On local nonreflecting boundary conditions for time dependent wave propagation

Chinese Annals of Mathematics (Impact Factor: 0.5). 01/2009; 30(5):589-606. DOI: 10.1007/s11401-009-0203-5

ABSTRACT The simulation of wave phenomena in unbounded domains generally requires an artificial boundary to truncate the unbounded
exterior and limit the computation to a finite region. At the artificial boundary a boundary condition is then needed, which
allows the propagating waves to exit the computational domain without spurious reflection. In 1977, Engquist and Majda proposed
the first hierarchy of absorbing boundary conditions, which allows a systematic reduction of spurious reflection without moving
the artificial boundary farther away from the scatterer. Their pioneering work, which initiated an entire research area, is
reviewed here from a modern perspective. Recent developments such as high-order local conditions and their extension to multiple
scattering are also presented. Finally, the accuracy of high-order local conditions is demonstrated through numerical experiments.

KeywordsAbsorbing boundary conditions-Scattering problems-Wave equation
2000 MR Subject Classification65M99

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