A 3-D Interface-Enriched Generalized FEM for Electromagnetic Problems With Nonconformal Discretizations

Abstract

An interface-enriched generalized finite-element method (IGFEM) is introduced for efficient 3-D electromagnetic analysis of heterogeneous materials. Without using meshes that conform to the material microstructures, which greatly lessens the burden of mesh generation, the method assigns generalized degrees of freedom (DOFs) at material interfaces to capture the discontinuities of the field and its derivatives. The generalized DOFs are supported by enriched vector basis functions (VBFs), which are constructed through a linear combination of the VBFs from the subelements. Several verification examples are provided to show that the IGFEM is not sensitive to the quality of the subelements and maintains the same level of solution accuracy and computational complexity as the standard finite-element method (FEM) based on conformal meshes. The potential of the proposed IGFEM is demonstrated by simulating some engineering problems with complex, periodic internal structures, including composite materials with randomly distributed spherical particles and ellipsoidal inclusions and microvascular channels.