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rick
5 Posts |
 Posted - Sep 02 2025 : 16:34:23
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Dear Enrico,
Professor Enrico, hello. I’d like to ask you a question. The website mentions that #8203;#8203;FasterCap#8203;#8203; is faster and uses less memory compared to #8203;#8203;FastCap#8203;#8203;. I’m a bit confused about this.
In FastCap, the acceleration algorithm used is the #8203;#8203;Fast Multipole Method (FMM)#8203;#8203;, while FasterCap employs a #8203;#8203;hierarchical algorithm#8203;#8203;. Currently, the most widely used acceleration algorithm in the Method of Moments is indeed the FMM. In particular, the Fast Multipole Method is based on spherical harmonic expansions, which naturally align with the principles of FMM—both from a physical perspective (the potential field generated by a point source has spherical symmetry in three-dimensional space) and a mathematical one (spherical harmonics are eigenfunctions of the Laplace equation).
Why did FasterCap abandon the FMM in favor of a seemingly less ideal hierarchical algorithm? |
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Enrico
548 Posts |
Posted - Sep 04 2025 : 18:12:29
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Hi Rick,
thank you for your interest and for the title "professor" but I must confess that while I do have a Master degree in electronics and I am working in this field since 1998, I can not claim this title :).
Answering your question, actually there are many acceleration strategies being used in numerically solving BEM problems. Apart FMM and its many variations, there are also FFT methods, the Appel's method, .. and direct methods as well as H-matrices, etc.
I might go as far as saying that there is no 'best' method in absolute terms, but it really depends on many factors and considerations.
Stated that, the reason why in FasterCap we decided to use Appel's method instead of FMM is related to two main considerations:
1) we wanted an algorithm that was able to deal with automatic meshing in a simple way. This is not so straightforward using FMM.
2) we wanted an algorithm that was not kernel dependent. The multipole expansion functions in the FMM are instead dependent on the specific Green's kernel. For instance, managing dielectric interface panels require a different type of expansion. The same would be true if you want to incorporate in the Green's kernel also infinite dielectric discontinuity planes, or a ground plane (this eventually was not done in FasterCap, but we wanted the code to be flexible enough).
Best,
Enrico
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rick
5 Posts |
Posted - Sep 08 2025 : 16:54:29
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Dear Enrico,
Thank you very much for your response. I would also like to discuss a couple of issues with you.
1.
Automatic mesh refinement is an excellent idea. However, the mesh refinement approach in FasterCap may lead to poor mesh quality (particularly when processing non-Manhattan structures of conductors). Would it be more appropriate to introduce a dedicated mesh engine to handle the refinement?
2.
In my opinion, the MoM might not be well-suited for handling multilayer media or dielectrics. FasterCap also struggles with convergence when dealing with dielectric problems, even when switched to the Galerkin method. |
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Enrico
548 Posts |
Posted - Sep 08 2025 : 18:09:04
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Hi Rick,
1. Yes this is a possibility; not sure if you are true about manhattan / non-manhattan, but surely it would be possible to introduce a more advanced meshing algorithm based on some upper boundary error. Still, this I believe should be implemented for the outer iterations (when finding the right discretization), not in place of the meshing, that is also used to create the hierarchical structure for matrix compression.
If you have any idea, you are welcome to share.
2. Not sure what is your proposal here. FasterCap can be enhanced to use multi-layer Green's formulae, so you can more efficiently deal with multiple dielectris, as long as they are planar. Other ideas?
Best,
Enrico
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rick
5 Posts |
Posted - Sep 13 2025 : 15:06:53
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Dear Enrico,
Apologies for my delayed response.
1.
I find that the mesh refinement function in FasterCap is relatively basic, and the quality of the refined mesh is not ideal, which may affect the accuracy of the results. I am considering using more professional mesh refinement tools (such as TetGen, Gmsh, or MeshLab) for this purpose.
2.
When using FasterCap to extract structures involving dielectrics, I often encounter convergence issues or even failure to converge. I suspect that since the Method of Moments (MoM) solves surface integral equations, it requires approximating the interior physics to the boundary when handling dielectric problems. This approximation might compromise the accuracy of the results. |
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Enrico
548 Posts |
Posted - Sep 16 2025 : 10:55:34
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Dear Rick,
quote:
1.
I find that the mesh refinement function in FasterCap is relatively basic, and the quality of the refined mesh is not ideal, which may affect the accuracy of the results. I am considering using more professional mesh refinement tools (such as TetGen, Gmsh, or MeshLab) for this purpose.
I see now your point. You may use other tools; but I'm afraid that this will not improve, per se, the accuracy of the results. The hierarchical algorithm works best when it is able to partition the geometry in the best way according to the criteria used for the matrix compression itself, that is not a purely geometrical one. Starting with a pre-meshed structure will lead to worse results, as the algorithm will need to try and merge different panels in super-panels, and this is not in general possible in the 'best' way, while you can always partition existing panels dividing them in two (top-down transversal of the tree). I think we briefly touched this point in the other thread "In FasterCap, the high permittivity ratio".
I should add that a geometrical quality triangulation is not necessarily improving the quality of the result also for FMM methods. Actually, you can directly compare FastCap (that is fully FMM) with FasterCap. You can get much better results, instead, if you use a criteria that is not only geometrical, but based on some error measure stemming from the actual knowledge of the underlying EM problem. To make a practical example, you know that the charge tends to crowd around the edges; the sharper the edge, the higher the charge density. If you can capture this phenomenon, and have a denser mesh near the edges, you surely get better results for the same number of panels.
A paper that explores this concept is Tausch, J., & White, J., "Mesh refinement strategies for capacitance extraction", Proc. IEEE Workshop on Electrical Performance of Electronic Packaging, 10/96.
quote:
2.
When using FasterCap to extract structures involving dielectrics, I often encounter convergence issues or even failure to converge. I suspect that since the Method of Moments (MoM) solves surface integral equations, it requires approximating the interior physics to the boundary when handling dielectric problems. This approximation might compromise the accuracy of the results.
Are you sure you are 1) correctly modelling the dielectic as a closed surface 2) not overlapping dielectric panels with conductive panels?
Surely handling dielectrics is more critical than handling conductors only. Still, you should not find failure in convergence.
Have you tried running the same geometry in FastCap?
Best,
Enrico
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FasterCap vs. FastCap Comparison
