×

zbMATH — the first resource for mathematics

Absorbing boundary conditions for the numerical simulation of waves. (English) Zbl 0367.65051

MSC:
65N06 Finite difference methods for boundary value problems involving PDEs
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
35L20 Initial-boundary value problems for second-order hyperbolic equations
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Heinz-Otto Kreiss, Initial boundary value problems for hyperbolic systems, Comm. Pure Appl. Math. 23 (1970), 277 – 298. · Zbl 0188.41102 · doi:10.1002/cpa.3160230304 · doi.org
[2] 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 · doi:10.1002/cpa.3160280504 · doi.org
[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. · Zbl 0267.35001
[4] 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 · doi:10.1002/cpa.3160280403 · doi.org
[5] 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. · Zbl 0282.35014
[6] DAVID M. BOORE, ”Finite difference methods for seismic wave propagation in heterogeneous materials,” Methods of Comp. Physics (Seismology), v. 11, 1972, pp. 1-37.
[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. · Zbl 0335.65053
[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. · Zbl 0247.76035
[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. 132-156.
[10] E. L. LINDMAN, ”Free space boundary conditions for the time dependent wave equation,” J. Computational Phys., v. 18, 197S, pp. 66-78. · Zbl 0417.73042
[11] I. ORLANSKI, ”A simple boundary condition for unbounded hyperbolic flows,” J. Computational Phys., v. 21, 1976, pp. 251-269. · Zbl 0403.76040
[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. 333-339.
[13] W. D. SMITH, ”A nonreflecting plane boundary for wave propagation problems,” J. Computational Phys., v. 15, 1974, pp. 492-503. · Zbl 0287.73024
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.