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.


Mathematics and Statistics

Research Center/Lab(s)

Center for High Performance Computing Research


This work was supported by the National Natural Science Foundation of China (Grant number 11175052); the Open fund for Science and Technology on Vacuum Technology and Physics Laboratory, Lanzhou Institute of Physics, under Contract no. ZWK1703; and the Program of Shenzhen Technology Projects (JCYJ20160817172025986, JCYJ20180306171941256, and ZDSYS201707280904031).

Keywords and Phrases

Anisotropic Interface Problem; Cartesian Meshes; Immersed Finite Elements; Nonhomogeneous Flux Jump

International Standard Serial Number (ISSN)

0029-5981; 1097-0207

Document Type

Article - Journal

Document Version


File Type





© 2020 John Wiley & Sons Ltd, All rights reserved.

Publication Date

01 May 2020