Immersed finite element methods for unbounded interface problems with periodic structures

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.