Hello everyone, I’m Evan Huang. I’ve worked as an application engineer for electromagnetic simulation for 3 years. Recently, I got in touch with a new algorithm called EIT (which has been applied to ZWSim-EM
, a 3D full-wave electromagnetic simulator from ZWSOFT), and in order to have a better understanding of it, I've also gone over other algorithms.
So in this article, I want to share with you a brief summary of some mainstream electromagnetic algorithms on the market, based on my own understanding and experience. I would not dig deep into the theories, but focus on their main characteristics and application ranges. Hope it will do a little help for those of you who are studying or undertaking relative work.
I’ll cut it roughly in two main kinds – time-domain and frequency-domain. Time-domain method is mainly applied to broadband, simple geometry, electrically enormous structures and various kinds of media, while frequency-domain has an advantage in narrowband, complicated geometry, electrically fine structures and linear media. It’s worth mentioning that by hinting time step, electrically fine structures can also be calculated by the time-domain method, but with more complex calculation for a single step.
There are currently two mainstream time-domain algorithms: FDTD and FETD. FDTD (finite-difference time-domain) utilizes central difference approximations to the time partial derivatives. Its solution matrix is diagonal with the whole field discretized. Since it’s a time-domain method, a wideband can be covered only by a single simulation. It is more intuitive because the field behaviors can be reflected simultaneously along with time. It can be applied to optical and radio frequencies, bio-imaging, photonic crystals, etc. Although its adaptability to complex geometry is relatively weak, it can be compensated by subcell and subgrid methods.
[caption id="attachment_1887" align="aligncenter" width="400"]
Figure 1. The meshes of FDTD[/caption]
Note: Photo from the internet. In case of infringement, it will be deleted immediately.
FETD (finite-element time-domain) could be understood as a combination of time-domain technique and spatial discretization. Although it can deal with complex geometric models by discretizing the geometry into much smaller polygons (finite elements), the calculation speed is slower than FDTD with the same amount of unknowns, and more steps are required when dealing with electrically fine structures.
FIT (finite integration technique) is also a time-domain algorithm. The difference between it and FDTD is that the latter uses the central difference method to discretize Maxwell's differential equations, while FIT uses the loop integration method to discretize Maxwell's integral equations. Similar to FDTD, FIT is capable of dealing with broadband and a variety of media. The difference is that it can also solve complex geometric problems, although it doesn’t perform that well in the case of electrically fine structures or super-complex geometry. The electromagnetic simulation software adopting this algorithm on the market is CST
Based on FDTD, there is another algorithm you may be new with, that is, EIT (Embedded Integral Technique), which I’ve mentioned at the beginning of this article. Developed by ZWSOFT, it is applicable to broadband, complicated geometry, and different media. It makes up FDTD’s weakness in complex geometric processing by its conformal technology, to ensure second-order accuracy and efficiency; and also makes up Conformal-FDTD’s weakness in time step, to ensure calculation efficiency without reducing time step by its unique technology to deal with irregular meshes. What’s out of my expectation it that its model discreteness can solve any pathological triangle models, including the ones that degenerate into points and lines.
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Figure 2. The meshes of EIT[/caption]
For frequency-domain algorithms, there are mainly FEM and MoM. FEM (finite element method) is a numerical method used to figure out the approximate solutions of partial differential equations (PDEs), such as Maxwell’s equation, diffusion equation, elastic wave equation, etc. Its mesh is a tetrahedron, and its solution matrix is sparse. It can simulate dispersions and anisotropic materials, narrow-band, complex structures and linear media. A typical CAE solution using this algorithm on the market is HFSS
[caption id="attachment_1889" align="aligncenter" width="800"]
Figure 3. The meshes of FEM[/caption]
MoM (Method of Moments) is another frequency-domain algorithm that solves dense matrices. Its mesh is triangular, enabling it to accurately generate meshes for objects of any shape, theoretically, and thus adapt to complex geometric models. However, solving the Z matrix can be time- and hardware-consuming. A representative adopting this algorithm is FEKO
, which can be used to analyze radiation, scatter, and electrically enormous structures. However, its meshes can be relatively difficult to generate, requiring the import of external meshes, and its modeling capability is also relatively weak.
[caption id="attachment_1891" align="aligncenter" width="800"]
Figure 4. The meshes of MoM[/caption]
All the above are some mainstream electromagnetic algorithms, which play a decisive role in the solution methods and application of electromagnetic CAE. Of course, there’s no such a comparison of which one is better or worse. It’s just that they are suitable for different circumstances. Which algorithm to choose is up to what objects you are going to analyze, and what analysis results you want to get.
This summary is based on my own experience, and “not suitable” doesn’t necessarily mean “cannot”, but more calculation time and memory footprint are needed. Hope it gives you some ideas about different electromagnetic algorithms.