## 5 Conclusions  
This paper proposed a method that combines the implicit function and transformation optics to compute the heating cavity with two types of moving elements and solves the challenge of the multi-physical field in the microwave heating process with spiral motion. The rotating motion of samples was computed by the transformation optics method, and the lifting motion of the sample was computed by the implicit function and level set methods. A 3D computation model was proposed, and the proposed method's correctness was verified by computing regular samples. The outstanding contributions of this paper are that (1) we propose to use two transform optical regions for computing the rotating motion of the sample, and we propose to couple the transformation optics method with the implicit function and level set method. The results show that the two methods are well coupled. (2) The accuracy of the proposed method was verified through experiments, and the computation accuracy of the proposed method was better than that of the implicit function and level set method only. Moreover, we compared the computational details between the proposed method and the implicit function and level set method, and the results show that the proposed method takes longer but has a lower _RMSE_ when both methods have the same number of elements. When the two methods have similar _RMSE_, the proposed algorithm takes 62.8% less computational time. (3) We used the proposed method to compute and analyze the effects of fixed-position heating, only rotating heating, or only lifting heating and lifting rotary heating on the heating uniformity and heating efficiency of samples. The results show that although the heating efficiency of the sample may be higher in a few locations, the hot spot distribution is only on one side, and the rotating motion can improve the heating uniformity of the sample more significantly. Therefore, the two motion modes can be combined in the heating process so that the spiral motion can further improve the heating uniformity and heating efficiency of the sample. However, the proposed method is currently only able to compute the spiral heating motion of a regular sample due to the limitation of the need to characterize the boundaries of the sample as a function.  
The proposed method combines the transformation optics method with the implicit function and level set methods and provides a case for solving other microwave heating cavities with different moving elements. In the future, it is hoped that the proposed method can be applied to the multi-physical field computation of complex samples.  
**Author Contributions:** H.C., conceptualization, methodology, software, writing--original draft preparation. H.G., data curation, writing--original draft preparation. H.Z. and Y.Y., project administration, resources, visualization, funding acquisition. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This work was supported by the National Natural Science Foundation of China (Grant No. 61971295), in part by the National Key Project GJXM92579.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The data presented in this study are available in article.  
**Acknowledgments:** Thanks to [PERSON] and [PERSON] for financial support. Thanks to [PERSON] and [PERSON] for help during the experiment and English editing.  
**Conflicts of Interest:** The authors declare no conflict of interest.