Extended Finite Element Method for Electromagnetic Fields

This paper presents the fundamental principle of the extended finite element method (XFEM) for electromagnetic field analysis. This method provides an accurate approximation for locally non-smooth features within finite elements, such as singularities, discontinuities, and high derivatives. An alternative enrichment function is introduced to improve the approximation space of the conventional finite element method (CFEM) such that non-smooth solutions are modeled independent of the mesh. The level set method is employed to describe the interfaces among different materials. To demonstrate the advantages, the XFEM is compared with CFEM by solving a 1D electrical field problem.