Abstract
AbstractIn [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)
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