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Halpern, Laurence

Absorbing boundary conditions for the discretization schemes of the one- dimensional wave equation. (English) Zbl 0482.65053

Math. Comput. 38, 415-429 (1982).
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Cited in 24 Documents

MSC:

65N06 Finite difference methods for boundary value problems involving PDEs
35L05 Wave equation
65N15 Error bounds for boundary value problems involving PDEs

Keywords:

absorbing boundary conditions; artificial boundaries; ill-posed problem; stable boundary conditions fitting to the discretization scheme
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\textit{L. Halpern}, Math. Comput. 38, 415--429 (1982; Zbl 0482.65053)
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References:

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[2] R. W. Clayton & B. Engquist, ”Absorbing boundary conditions for the numerical solution of wave propagation problems,” SSA Bull., v. 6, 1977, pp. 1529-1540.
[3] R. W. Clayton & B. Engquist, ”Absorbing boundary conditions for wave-equation migration,” Geophysics, v. 45, 1980, pp. 895-904.
[4] Bjorn Engquist and Andrew Majda, Absorbing boundary conditions for the numerical simulation of waves, Math. Comp. 31 (1977), no. 139, 629 – 651. · Zbl 0367.65051
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[6] L. Halpern, Etude de Conditiones aux Limites Absorbantes pour des Schémas Numériques Relatifs à des Equations Hyperboliques Linéaires, Thèse de 3éme cycle, Université Paris VI, Septembre 1980.
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[9] Andrew Majda and Stanley Osher, Reflection of singularities at the boundary, Comm. Pure Appl. Math. 28 (1975), no. 4, 479 – 499. , https://doi.org/10.1002/cpa.3160280404 Andrew Majda and Stanley Osher, Erratum: ”Reflection of singularities at the boundary” (Comm. Pure Appl. Math. 28 (1975), no. 4, 479 – 499), Comm. Pure Appl. Math. 28 (1975), no. 5, 677. · Zbl 0314.35061
[10] 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. · Zbl 0267.35001
[11] A. C. Reynolds, ”Boundary conditions for the numerical solution of wave propagation problems,” Geophysics, v. 43, 1978, pp. 1099-1110.
[12] W. D. Smith, ”A non reflecting plane boundary for wave propagation problems,” J. Comput. Phys., v. 15, 1974, pp. 492-503. · Zbl 0287.73024
[13] Gilbert Strang and George J. Fix, An analysis of the finite element method, Prentice-Hall, Inc., Englewood Cliffs, N. J., 1973. Prentice-Hall Series in Automatic Computation. · Zbl 0356.65096
[14] Michael E. Taylor, Reflection of singularities of solutions to systems of differential equations, Comm. Pure Appl. Math. 28 (1975), no. 4, 457 – 478. · Zbl 0332.35058
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