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What is Yee grid? How does it become the core of FDTD?
In numerical analysis, the Yee lattice is undoubtedly the core element that drives the computational electrodynamics (FDTD) model. This technology was first proposed by the famous Chinese-American mathematician Yee in 1966. Its basic concept is to disperse the electric and magnetic fields of Maxwell's equations on a staggered grid. In short, the innovation of Yee lattice is that it can naturally handle the time and space characteristics of electromagnetic fields and is suitable for various material structures.
The FDTD method not only covers multiple frequency ranges, but also handles nonlinear material properties naturally.
The main contribution of the Yee lattice is that it can store the electric field (E-field) and the magnetic field (H-field) in a saturated grid point respectively, which enables more accurate numerical solutions to be obtained in calculations. The core of the FDTD method is to understand the relationship between the electric field and magnetic field in Maxwell's equations with time and space. Through this relationship, the Yee grid can estimate the electric and magnetic fields at each point in time with a "jumping" progress, which is why its name comes from the concept of "lattice".
Since then, FDTD technology has rapidly been applied in many fields of science and engineering, especially in wireless communications, radar technology, medical imaging, etc. For example, in wireless communications, FDTD can simulate the propagation characteristics of signals between different materials, allowing designers to accurately predict the performance of equipment in actual environments.
In 2006, it is estimated that more than 2000 FDTD-related publications appeared in the scientific and engineering literature.
The operating principle of FDTD is to numerically discretize the electric and magnetic fields of Maxwell's equations, and then repeatedly update the values of these field quantities through time. Specifically, at one time, the value of the electric field is calculated and then updated based on the known magnetic field value, and then at the next time the value of the magnetic field is updated. This jumping time calculation method allows FDTD to cover a wide frequency range simultaneously in a single simulation without having to perform multiple simulation calculations repeatedly.
Before using the FDTD method for simulation, you need to first establish the calculation area, which is the physical area for simulation. The material properties of each grid point must be explicitly set, usually including free space (such as air), metal or dielectric, etc. It is worth mentioning that for some dispersive materials, the required dielectric constant needs to be obtained through some approximation methods.
FDTD is an intuitive modeling technique that allows users to easily understand how to use it and predict the results that will be obtained under a specific model.
Although FDTD has many advantages, it also has some limitations. The time taken when dealing with large computational domains can be very long since the entire computational domain needs to be meshed and the spatial discretization should be fine enough to resolve the highest frequency electromagnetic waves. In addition, for long and thin geometric features (for which FDTD does not perform well), researchers may need to consider other efficient methods to solve the problem.
With the advancement of computer technology and the development of parallel processing technology, the practicability of FDTD is becoming more and more widespread. Today, many software vendors provide commercial and open source FDTD simulation tools, making it easier for researchers and engineers to conduct electromagnetic field analysis.
In the future, the development prospects of FDTD are still promising, especially with further research on quantum electrodynamics, this method has the potential to be combined with other complex problems. Will new breakthroughs be born based on this computing tool?
