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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Absorbing boundary conditions for the numerical simulation of waves
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by Bjorn Engquist and Andrew Majda PDF
Math. Comp. 31 (1977), 629-651 Request permission

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
  • Heinz-Otto Kreiss, Initial boundary value problems for hyperbolic systems, Comm. Pure Appl. Math. 23 (1970), 277–298. MR 437941, DOI 10.1002/cpa.3160230304
  • Andrew Majda and Stanley Osher, Reflection of singularities at the boundary, Comm. Pure Appl. Math. 28 (1975), no. 4, 479–499. MR 492792, DOI 10.1002/cpa.3160280404
  • Louis Nirenberg, Lectures on linear partial differential equations, Conference Board of the Mathematical Sciences Regional Conference Series in Mathematics, No. 17, 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. 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 10.1002/cpa.3160280403
  • 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 10.1090/S0002-9947-1974-0340832-0
  • 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.
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Additional Information
  • © Copyright 1977 American Mathematical Society
  • Journal: Math. Comp. 31 (1977), 629-651
  • MSC: Primary 65M05; Secondary 65N99
  • DOI: https://doi.org/10.1090/S0025-5718-1977-0436612-4
  • MathSciNet review: 0436612