Three-dimensional immersed finite-element method for anisotropic magnetostatic/electrostatic interface problems with nonhomogeneous flux jump

Anisotropic diffusion is important to many different types of common materials and media. Based on structured Cartesian meshes, we develop a three-dimensional (3D) nonhomogeneous immersed finite-element (IFE) method for the interface problem of anisotropic diffusion, which is characterized by an anisotropic elliptic equation with discontinuous tensor coefficient and nonhomogeneous flux jump. We first construct the 3D linear IFE space for the anisotropic nonhomogeneous jump conditions. Then we present the IFE Galerkin method for the anisotropic elliptic equation. Since this method can efficiently solve interface problems on structured Cartesian meshes, it provides a promising tool to solve the physical models with complex geometries of different materials, hence can serve as an efficient field solver in a simulation on Cartesian meshes for related problems, such as the particle-in-cell simulation. Numerical examples are provided to demonstrate the features of the proposed method.