## 1 Introduction  
As a highly reliable and environmentally adaptable heat dissipation device, axial flow fans are widely used in land-based, sea-based, aerospace, and other fields to dissipate heat from electronic equipment. As shown in Figure 1, an axial flow fan is usually composed of a fan frame, an impeller, and a motor, in which the brushless DC motor is directly connected to the impeller, driving it to rotate and forcing the air to flow in the axial direction to realize convection heat transfer. To meet the heat dissipation requirements of different working conditions, the fan will continuously adjust the speed according to the change in the heat load. Due to high rates of variations in current and voltage, the use of PWM technology in the speed regulation process can generate conducted interference and form a radiated interference through the inner components, affecting the proper operation of electronic equipment. Therefore, it is necessary to predict and control the electromagnetic radiation emissions from the fans [1, 2, 3, 4]. Currently, numerical simulation methods are mostly used for the analysis of electromagnetic radiation interference. Commonly used numerical analysis methods include the equivalent circuit method [5; 6], the finite difference time domain (FDTD) method [7], the finite element method (FEM) [8], the partial element equivalent circuit (PEEC) method [9], and the finite integration technique (FIT) [10]. The equivalent circuit method is computationally fast and suitable for small-volume structures, but it is difficult to show the details of the field distribution in space. The FDTD method can effectively deal with electromagnetic wave problems, but the computational accuracy is limited by the metric mesh step approximation. FEM is suitable for dealing with complex dielectric distributions, but the number of meshes is large and the calculation speed is slow. The PEEC method can link the transient models of multi-conductor systems to circuits, but it is more difficult to model structures with magnetic materials. The finite integration method is a numerical solution method derived directly from the integral form of [PERSON]'s equations. It defines the integral quantities of field variables on the edges or faces of a grid as the degrees of freedom to be solved. Discrete matrix equations can be directly obtained within the solution domain via this method. Compared to the FDTD method and the FEM, the FIT utilizes integral quantities as state variables, which confers a speed advantage in solving fast transient and complex structures. In addition, the finite integration method supports parallel computation resulting in reduced memory consumption and computation time. In related research, [PERSON] [11] implemented the field-circuit coupling method, which integrates nonlinear circuit components with spatially discretized field models into the system equations for resolution. Other scholars have presented simulation analyses based on finite integral theory for electrostatic discharge generators, grounding networks considering frequency-variable parameters, power transformers, and motor drive systems [12; 13; 14; 15]. The studies above indicate that the finite integral method demonstrates high efficiency and accuracy in solving electromagnetic field problems and represents a numerical method for solving complex systems efficiently. In the process of electromagnetic radiation analysis of electronic equipment, as a local radiation source, the dimensions of the axial flow fan are typically significantly different from the entire dimensions of the equipment. Due to the complex internal structure and small size of the fan, if a refined meshing is used to discretize the entire region, it will result in a large number of grids, making the simulation difficult to complete. While non-uniform  
Figure 1: Electronic enclosure with axial flow fans for heat dissipation.