Calculation of microwave heating temperature distribution based on SVD truncation

Abstract

In mathematical models of microwave heating with infinite-dimensional characteristics, it is difficult to use traditional numerical methods to improve computational efficiency. In this work, we propose a fast and accurate method to calculate the temperature distribution of materials under microwave heating. First, we analysed the relationship between the choice of model order and the solution accuracy by downscaling the infinite-dimensional heat conduction partial differential equation (PDE) model into a finite-dimensional ordinary differential equation (ODE) model. Additionally, the effect of different boundary conditions on the global temperature distribution was analysed. Second, the equilibrium conversion matrix was calculated using the singular value decomposition (SVD) truncation method under homogeneous boundary conditions. Using this matrix, a lower-dimensional microwave heating ODE model was further obtained. Finally, the numerical simulation results showed that the root mean square error (RMSE) was only 0.07 and the maximum relative error was only −0.85%. The computation time of the equilibrium conversion matrix was 2.12 ∼ 3.00 ms, and the model calculation time was reduced by 97.78%. We compared the calculated temperature rise curves with those obtained using the conventional COMSOL model. The SVD truncation method achieved an efficient and accurate solution for the microwave heating model.