Immersed finite element methods for unbounded interface problems with periodic structures

• Published in: Journal of computational and applied mathematics Vol. 307; pp. 72 - 81
• Main Authors: Cao, Yong, Chu, Yuchuan, Zhang, Xiaoshi, Zhang, Xu
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.12.2016
• Subjects: Computer simulation; Electrostatic field; Electrostatic fields; Finite element method; Immersed finite element; Linear systems; Mathematical analysis; Mathematical models; Particle in cell technique; Periodic boundary condition; Periodic structures; Unbounded interface problem; Periodic boundary condition; Electrostatic field; Immersed finite element; Unbounded interface problem; Periodic structures
• ISSN: 0377-0427; 1879-1778
• DOI: 10.1016/j.cam.2016.04.020

Interface problems arise in many physical and engineering simulations involving multiple materials. Periodic structures often appear in simulations with large or even unbounded domain, such as magnetostatic/electrostatic field simulations. Immersed finite element (IFE) methods are efficient tools to solve interface problems on a Cartesian mesh, which is desirable to many applications like particle-in-cell simulation of plasma physics. In this article, we develop an IFE method for an interface problem with periodic structure on an infinite domain. To cope with the periodic boundary condition, we modify the stiffness matrix of the IFE method. The new matrix is maintained symmetric positive definite, so that the linear system can be solved efficiently. Numerical examples are provided to demonstrate features of this method.