonnet does not use that either. I will be happy to give you a reference or two to read if you are interested.

For arbitary structures in a shielded environment, one or another of the volume meshing tools would be best. Might be FEM. Might not be. Depends on the problem.

 

[adel_48]

sonnet de-embedding

Dear Dr. Rautio,

Thank you Dr. rautio, Actually you made me reconsider a very important point, as most of my work has been on antennas so I was mainly interested in the free space green's functions which become singular for some cells and in most cases cannot be integrated easily, and so most of my ideas were based on this.

I completely agree with you that in closed structures the integrations of green's functions are much more simpler and can be easily done.

But still there are some MoM based commercial software such as WIPL-D which uses the free space green's functions and IE3D which uses the layered media green's functions.

I think that the assumption of closed structure might not be valid for special planar structures e.g. when there is a radiating slot in the ground plane. I once simulated a DGS on Microwave Office (a MoM based simulator which assumes closed structure) its results were not the same as the measurements, so I used Microwave Studio once with perfect E boundary conidtions (and gave approximately the same results as Microwave office) and the other with open boundary conditions which had a very good agreement with the measurements.

Actually, I am very interested in the de-embedding technique used in sonnet software. I will be happy if you can give me some sources about it. A friend of mine uses sonnet in his planar structures (mainly co-planar with multi-layer) and he gets very good results using it.

Also there is a small point I did not mention conerning FDTD, the problem if launching a mode in the time domain. For closed non dispersive structures, launching the modes is quite straight forward, however for dispersive structures launching the modes may lead to inaccurate results. I once tried to simulate a dielectric rod antenna using FDTD but I was faced with a big problem since the transverse field distribution at the port changes with frequency (at low frequencies the field is concentrated outside the rod, for higher frequencies it becomes concentrated in it) and the only method that can be done is either de-embedding (which I don't know how to implement in such a case due to the strong dispersive properties of the structure at the port) or by taking the inverse fourier transform of the analytical field distribution multiplied by a gaussian pulse in the frequency domain and use it to excite the structure in the time domain, but I didn't find any commercial FDTD software that uses this method. I think in such case fequency domain techniques such as FEM or FDFD are the only way.

Best Regards,
Adel

 

[rautio]

mom moment internal problem

Hi Adel -- Thanks for carefully considering my comments, and for providing your comments.

I have only a high level understanding of FDTD, so I can not comment on your detailed observations there, but your comments do certainly sound reasonable to me. It is certainly very very clear that limiting one self to just one or two EM tools is often a big mistake.

As for papers on Sonnet de-embedding, the most recent is:

James C. Rautio and Vladimir I. Okhmatovski, "Unification of Double-Delay and SOC Electromagnetic Deembedding," IEEE Transactions on Microwave Theory and Techniques, Vol. 53, No. 9, September 2005, pp 2892 - 2898.

and my original paper is:

J. C. Rautio, "A De-Embedding Algorithm for Electromagnetics," International Journal of Microwave & Millimeter-Wave Computer-Aided Engineering, Vol.1, No. 3, July 1991, pp. 282-287.

I have also solved the problem of de-embedding internal ports exactly. Internal ports are important for SMD, transistors in RFIC, and even in power FET modeling. (Just last Thursday, a very knowledgeable EM researcher told me such a solution is impossible!) The paper is:

James C. Rautio, "Deembedding the Effect of a Local Ground Plane in Electromagnetic Analysis," IEEE Transactions on Microwave Theory and Techniques, Vol. 53, No. 2, February 2005, pp. 770 - 776.

If you want to find more papers on Sonnet, go to www.sonnetsoftware.com, click on Products->Sonnet Bibliography. You can get the first and third papers from IEEE Xplore, or I can email a pdf of any of them to you, just let me have your email address, or email a request to info@sonnetsoftware.com.

For terminology, I now always say "shielded" and "unshielded". I talk to a lot of newbies in EM and I have found some confusion when we say "closed" and "open". Sometimes newbies think "closed" means Sonnet does not interface to anything else, when we actually interface to more frameworks than any other tool out there. And on the opposite side, there are several unshielded tools that interface to only one framework, they are most certainly not "open", even though they are unshielded.

I always recommend having at least one shielded and one unshielded tool for planar EM design. For important ("must work the first time") designs, one should analyze the circuit in both, as you have done. Any differences must be understood before going to fabrication. In the case you described, I would guess that the unshielded analysis gave a better match to measurement because you measured it unshielded. If this is the case, then we can conclude that the box sidewalls in your shielded analysis have some effect on the circuit. This means that the fields from your circuit extend out to where the box sidewalls are. This means that if you place other electronic components at that distance, they are likely to couple to your circuit. This is important to realize before fabrication. You do not want to have the system integration people coming after you with baseball bats! Analysis with both shielded and unshielded lets you make corrections before fabrication.