Dear loucy,
The confusion is due to not updating your list of references on conformal FDTD. You can find my comments on Dey-Mittra CFDTD, or D-FDTD as known in literature, on this page (Already mentioned as an attached file). Note that you had mentioned small parts of the references [2] and [6]. I have used [6] in favor of D-FDTD.
Best regards
wave-maniac
***************** My comments *********************
Prior to Dey-Mittra work, some methods had been published on conformal FDTD by various authors, which were sort of complex. The best ones used the idea of borrowing and interpolation of electric fields from the neighboring cells, at the object boundary. Dey-Mittra presented a novel method, first in [1] and [2] and then modified in [3], whose pros and cons are as follow:
Pros:
1) It’s very simple. This has been admitted by many including in [6].
2) It’s accurate. Please read the conclusion in [6].
3) It doesn’t need the borrowing/interpolation stuff [1] to [4], and [6].
4) The standard update equations for the E-fields are unchanged ([1] to [13]).
5) The inclusion of FDTD formulations such as radiation boundary conditions, total-field/scattered field surfaces, and near-to-far field transformations may be used without alteration [13].
Cons:
1) The time step has to be 50 to 70 percent of Courant limit, which according to the conclusion in [6], “is a small price in view of the much greater saving of resources which result from using the method ”.
2) To use their idea, one has to create a particular FDTD mesh near the PEC surfaces. There were two restrictions, including the “length to area ratio”, which I’ll mention later. However, it’s not a big deal. The FDTD guru, Allen Taflove found the method worth of developing a special mesh generator [13]. Note the paper date is 2002. It is also mentioned in his homepage.
Dealing with arbitrary shaped dielectric objects:
In [4] and [5], Dey-Mittra extended their method to include arbitrary shaped dielectric objects. They actually used sort of effective permittivities of FDTD cells.
Final Modification, Yu-Mittra Method:
In 2000, Yu and Mittra modified the original method to get rid of the first disadvantage, using a simple change in H-field updating ([7], [8], [9] and [10]). They actually used the entire cell area instead of the deformed cell area. Thus they were able to use time steps equal to 99.5 percent of Courant limit. They also extended it to include arbitrary shaped dielectric objects in [11]. There, instead of using a volume average, their conformal dielectric algorithm utilizes a linear average concept. They have developed software based on their algorithm. You can download the demo version (20.3 MB) from the following link:
**broken link removed**
Mittra’s team have recently published a lot of papers (e.g. [12]) on various applications of the method and/or software, indicating their versatility.
Line to Area ratio Criterion:
I think they meant a dimensionless, normalized distorted cell geometry. Otherwise it would be a meaningless criterion. As you might see in [6], it has been mentioned the restriction can be meaningfully interpreted for cells with equal lengths. I really doubt Railton, et al, didn’t realize the criterion to be nonsense. By normalized geometry, I mean normalizing by the maximum, particularly distorted, length of the cell. By the way, don’t you think there is no use to think about it? As was mentioned before, the distorted area is no longer used in H-field updating procedure.
Note and conclusion:
By no means I believe that the Mittra’s team is the best forever. But up to now, no other conformal FDTD method has been reported which is very simple in formulation and yet accurate. As I mentioned before, even FDTD giants such as Taflove and Weiland are either using the algorithm or are going to use “their own version of Mittra’s team algorithm. By the way, some guys, including Kosmanis and Tsiboukis have presented some rigorous methods for conformal FDTD, which seem powerful, but by no means simple. [14] is one of their papers.
Anyway, you can use
www.fdtd.org or IEEE Xplore to keep yourself updated.
References:
[1] A Locally Conformal Finite Difference Time Domain (FDTD) Algorithm for Modeling 3-D Objects with Curved Surfaces, S. Dey and R. Mittra, IEEE Antennas and Propagat. Soc. Int. Symp., Montréal, Canada, vol. 4, 2172-2175, July, 1997
[2] A Locally Conformal Finite-Difference Time-Domain (FDTD) Algorithm for Modeling Three-Dimensional Perfectly Conducting Objects, S. Dey and R. Mittra, IEEE Microwave Guided Wave Letters, vol. 7, no. 9, 273-275, September, 1997
[3] A Modified Locally Conformal Finite-Difference Time-Domain Algorithm for Modeling Three-Dimensional Perfectly Conducting Objects, S. Dey and R. Mittra, Microwave and Optical Technology Letters, vol. 17, no. 6, 349-352, April, 1998
[4] A locally conformal finite difference time domain technique for modeling arbitrary shaped objects, S. Dey and R. Mittra, IEEE Antennas Propagat Soc Int Symp, June 1998, vol. 1, pp. 584-587.
[5] A Conformal Finite-Difference Time-Domain Technique for Modeling Cylindrical Dielectric Resonantors, S. Dey and R. Mittra, IEEE Transactions on Microwave Theory and Techniques, vol. 47, no. 9, 1737-1739, September, 1999
[6] An Analytical and Numerical Analysis of Several Locally Conformal FDTD Schemes, C. J. Railton and J. B. Schneider, IEEE Transactions on Microwave Theory and Techniques, vol. 47, no. 1, 56-66, January, 1999
[7] Novel Conformal FDTD Approach for Modeling Monolithic Microwave Integrated Circuits (MMIC), W. Yu and R. Mittra, IEEE Antennas and Propagat. Soc. Int. Symposium, Salt Lake City, UT, vol. 1, 244-247, July, 2000
[8] A Conformal FDTD Algorithm for Modeling Perfectly Conducting Objects with Curve-Shaped Surfaces and Edges, W. Yu and R. Mittra, Microwave and Optical Technology Letters, vol. 27, no. 2, 136-138, October, 2000
[9] A Conformal FDTD Software Package Modeling Antennas and Microstrip Circuit Components, W. Yu and R. Mittra, IEEE Antennas and Propagation Magazine, vol. 42, no. 5, 28-39, October, 2000
[10] Accurate Modeling of Planar Microwave Circuit Using Conformal FDTD Algorithm, W. Yu and R. Mittra, Electronics Letters, vol. 36, no. 7, 618-619, 2000
[11] A Conformal Finite Difference Time Domain Technique for Modeling Curved Dielectric Surfaces, W. Yu and R. Mittra, IEEE Microwave and Wireless Components Letters, vol. 11, no. 1, 25-27, January, 2001
[12] Application of FDTD Method to Conformal Patch Antennas, W. Yu, N. Farahat, and R. Mittra, IEE Proceedings H: Microwaves, Antennas and Propagation, vol. 148, no. 3, 218-220, June, 2001
[13] Three-Dimensional CAD-Based Mesh Generator for the Dey-Mittra Conformal FDTD Algorithm, G. Waldschmidt and A. Taflove, IEEE Antennas and Propagat. Soc. Int. Symposium, San Antonio, TX, vol. 3, 612-615, June, 2002.
[14] A Systematic Conformal Finite-Difference Time-Domain (FDTD) Technique for the Simulation of Arbitrarily Curved Interfaces between Dielectrics, T. I. Kosmanis and T. D. Tsiboukis, IEEE Transactions on Magnetics, vol. 38, no. 2, 645-648, March, 2002.