# A Fast and Accurate Method for Computing the Microwave Heating of Moving Objects
## 3 Results and Discussion
### Temperature Distribution inside the Heated Potato  
The scattering parameters of the waveguide port are also plotted at the end of each second during the entire heating process. As shown in Figure 6, the two curves fit very well and the average relative error of the scattering parameters is only about 0.53% [12]. This further confirms that the proposed method can calculate the electric field distribution inside the microwave oven with good predictability.  
Figure 7 displays the outline of the potato and the temperature distributions on the upper surface of the potato at the 10 th second. It clearly shows that the temperature distributions are obviously non-uniform and their shapes are very similar. For example, both of them have a \"hot ring\" at the center of the potato and the four corners are relatively cool. For further quantitative verification, Figure 8 gives the temperature profile of a potato sample as a function of time at five specific locations defined in Figure 9. As shown in Figure 8a to Figure 8e, the temperatures calculated by the two methods are matched very well, too. Meanwhile, the average temperature curves obtained by these two methods are also in good consistency as plotted in Figure 8f. The qualitative and quantitative analyses of the temperature field prove that the proposed method can be applied to calculate the temperature field of the food with good predictability.  
Figure 5: Multislices of the electric field of the potato inside of a microwave oven computed by the ALE method and the proposed method after heating 0 s, 0.834 s, 1.667 s, and 2.5 s (unit: V/m).  
Figure 6: \(|\mathrm{S}_{11}|\) computed by the proposed method and the ALE method.  
To further evaluate the reliability and efficiency of our method, the standard deviation (\(SD\)) of a point P is defined by [16]:  
\[SD=\sqrt{\frac{1}{n-1}\sum_{i=1}^{n}{(T_{i}-\overline{T}_{i})}}, \tag{7}\]  
Figure 8: Comparison of the time-dependent temperature calculated by the proposed method and the ALE method at the five specific points.  
Figure 7: Outline of potato and temperature distributions on the upper surface of the potato obtained by the ALE method and the proposed method at the 10 th second (top view, unit: \({}^{\circ}\)C).  
Figure 9: The specific locations of the five points (7.5 mm from the top surface).  
where \(T_{i}\) is the temperature of point P at a specific time step \(i\) and \(\overline{T}_{i}\) is the average temperature of the whole potato, and \(n\) is the total time steps of the calculation. The \(SD\) values of the points P1 to P5 and the total computing time are listed in Table 2. It can be clearly noticed that the \(SD\)s calculated by the proposed method are very close to those obtained by the ALE method. It is worth mentioning that compared with the ALE method, the proposed method provides almost the same accuracy only using 5555/50117 or 11% of the computing time. This may possibly be attributed to the movement of the turntable. To guarantee the reliability of the deformed mesh and the continuous rotating in the ALE method, the turntable can only move a small angle and at each step the EM fields and the heat transfer analysis should be solved, which greatly increases the computational time because many steps are needed to simulate rotating a circle. Moreover, the meshes in the air domain of the ALE method are deformed as the turntable moves, causing a decrease in the mesh element quality (MEQ). To solve this problem, the meshes in the air domain will be remeshed when MEQ \(<\) 0.2, which also requires a lot of calculation time. This confirms that the proposed method is much more efficient than the ALE method with desirable accuracy.