  This paper is concerned with a numerical solution to the scattering of a
time-harmonic electromagnetic wave by a bounded and impenetrable obstacle in
three dimensions. The electromagnetic wave propagation is modeled by a boundary
value problem of Maxwell's equations in the exterior domain of the obstacle.
Based on the Dirichlet-to-Neumann (DtN) operator, which is defined by an
infinite series, an exact transparent boundary condition is introduced and the
scattering problem is reduced equivalently into a bounded domain. An a
posteriori error estimate based adaptive finite element DtN method is developed
to solve the discrete variational problem, where the DtN operator is truncated
into a sum of finitely many terms. The a posteriori error estimate takes into
account both the finite element approximation error and the truncation error of
the DtN operator. The latter is shown to decay exponentially with respect to
the truncation parameter. Numerical experiments are presented to illustrate the
effectiveness of the proposed method.
