On the accurate longtime solution of the wave equation in exterior domains: asymptotic expansions and corrected boundary conditions
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 by Thomas Hagstrom, S. I. Hariharan and R. C. MacCamy PDF
 Math. Comp. 63 (1994), 507539 Request permission
Abstract:
We consider the solution of scattering problems for the wave equation using approximate boundary conditions at artificial boundaries. These conditions are explicitly viewed as approximations to an exact boundary condition satisfied by the solution on the unbounded domain. We study both the short and longtime behavior of the error. It is proved that, in two space dimensions, no local in time, constantcoefficient boundary operator can lead to accurate results uniformly in time for the class of problems we consider. A variablecoefficient operator is developed which attains better accuracy (uniformly in time) than is possible with constantcoefficient approximations. The theory is illustrated by numerical examples. We also analyze the proposed boundary conditions, using energy methods and leading to asymptotically correct error bounds.References

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Additional Information
 © Copyright 1994 American Mathematical Society
 Journal: Math. Comp. 63 (1994), 507539
 MSC: Primary 65N12; Secondary 35B40
 DOI: https://doi.org/10.1090/S00255718199412489701
 MathSciNet review: 1248970