Many numerical methods have been developed in the past for solving electromagnetic problems. In this paper, we first present the development of these numerical methods with a single mathematical framework of the method of weighted residuals. We then propose a unifying computational platform with the node-based meshless method. It not only unifies the numerical methods developed so far, but also allows easy hybridization of different methods. A numerical example of H-shape cavity is shown to verify the efficiency and accuracy of the proposed platform.

The reliability design of automotive structures is characterized by numerous variables and implicit responses. The traditional design of experiments for metamodel construction often requires manual adjustment of model parameters and extensive finite element analysis, resulting in inefficiency. To address these issues, active learning-based reliability methods are effective solutions. This study proposes an active-learning reliability analysis method based on multi-software interaction. Firstly, through secondary development of different software and MATLAB (version 2023a)’s batch processing function, a multi-software interactive reliability analysis method is developed, achieving automation in structural parametric design, finite element analysis and post-processing. This provides a more efficient and convenient platform for the implementation of active learning. Secondly, the polynomial chaos–kriging (PCK) active-learning method is introduced, combining the advantages of polynomial chaos expansion (PCE) and kriging. The PCK method captures the global behavior of the computational model using regression-based PCE and local variations using interpolation-based kriging. This metamodel is constructed with fewer training samples, effectively replacing the real multi-dimensional implicit response relations, thereby improving the efficiency of modeling and reliability analysis. Finally, the specific implementation scheme is detailed. The accuracy and efficiency of the proposed method are verified by a reliability engineering example of body-in-white bending and torsional stiffness.