Exact local nonreflecting boundary conditions for time-dependent multiple scattering

In [2, 3] a nonreflecting boundary condition(NBC) for time-dependent multiple scattering was derived, which is local in time but nonlocal in space. Here, based on a high-order local nonreflecting boundary condition (NBC) for single scattering [4], we seek a local NBC for time-dependent multiple scattering, which is completely local both in space and time. To do so, we first develop a high order representation formula for a purely outgoing wave field, given its values and those of certain auxiliary functions needed for the artificial boundary condition. By combining that representation formula with a decomposition of the total scattered field into purely outgoing contributions, we obtain the first exact, completely local, NBC for time-dependent multiple scattering. The accuracy and stability of this local NBC is evaluated by coupling it to standard finite element and finite difference methods. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)