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Nonreflecting Boundary Conditions for Time Dependent Wave Propagation

by M. J. Grote

(Report number 2000-04)

Abstract
Time dependent problems in unbounded media arise in many applications such as acoustic or electromagnetic scattering. Numerical methods can handle complicated geometries, inhomogeneous media, and nonlinearities. However, they require an artificial boundary, which truncates the unbounded exterior domain. Therefore an absorbing boundary condition needs to be applied at the artificial boundary to minimize the amount of spurious reflection from it. First, the derivation of the exact nonreflecting boundary condition for the one-dimensional wave equation is briefly reviewed. Next, the two- and three-dimensional cases are discussed, and the trade-off between exactness and locality exemplified through a short discussion of local absorbing boundary conditions. Then, the derivation of the nonreflecting boundary condition for the time wave equation in three space dimensions (Grote and Keller, 1995) is reviewed. The derivation is outlined without all the technical details and proofs, but instead by emphasizing the underlying main ideas. It is also shown how to combine the nonreflecting boundary condition both with the finite difference and the finite element methods. Finally, the accuracy and convergence properties of various absorbing and nonreflecting boundary conditions are compared via two numerical experiments.

Keywords:

@Techreport{G00_263,
  author = {M. J. Grote},
  title = {Nonreflecting Boundary Conditions for Time Dependent Wave Propagation},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2000-04},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2000/2000-04.pdf },
  year = {2000}
}

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