Electro-Magnetica Numerica version 1.4.8 is examined with a simple microwave resonator case to comfirm if the numerical solution is reliable or not. Comparing the analytical solutions with the numerical results it shows a good agreement. The accuracy of the numerical results goes to be better as is the grid becomes finer. The report, TR-HA-023 (html),(pdf) is opened (in Japanese only).
Applying electromagnetic wave to a dielectric spherical resonator, the partial em-wave is trapped inside of the resonator. The rosonant eigen mode waves are categorized in Transversal Electric (TE) mode and in Transversal Magnetic (TM) mode. They are perpendicular with respect to the radial direction of the sphere. The equation for the solution is derived by Gastine[1] et al.. The equation includes special functions such as Bessel function so it was not easy one to solve analytically. But we now have a powerful tool to evaluate the solution numerically. We use Octave [2] to evaluate the solution. The solutions of the Gastine's equation of a particular dielectric sphere are shown in the table. They are the case of TE mode.
| n | Hz |
| 1 | 2.3161 x 10^8 |
| 2 | 3.2638 x 10^8 |
| 3 | 4.3117 x 10^8 |
| 4 | 5.2364 x 10^8 |
Next, we perform numerical simulation using our EM to compare the evaluated Gastine's solutions. The simulation model has the dielectric resonator at the origin and a impulsive plane wave is applied to the resonator. As the simulation goes on several resonant mode waves are remained in the simulation. We probed the electricmagnetic field at several locations and got time series of the physical values. The time series were Fourier-trnasformed to obtain the frequency components. We had several peak in the Fourier domain as is shown in the following figures. Each figure are close view of the corresponding resonant frequencies which are Gastine's solutions. All figure shows the EM solutions give good agreement with the Gastine's solutions. It is noteworthy that the EM solutions of Grid Level 5-3 give the closest solutions to the Gastine's solutions. This means our Blocked Adaptive Cells works very well with this application.
 diel_sphere1.em3 | [ ] | 2 kB |
日本語 (JP)