For the wood moisture content (MC) detection engineering problem by planar capacitive sensors, a high accuracy is required. To meet this demand, we constructed a mathematical model in this paper, as this is an inverse problem in the multi-physics fields. Furthermore, we proposed a new numerical method with high accuracy, which is called the multiple varying bounds integral method. We applied this numerical method to establish a high accuracy and compact numerical scheme for solving this model. Because the unknown function is continuous in some physical fields and discontinuous in others, we needed to use different numerical methods to construct numerical schemes in these fields. For example, we used the multiple varying bounds integral (MVBI) method and interpolation methods. Next, based on the results of the numerical experiments, a regression model was established between capacitance and the dielectric constant of wood. The results indicated that the larger the value of dielectric constant, the larger the value of capacitance. This is consistent with the physical principle. Moreover, the determination coefficient $R^2$ of the regression model was greater than 0.91. Additionally, the confidence degree exceeded 0.99, which implies that the reliability of the regression model is strong. This indicates that the regression model shows a high goodness of fit and high confidence degree.