An interface‐enriched generalized finite element analysis for electromagnetic problems with non‐conformal discretizations

Abstract

SUMMARYAn interface-enriched generalized finite element method is presented for analyzing electromagnetic problems involving highly inhomogeneous materials. To avoid creating conformal meshes within a complex computational domain and preparing multiple meshes during optimization, enriched vector basis functions are introduced over the finite elements that intersect the material interfaces to capture the normal derivative discontinuity of the tangential field component. These enrichment functions are directly constructed from a linear combination of the vector basis functions of the sub-elements. Several numerical examples are presented to verify the method with analytical solutions and demonstrate its h-refinement convergence rate. The proposed interface-enriched generalized finite element method is shown to achieve the same level of accuracy as the standard finite element method based on conformal meshes. Two examples, involving multiple microvascular channels and circular inclusions of different radii, are analyzed to illustrate the capability of the proposed approach in handling complicated inhomogeneous geometries.

Multiscale design of three‐dimensional nonlinear composites using an interface‐enriched generalized finite element method

“…The nonlinear equations describing the equilibrium at the microscale are solved using the IGFEM. A recent addition to the family of generalized (GFEM) or extended (XFEM) finite element methods, the IGFEM allows for the simulation of the thermal, 22,23,37 structural, 24,38 and/or electromagnetic 39,40 response of heterogeneous materials using finite element meshes that do not conform to the material microstructure. As its GFEM and XFEM counterparts, the method relies on the enrichment of the finite element solution in the elements traversed by the material interfaces.…”