Local nonreflecting boundary condition for Maxwell’s equations

Abstract

An exact nonreflecting boundary condition is derived for the time dependent Maxwell equations in three space dimensions. It is local in space and time, and it holds on a spherical surface B of radius R, outside of which the medium is assumed to be homogeneous, isotropic, and source-free. This boundary condition does not involve high-order derivatives, but instead an infinite sequence of auxiliary variables defined on B . In practice, only a finite number, P, of auxiliary variables is used. Then, the boundary condition remains exact for any combination of spherical harmonics up to order P, while the error introduced at B generally behaves like R −2( P+1) . Hence, P can always be chosen large enough to reduce the error introduced at B below the discretization error inside the computational domain, at any fixed R. Because it does not involve high-order derivatives, this local boundary condition is easily combined with standard numerical methods and enables arbitrarily high order implementations. Numerical examples with the FDTD method demonstrate the usefulness and high accuracy of this local nonreflecting boundary condition.