Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Absorbing boundary conditions for the numerical simulation of waves

Authors: Bjorn Engquist and Andrew Majda
Journal: Math. Comp. 31 (1977), 629-651
MSC: Primary 65M05; Secondary 65N99
MathSciNet review: 0436612
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In practical calculations, it is often essential to introduce artificial boundaries to limit the area of computation. Here we develop a systematic method for obtaining a hierarchy of local boundary conditions at these artificial boundaries. These boundary conditions not only guarantee stable difference approximations but also minimize the (unphysical) artificial reflections which occur at the boundaries.

References [Enhancements On Off] (What's this?)

  • Heinz-Otto Kreiss, Initial boundary value problems for hyperbolic systems, Comm. Pure Appl. Math. 23 (1970), 277–298. MR 437941, DOI
  • Andrew Majda and Stanley Osher, Reflection of singularities at the boundary, Comm. Pure Appl. Math. 28 (1975), no. 4, 479–499. MR 492792, DOI
  • Louis Nirenberg, Lectures on linear partial differential equations, American Mathematical Society, Providence, R.I., 1973. Expository Lectures from the CBMS Regional Conference held at the Texas Technological University, Lubbock, Tex., May 22–26, 1972; Conference Board of the Mathematical Sciences Regional Conference Series in Mathematics, No. 17. MR 0450755
  • Michael E. Taylor, Reflection of singularities of solutions to systems of differential equations, Comm. Pure Appl. Math. 28 (1975), no. 4, 457–478. MR 509098, DOI
  • Jeffrey B. Rauch and Frank J. Massey III, Differentiability of solutions to hyperbolic initial-boundary value problems, Trans. Amer. Math. Soc. 189 (1974), 303–318. MR 340832, DOI
  • DAVID M. BOORE, "Finite difference methods for seismic wave propagation in heterogeneous materials," Methods of Comp. Physics (Seismology), v. 11, 1972, pp. 1-37.
  • K. R. Kelly, R. M. Alford, S. Treitel, and R. W. Ward, Application of finite difference methods to exploration seismology, Topics in numerical analysis, II (Proc. Roy. Irish Acad. Conf., Univ. College, Dublin, 1974) Academic Press, London, 1975, pp. 57–76. MR 0408753
  • Patrick J. Roache, Computational fluid dynamics, Hermosa Publishers, Albuquerque, N.M., 1976. With an appendix (“On artificial viscosity”) reprinted from J. Computational Phys. 10 (1972), no. 2, 169–184; Revised printing. MR 0411358
  • T. ELVIUS & A. SUNDSTRÖM, "Computationally efficient schemes and boundary conditions for a fine mesh barotropic model based on the shallow water equations," Tellus, v. 25, 1973, pp. 132-156. E. L. LINDMAN, "Free space boundary conditions for the time dependent wave equation," J. Computational Phys., v. 18, 197S, pp. 66-78. I. ORLANSKI, "A simple boundary condition for unbounded hyperbolic flows," J. Computational Phys., v. 21, 1976, pp. 251-269. M. E. HANSON & A. G. PETSCHEK, "A boundary condition for sufficiently reducing boundary reflection with a Lagrangian mesh," J. Computational Phys., v. 21, 1976, pp. 333-339. W. D. SMITH, "A nonreflecting plane boundary for wave propagation problems," J. Computational Phys., v. 15, 1974, pp. 492-503.

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65M05, 65N99

Retrieve articles in all journals with MSC: 65M05, 65N99

Additional Information

Article copyright: © Copyright 1977 American Mathematical Society