A non-overlapping domain decomposition for low-frequency time-harmonic Maxwell's equations in unbounded domains

In this paper, we are concerned with a non-overlapping domain decomposition method for solving the low-frequency time-harmonic Maxwell’s equations in unbounded domains. This method can be viewed as a coupling of the finite element and the boundary element in unbounded domains, which are decomposed into two sub-domains with a spherical artificial boundary. We first introduce a discretization for the coupled variational problem by combining Nédélec element of the lowest order and a curvilinear element. Then we design a D-N alternating method for solving the discrete problem. In the method, one needs only to solve the finite element problem (in a bounded domain) and to calculate some boundary integrations, instead of solving a boundary integral equation. It will be shown that such iterative algorithm converges with a rate independent of the mesh size.