Search

PurposeThis paper proposes to extend the combination of Extended Finite Element Method (XFEM) and Level Set Method (LSM) from structural mechanics to electromagnetics. Based on this approach, the actual stage of the research work, dedicated to the investigation, development, implementation and validation of a shape optimization methodology, particularly tailored for 2D electric structures is described.Design/methodology/approachThe proposed numerical approach is based on the efficiency of the XFEM and the flexibility of the LSM, to handle moving material interfaces without remeshing the whole studied domain at each optimization step.FindingsThis approach eliminates the conventional use of discrete finite elements and provides efficient, stable, accurate and faster computation schemes in comparison with other methods.Research limitations/implicationsThis research is limited to shape optimization of two‐dimensional electric structures, however, the work can be extended to 3D ones too.Practical implicationsThe implementation of the proposed numerical approach for the shape optimization of a planar resistor is hereby described.Originality/valueThe main value of the proposed approach is a powerful and robust numerical shape optimization algorithm that demonstrates outstanding suppleness of handling topological changes, fidelity of boundary representation and a high degree of automation in comparison with other methods.

This paper proposes a method for multi‐terminal resistor optimal design based on a stochastic optimization algorithm coupled with a high accuracy boundary element method numerical analysis module using spline boundary elements. The aim of the optimization process is to find out the optimal shape of the resistor so that the values of the partial resistances between its terminals can be globally reduced. In the first part of the paper, a short introduction to the boundary element method formulation using spline interpolation of the boundary unknowns is performed. Then, the genetic algorithm optimization method is briefly described, emphasising the numerical implementation particularities related to the actual application. In the second part of the paper, three numerical examples are proposed and the final conclusions are outlined.