Welcome to our site! EDAboard.com is an international Electronics Discussion Forum focused on EDA software, circuits, schematics, books, theory, papers, asic, pld, 8051, DSP, Network, RF, Analog Design, PCB, Service Manuals... and a whole lot more! To participate you need to register. Registration is free. Click here to register now.
According to MWS 5 documents, not all the claimed features exist in this release (such as tetrahedral mesh generation for frequency domain, as Mesh on Demand), or implemented efficiently (such as multilevel multigrid mesh generation, which exists but its implementation saves only time not memory). It has been promised that in service packs of mws 5, such issues will be addressed. By the way, some claimed new features for MWS 5 existed before (such as internal waveguide ports). Although a powerful software, but I wish they had done their job much better than what it is now.
The fact that they are using subgridding indicates the PBA has not been "Perfect". So my impression is that what they claim as new features have been somewhat exaggerated.
I have been trying to find out what is the magic behind this "PBA". This 5.0 make me feel that there is actually nothing magical there.
What do you think???
by the way, PBA=Perfect Boundary Approximation. I have been troubling with this term: it (mesh?) is perfect, but it is also an approximation.
How do you feel about the trade marks of EM softwares? e.g. Do you think Sonnet is marketing their conformal mesh now?
(I know MWS is still the market leader in FDTD software. Please don't say I intend to defame it here.)
1) As far as I know, PBA has nothing to do with subgridding. MSS has been intended to relax the mesh by preventing the refinements from extending to all the 6 main outmost faces of the domain. It has not been successful at least for this release. To find out what PBA is, you could study their papers on this topic.
2) As to Sonnet conformal mesh, I doubt it deserves the word "conformal". Its only an ad hoc trick. I suggest you read the recent paper coauthored by Dr. Jim Rautio in IEEE in this regard. By trick, I mean something like the IE3D method to consider the effect of thickness, included from version 9 something. One can easily define a specific structure, like an spiral inductor, in different ways so that the resistance would be different for each case. One should know how to use the new tricks, considering their effective domain of application to get a reasonable accuracy.
By the way, although tetrahedral mesh generation is not mentioned in any of the MWS documents (even the online help), the mesh could be activated and created. Could it be used in a frequency domain simulation? I doubt.
I understand PBA has nothing to do with subgridding. Although I know nothing about PBA, I can imagine that these two are completely different approach to the problem of modelling curved and fine geometrical features within the framework of FDTD. I guess the PBA is something like a finite difference (or finite integration) scheme defined on irregular grid. Since subgridding was earlier than the PBA, I expect that PBA is more advanced. Now CST is developing/releasing/marketing the subgridding, to me it indicates some problem with PBA, they can't advance it any further.
I should emphasize the above is just my impression. I'd love to read and learn more about PBA. But I haven't seen any paper discussing its internal working principles. I did see some "papers" simply showing some mesh related to PBA, but that is useless. You can't judge the accuracy by looking some simple mesh. Please post your list of reference on PBA. I am very interested in it.
I've read the Jan 2004 MTT paper about Sonnet's "conformal" mesh. I agree with you it is not a general conformal technique. I look at it as a way for making use of the well known singular behavior of current distribution along a microstrip line. It works only for special cases because that singular behavior would change even for the case of un-symmetric coupled line. If I had the the new version, I would test it on this simple geometry to find out its accuracy: an un-symmetric coupled line titled 45 degrees from the x-axis. Attach ports via some bends, check out the S21 and resonance frequency...
Note that the conformal mesh problem for Sonnet is somewhat similar to the conformal FDTD. Sonnet's mom method starts with uniform regular grid.
I don't have doubt on CST's ability to use tetrahedral mesh in their frequency domain solver. Although they call their method Finite Integration, it is very similar to FDTD. So one can sense that the method is somewhat related to both finite difference (FD) and some integration. Now if it is applied only for one frequency, one can look at it as a mixture of finite difference and finte element method in Frequency domain. Every one knows that finite element method can use tetrahedral mesh.
When using tetrahedral mesh, they clearly call it finite element (in one of the message windows). The problems:
1) The mesh is not completely graded but created using the initial Cartesian mesh. So it's unnecessarily dense for a given minimum density.
2) (perhaps my problem), I've not been able to use the created tetrahedral mesh for even a very simple case, i.e. a piece of rectangular waveguide. An error message says that it can't compute the modal fields in the ports.
BTW,I'll provide you with the PBA paper address today or tmorrow.
Here is the address to a paper which discusses some aspects of FIT technology as used by CST, including PBA: https://epaper.kek.jp/l98/PAPERS/TH4041.PDF
Please note that their next step will be non-orthogonal grids which is much more powerful than PBA. The non-orthogonal algorithm has been implemented in MAFIA (experimental status) and the results have been calimed to be promising.
This is the only material available on PBA and has been presented in LINAC98 conference. But it does not give any information about it:
PBA and the newly MSS (subgridding scheme) has been proprietary code and no details have been released on their implementation...
Some papers on MSS appear on IEEE Trans. on Magnetics (mostly) if you search for "Multilevel subgridding scheme" and check all pubs with author Thomas Weiland (CST founder)...
The level of conspiracy at CST borders paranoia.
What is really striking is that one can find 150+sites on FEM and a lot of info on nearly ANY feature of ANY FEM solver unlike the magic CST is taking out of their sleeves.
Two things are very interesting to me:
1. How is it possible that the inherently ill-posed problem of non-orthogonal grid, leading to unstable solution is implemented. This is on math grounds.
2. How do they maintain the aledged accuracy of the eigenvalues and eigenvectors when they use the discreet differential operatiors that need much finer grid to converge to the "analytical" values. I failed badly on every occasion when used their Eigenmode solver. When I say badly, it is badly. After the third or forth mode the eigenvalues were patently wrong
Many thanks to Wave-Maniac for posting the paper on PBA. Unfortunately, it is just hand-waving, doesn't give any details.
I don't quite understand Cheng's comment. Are you saying the "finite difference/integration" scheme is fundamentally ill-posed when applied on non-orthogonal grid? I believe this is not the case. Whatever the updating equation is, it would have come from (or be interpreted as) approximating integrals with summations under some assumptions (e.g. linear/quadratic local behavior of the fields). The accuracy and stability are directly related to these assumptions. I haven't seen any proof and I don't see any reason that any/all updating scheme defined on non-orthogonal grids are necessarily bad. If one doesn't need to worry about the speed, then I guess he can easily come up with a scheme that is accurate. The problem, of course, is you need to be both accurate and fast (practical).
About the eigenvalue and eigenvector, can Cheng tell us what were the geometries in your "occasions"?
In the few occasions that I have tested MWS on finding the eigenvalues of some problems with curved boundaries (sphere, cylinder etc.) I've got amazingly accurate results. I said amazing because those curved boundaries are not easy to capture with finite difference on Cartesian grids. I guess anyone who has CST can test it quite easily.
I think there's a confusing mistake about the actual FIT algorithm. All say that it is inherently derived from Finite Differences, but in fact there is a whole different concept behind FIT (expect leap-frog time marching scheme which is borrowed from FDTD).
The discretization of Maxwell Equations is exact and no approximations are made in this process (therefore, no integrals are approxiamted by sums...).
The approximation comes in place when discretizing the material constitutive parameters... I have seen papers that discuss the application of non-orthogonal grids with this technique. All this ofcourse mostly for time-domain implementation. I have never tried the eigensolver
I must disagree with cheng in his first remark (about the almost paranoid behavior of CST people). I think its not bad to have proprietary code (and be mystical) for something that you believe its cutting-edge in this field of science. But there is an enormous amount of papers published on many aspects of FIT (e.g. time-stability and energy conservation).
Search for the author "Weiland" in:
IEEE trans. on Magnetics and
Wiley's Intl. Journal of Numerical Modelling: Electronic Networks, Devices and Fields...
ok. Let say that some information passed off the wizards at Darmstadt. They are having accuracy issues with the PBA and is why they pushed subgridding. Whoever said that before, was right.
Second, about unstructured grids. True, the problem is not in the speed, the problem is ill-posed and causes troubles with stability. You'll never hear FDTD people say that, but the problem has been looked at (MIT and Berkeley if I remember) and was considered ill-posed. For short times, however it may yield good results. Waiting longer will diverge.
Third, my examples were with whispering gallery modes in dielectric resonators as well as some DR filters, that put the CST eigensolver to a shame.
For that application I believe that spectral methods (FEM included) is the way to go. Specifically, a higher order of the interpolant (say 6) in the FEM case will deliver the spectral accuracy of the entire domain spectral methods that are the most accurate to date. In fact, I mean the pseudospectral and not Galerkin, although Galerkin is somewhat better for smaller N (number of expansion polynoms).
Dear loucy and mogwai,
If you take a closer look at the figures in the paper, you can easily find out what their so-called proprietary PBA technique is, or at least to what types of approximate methods it belongs. It doesn't deserve the name. That's why they are trying to use non-orthogonal grids, which will provide them accuracy of FE in modeling material interface. PBA has been described in other papers by Weiland under another names. According to him, it's similar to the work by Mittra team (the one I had mentioned in my discussion of CFDTD with loucy). I'll provide you with more info on the papers.
It is wrong to say that "All say that it(FIT) is inherently derived from Finite Differences". I think nobody in this forum has said that and everybody knows that the "Integration" means something.
Discretization of the Maxwell's equations CAN'T be exact. You won't call it discretized equation if it is exact.
I guess people seldom say "discretizing the material constitutive parameters". What does it mean to discretize a parameter(real/comple value)? True, you can say that you need to discritize the material parameter as a function of spatial variables. But that is not a main step in the numerical solution of maxwell's equations. Because the material parameter is mostly piecewise constant, it is not part of the waves (fields) we are after. In stead the discretization of the E or H fields is the main step. That is main source of approximation.
We don't want to pretend knowing much about FIT method, but one thing seems clear: the method involves discretizing the integral form of Maxwell's equations. If they haven't approximated the integrals with summations, how could they obtain the updating equations and program them to processors?
I didn't wanted to start an arguing thread, and this wasn't my intention at all
After all, I agree to most of what you are saying...I'm just curious as all of you about what is actually true...
wave-maniac: Yes, PBA is definately NOT a perfect method. I have read some things about Mittra's methods but if you have more materials on Weiland's pba technique it would be great to get them too...
loucy: sorry, i didn't implied that someone on this board said this. I have read it in books though and it's a bit confusing before you get into the method itself...
About the discretization process: turning Maxwell's equations into a discrete form could only mean that in a well posed spatial grid (orthogonal mostly) you can set your own paths for the closed form integrals and get the results for all parameters. There's no approximation when you select your faces and edges correctly and define some basic orientations for the vectors. The resulting equations have algebraic properties that match with analytic equations, a fact that could not be achieved by any approximation.
I'm not pretending to know much about the FIT either, but some things are not clear with the method...I'm just trying to figure them out
Well, I think we may have some confusion over here concerning discretized, non-discretized etc.
There are basically 2 dissimilar approaches to "discretize" the differential equations - one is to discretize the differential operators - FD, FDTD etc.
The other discretization is the one used in FEM - on each mesh cell, the approximant is a piecewise polynomial (overlapped to preserve the boundary between the cells) but the differentiation is retained analitically because it is easy to compute for polynoms. Thus, no operator discretization errors incurred. In both cases we end up with matrices - but they are of different nature. There are limit cases where the 2 approaches will lead to similar data, but all things equal, if one employs higher order interpolant, the "local" FEM solutions are EXTREMELY good. Problem over here is that to make is easier to solve, FEM is using the "first-order" Galerkin approximation (weak form) which limits the smootness of the interpolant. But on theoretical grounds FEM CAN BE as accurate as the pure spectral methods, that are the best by far, leading to 10-15 digits accuracy - and it is why MoM is so accurate for structures prone to it.
So, let's not make confusion with the discretization - they are here, yet they are different. It can be shown though that certain quadrature procedures will lead to similar results, mainly because the order of the interpolant is finite and therefore the corresponding error in the interpolated function is fixed by Chebyshev Theorem.
regards,
cheng
P.S After all, I am using mw$ on its own right exlusively in time domain simulations and can say that results are most of the time (provided good set up) very good. I mean, for freq. domain I certainly trust on HFSS or sth. alike and will never go to mw$. After all, elektrodians know how to use them both :wink:
Here are the addresses of the papers, I had promised, with some dicussions:
1) The Perfect Boundary Approximation Technique Facing the Big Challenge of High Precision Mode Computation
By: P. THOMA, CST GmbH; B. KRIETENSTEIN, T. WEILAND, TU-Darmstadt
Fig.1d indicates that PBA is not perfect perfect. Actually it utilizes the idea of partially filled cells. This clearly means sort of averaging material parameters. Actually the non-orthogonal grid method, in which any cell is completely filled with a single material and conforms to the boundary, deserves the name better.
2) Discrete Electromagnetism with the Finite Integration Technique
By: M. Clemens and T. Weiland
**broken link removed**
On page 7, it mentions 3 schemes for geometry approximation with FIT, which are based on material averaging. One of them is PBA.
3) M. Clemens, T. Weiland: Magnetic Field Simulations Using Conformal FIT Formulations. IEEE Transactions on Magnetics, Vol. 38, N2, pp.389-392, 2002.
This paper describes PBA under another name, i.e. conformal FIT or C-FIT. In the last paragraph of the first column on page 2 it says the C-FIT was first proposed in the paper, which has been mentioned here as number 1. The authors say that C-FIT (PBA) is similar to the work presented in the following paper:
W. Yu, R. Mittra, “A Conformal Finite Difference Time Domain Technique for Modeling Curved Dielectric Surfaces”, in IEEE Microwave and Wireless Components Letters, Vol. 11, No. 1, pp. 25-27 (2001).
For those who have not access to IEEE Xplore, the following paper could be used instead of paper number 3:
Discrete Electromagnetics: Maxwell’s Equations Tailored to Numerical Simulations
By: Markus Clemens and Thomas Weiland
**broken link removed**
You’ll see the same discussion on page 9.
BTW, I'm going to begin a new topic on "hopefully" a future capability of HFSS.
This site uses cookies to help personalise content, tailor your experience and to keep you logged in if you register.
By continuing to use this site, you are consenting to our use of cookies.
