Absorbing boundary conditions for the numerical simulation of waves
Authors:
Bjorn Engquist and Andrew Majda
Journal:
Math. Comp. 31 (1977), 629651
MSC:
Primary 65M05; Secondary 65N99
MathSciNet review:
0436612
Fulltext 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.
 [1]
HeinzOtto
Kreiss, Initial boundary value problems for hyperbolic
systems, Comm. Pure Appl. Math. 23 (1970),
277–298. MR 0437941
(55 #10862)
 [2]
Andrew
Majda and Stanley
Osher, Reflection of singularities at the boundary, Comm. Pure
Appl. Math. 28 (1975), no. 4, 479–499. MR 0492792
(58 #11858a)
 [3]
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
(56 #9048)
 [4]
Michael
E. Taylor, Reflection of singularities of solutions to systems of
differential equations, Comm. Pure Appl. Math. 28
(1975), no. 4, 457–478. MR 0509098
(58 #22994)
 [5]
Jeffrey
B. Rauch and Frank
J. Massey III, Differentiability of solutions to
hyperbolic initialboundary value problems, Trans. Amer. Math. Soc. 189 (1974), 303–318. MR 0340832
(49 #5582), http://dx.doi.org/10.1090/S00029947197403408320
 [6]
DAVID M. BOORE, "Finite difference methods for seismic wave propagation in heterogeneous materials," Methods of Comp. Physics (Seismology), v. 11, 1972, pp. 137.
 [7]
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
(53 #12516)
 [8]
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
(53 #15094)
 [9]
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. 132156.
 [10]
E. L. LINDMAN, "Free space boundary conditions for the time dependent wave equation," J. Computational Phys., v. 18, 197S, pp. 6678.
 [11]
I. ORLANSKI, "A simple boundary condition for unbounded hyperbolic flows," J. Computational Phys., v. 21, 1976, pp. 251269.
 [12]
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. 333339.
 [13]
W. D. SMITH, "A nonreflecting plane boundary for wave propagation problems," J. Computational Phys., v. 15, 1974, pp. 492503.
 [1]
 H.O. KREISS, "Initial boundary value problems for hyperbolic systems," Comm. Pure Appl. Math., v. 23, 1970, pp. 277298. MR 0437941 (55:10862)
 [2]
 A. MAJDA & S. OSHER, "Reflection of singularities at the boundary," Comm. Pure Appl. Math., v. 28, 1975, pp. 479499. MR 0492792 (58:11858a)
 [3]
 L. NIRENBERG, Lectures on Linear Partial Differential Equations, C.B.M.S. Regional Conf. Ser. in Math., no. 17, Amer. Math. Soc., Providence, R. I., 1973. MR 0450755 (56:9048)
 [4]
 M. E. TAYLOR, "Reflection of singularities of solutions to systems of differential equations," Comm. Pure Appl. Math., v. 28, 1975, pp. 457478. MR 0509098 (58:22994)
 [5]
 F. J. MASSEY III & J. B. RAUCH, "Differentiability of solutions to hyperbolic initialboundary value problems," Trans. Amer. Math. Soc., v. 189, 1974, pp. 303318. MR 49 #5582. MR 0340832 (49:5582)
 [6]
 DAVID M. BOORE, "Finite difference methods for seismic wave propagation in heterogeneous materials," Methods of Comp. Physics (Seismology), v. 11, 1972, pp. 137.
 [7]
 K. R. KELLY, R. M. ALFORD, S. TREITEL & R. W. WARD, Applications of Finite Difference Methods to Exploration Seismology, Proc. Roy. Irish Acad. Conf. on Numerical Analysis, Academic Press, London and New York, 1974, pp. 5776. MR 0408753 (53:12516)
 [8]
 P. J. ROACHE, Computational Fluid Dynamics, Hermosa Press, Albuquerque, N. M., 1972. MR 0411358 (53:15094)
 [9]
 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. 132156.
 [10]
 E. L. LINDMAN, "Free space boundary conditions for the time dependent wave equation," J. Computational Phys., v. 18, 197S, pp. 6678.
 [11]
 I. ORLANSKI, "A simple boundary condition for unbounded hyperbolic flows," J. Computational Phys., v. 21, 1976, pp. 251269.
 [12]
 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. 333339.
 [13]
 W. D. SMITH, "A nonreflecting plane boundary for wave propagation problems," J. Computational Phys., v. 15, 1974, pp. 492503.
Similar Articles
Retrieve articles in Mathematics of Computation
with MSC:
65M05,
65N99
Retrieve articles in all journals
with MSC:
65M05,
65N99
Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718197704366124
PII:
S 00255718(1977)04366124
Article copyright:
© Copyright 1977
American Mathematical Society
