Shape Optimization of Microwave Cavity Using Arbitrary Lagrangian–Euler Method to Improve the Heating Uniformity

In the application of microwave heating, how to design and optimize a microwave cavity to improve heating uniformity is still a challenge. In this work, a shape optimization algorithm based on the arbitrary Lagrangian–Euler (ALE) method is developed to optimize the geometry of the microwave cavity. By introducing the ALE method, the precise boundary shape is obtained through optimization on the premise that the cavity structure topology remains unchanged to improve the heating uniformity. A 2-D model and a 3-D model are used to illustrate the proposed method in detail. The results of the 3-D model show that compared with the initial design, the heating uniformity of the optimal design is improved by 95%, and the heating efficiency is also improved by 29%. At the same time, the optimized boundary shape is 3-D printed for experimental verification, and the temperature is measured through the experiment, which verifies the rationality and accuracy of the proposed method.