# A Fast and Accurate Method for Computing the Microwave Heating of Moving Objects
## 1 Introduction  
Microwave heating has been widely used in many fields in the past few decades, including food processing, chemical engineering, medical health, and even graphene production [1; 2; 3; 4]. Compared with traditional heating methods, it has numerous advantages like selective energy absorption, high-speed startup, high energy efficiency, and volumetric heating [5; 6; 7]. However, uneven heating, mainly caused by the mixed modes of the microwave cavity, is still one of the major drawbacks, which hinders the widespread applications of microwave heating in various fields [8]. For a domestic microwave oven, adding a turntable is one of the most effective methods to improve the uniformity of temperature distribution during the microwave heating process [9; 10]. In this case, the heated sample goes through different locations with different intensities of electromagnetic fields by rotating with the turntable, so that each part of the sample absorbs roughly the same amount of microwave energy. However, as one of the most effective and economical methods for designing and optimizing microwave heating, numerical simulation of this process is quite difficult because its mathematical model simultaneously couples electromagnetic field, thermal field, and temperature-dependent moving objects [9]. To simulate this kind of microwave heating, [PERSON] et al. proposed dividing a continuous rotation cycle into 24 steps for the first time, i.e., the turntable rotates 15\({}^{\circ}\) per step. The electromagnetic field distribution of each step was calculated and stored as the heating source for the following heat transfer analysis [11]. However, in their computation the dielectric properties of the sample were considered as temperature-independent. Actually, they usually vary with temperature during the heating process, which may further affect the absorption of electromagnetic energy. As a result, the temperature field may change dramatically since the applied microwave power mostly reaches thousands of watts especially in industrial applications [12]. To solve this problem, [PERSON] et al. added a procedure to renew the dielectric properties after the temperature distribution was calculated for each time step [13; 14]. However, the heated objects should be remeshed after moving to another location and the mesh elements are normally different from those of the previous step. Therefore, the temperature of the new mesh node cannot exactly be inherited from that of the original mesh node, which creates calculation errors for each remeshing. For a long heating process, the errors will gradually be accumulated and the accuracy of the calculation will become worse and worse. To obtain a better mesh-match during the rotation, a definite sliding interface between the moving and fixed parts was introduced by [PERSON] et al. for ensuring that the nodes were connected during rotating [9]. However, this method is only suitable for heated objects with simple shapes such as cuboids and cylinders, because the setup of the sliding interface will be very complicated for an object with irregular shapes. To simplify the temperature iteration in the heated samples between the different rotational positions, [PERSON] et al. rotated the microwave cavity instead of the rotating object. At the same time, the dielectric properties of the heated samples were renewed when the turntable rotates to a new position (typical) or rotates a circle (simplified) (i.e., updating at the beginning of each rotational step (every 0.83 s) and at the beginning of each cycle (every 10 s).) [15]. However, their untimely updating strategy may lead to serious calculation errors especially for the temperature-sensitive samples heated by a high-power microwave because the dielectric properties can change significantly even in each time step [12]. Therefore, in order to obtain more accurate simulation results, the dielectric properties of the heated sample should be updated more frequently at each position, rather than assumed to be constant.