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We describe a new artificial boundary conditions technique proposed in our recent work and review the corresponding results

Numerical solution of problems on unbounded domains. a review

Applied Numerical Mathematics - Special issue on absorbing boundary conditions, no. 4 (1998): 465-532

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摘要

While numerically solving a problem initially formulated on an unbounded domain, one typically truncates this domain, which necessitates setting the artificial boundary conditions (ABC's) at the newly formed external boundary. The issue of setting the ABC's appears most significant in many areas of scientific computing, for example, in p...更多

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简介
  • Among other papers devoted to constructing the exact ABCs, the authors mention work by Fix and Marin [52], in which the authors solve the Helmholtz equation in an axially symmetric duct and construct the exact ABCs on its lateral boundary expanding the solution in terms of the trigonometric and Hankel functions; work by Poezd and Yakunin [165], in which the time-dependent propagation of waves through a semi-infinite cylindrical guide is considered and the exact solution of the wave equation is used to set the ABCs at the artificial boundary normal to the cylinder axis; work by Zornmski, Watson and Hodge [109,240,248,249], in which the exact ABCs at the transversal planar artificial boundary are developed for the Helmholtz equation in a semi-infinite rectangular constant-section duct and numerically compared against some localized versions of the boundary conditions by Engquist and Majda [40] and Giles [56]; work by Watson and Zorumski [241], in which the method of [109,248,249] is extended to treat the one-dimensional time-periodic duct acoustic phenomena described by the linearized Euler equations in the far field; work by Jiang and Wong [113], in which the exact NRBC that contains a oaDO is obtained at the planar artificial boundary for a general secondorder hyperbolic equation provided that the corresponding dispersion relation is known; and work by Guillaume and Masmoud [73], in which the boundary conditions for Helmholtz-type equations are obtained on a planar cross-section of a rectangular waveguide.
重点内容
  • Artificial boundary conditions (ABCs) furnish a widely used approach for the numerical treatment of boundary-value problems initially formulated on unbounded domains
  • These boundary conditions are typically set at the external boundary of a finite computational domain once the latter is obtained from the original unbounded domain by means of truncation
  • Among other papers devoted to constructing the exact artificial boundary conditions (ABCs), we mention work by Fix and Marin [52], in which the authors solve the Helmholtz equation in an axially symmetric duct and construct the exact ABCs on its lateral boundary expanding the solution in terms of the trigonometric and Hankel functions; work by Poezd and Yakunin [165], in which the time-dependent propagation of waves through a semi-infinite cylindrical guide is considered and the exact solution of the wave equation is used to set the ABCs at the artificial boundary normal to the cylinder axis; work by Zornmski, Watson and Hodge [109,240,248,249], in which the exact ABCs at the transversal planar artificial boundary are developed for the Helmholtz equation in a semi-infinite rectangular constant-section duct and numerically compared against some localized versions of the boundary conditions by Engquist and Majda [40] and Giles [56]; work by Watson and Zorumski [241], in which the method of [109,248,249] is extended to treat the one-dimensional time-periodic duct acoustic phenomena described by the linearized Euler equations in the far field; work by Jiang and Wong [113], in which the exact non-reflecting boundary conditions (NRBCs) that contains a oaDO is obtained at the planar artificial boundary for a general secondorder hyperbolic equation provided that the corresponding dispersion relation is known; and work by Guillaume and Masmoud [73], in which the boundary conditions for Helmholtz-type equations are obtained on a planar cross-section of a rectangular waveguide
  • In the context of geometrically universal global boundary conditions we refer the reader to Sections 3 and 4 of this paper, in which we describe the methodology based on the generalized potentials and difference potentials method (DPM) [171,172,175]
  • The flow regimes that we have studied numerically in our work [220,222,225] range from very low to transonic Mach numbers and include both attached and separated turbulent flows. (For the low speed flows (M0 = 0.01) the ABCs were constructed on the basis of the linearized incompressible equations in the far field.) In Table 2 we present the computational results for one standard transonic case
结果
  • Hagstrom and Lorenz [90] construct the nonlocal exact ABCs at the planar cross-stream artificial boundary for the unsteady compressible isentropic Navier-Stokes equations linearized against the constant background for the case of low speed flows; again, the boundary conditions are obtained by separating the variables and explicitly eliminating the growing modes in both upstream and downstream directions.
结论
  • The literature on the methods of this kind is broad, the authors will not concentrate much on it in this paper and rather mention only work by MacCamy [135], in which the global integral boundary condition is obtained for the two-dimensional Helmholtz equation that originates form considering the time-harmonic electromagnetic field, and work by Berger et al [19], in which the authors solve the transonic full-potential equation for airfoil by FEM and couple its solution at the external artificial boundary with the boundary element solution to the linearized exterior problem for the Prandtl-Glauert equation, see Section 4.
表格
  • Table1: RAE2822:M0 = 0.73, Re0 = 6.5 x 106, ~ = 2.79°
  • Table2: ONERA M6:M0 = 0.84, Re0 = 11.7 × 106, c~= 3.06°
Download tables as Excel
研究对象与分析
members: 3
Bielak, Kallivokas, and MacCamy [21,120] have been able to essentially reduce this geometric limitation; for a convex smooth artificial boundary in three dimensions they introduce a new coordinate system, for which this artificial boundary is a coordinate surface and the third coordinate direction is given by the normals to the artificial boundary. In these new coordinates the variables for the wave equation separate and the authors of [21,120] can explicitly write down the first three members of the sequence of operators similar to Bm (see (2.9b)); these operators, of course, contain metric coefficients of the surface (artificial boundary). For improving the stability properties of the resulting algorithm, a special artificial parameter (that essentially controls the dissipation) has to be introduced into the structure of boundary conditions [21,120]

dimensional cases: 3
[222] Tsynkov systematically describes the DPM-based ABCs for calculation of viscous flows about three-dimensional wings. It turns out that in all three-dimensional cases that have been studied numerically (see [220,222,225]), the DPM-based ABCs allow one to greatly reduce the size of the computational domain (compared to the standard local boundary conditions) while still maintaining high accuracy of the numerical solution. This actually means the overall increase of accuracy due to the improved treatment of the artificial boundary; it also implies the substantial economy of the computer resources

引用论文
  • S. Abarbanel, A, Bayliss and L. Lustman, Non-reflecting boundary conditions for the compressible NavierStokes equations, Institute for Computer Applications in Science and Engineering Report No. 86-9, NASA Langley Research Center, Hampton, VA (March 1986).
    Google ScholarFindings
  • S. Abarbanel and D. Gottlieb, A mathematical analysis of the PML method, J. Comput. Phys. 134 (1997) 357-363.
    Google ScholarLocate open access versionFindings
  • S. Abarbanel and D. Gottlieb, On the construction and analysis of the absorbing layers in CEM, in: 13th Annual Review of Progress in Applied Computational Electromagnetics (1997) 876-883.
    Google ScholarLocate open access versionFindings
  • S. Abarbanel and D. Gottlieb, On the construction and analysis of absorbing layers in CEM, Appl. Numer. Math. 27 (1998) 331-340 (this issue).
    Google ScholarLocate open access versionFindings
  • V.I. Agoshkov, Domain decomposition techniques for problems in mathematical physics, in: G.I. Marchuk, ed., Computational Processes and Systems 8 (Nauka, Moscow, 1990) 3-51 (in Russian).
    Google ScholarLocate open access versionFindings
  • D. Anderson, J. Tannehill and R. Pletcher, Computational Fluid Mechanics and Heat Transfer (Hemisphere, New York, 1984).
    Google ScholarFindings
  • R.J. Astley, Recent advances in applying wave-envelope elements to unbounded wave problems, in: T.L. Geers, ed., Collection of Abstracts of IUTAM Symposium on Computational Methods for Unbounded Domains, University of Colorado at Boulder, July 27-3 l, 1997 (Kluwer Academic, to appear).
    Google ScholarLocate open access versionFindings
  • H. Atkins and J. Casper, Nonreflective boundary conditions for high-order methods,AIAA J. 32 (1994) 512518.
    Google ScholarFindings
  • W. Bao and H. Han, Nonlocal artificial boundary conditions for the incompressible viscous flow in a channel using spectral techniques, J. Comput. Phys. 126 (1996) 52-63.
    Google ScholarLocate open access versionFindings
  • A. Barry, J. Bielak and R.C. MacCamy, On absorbing boundary conditions for wave propagation, £ Comput. Phys. 79 (1988) 449-468.
    Google ScholarLocate open access versionFindings
  • M. Baum, T.J. Poinsot and D. Th6venin, Accurate boundary conditions for multicomponentreactive flows, J. Comput. Phys. 116 (1994) 247-261.
    Google ScholarLocate open access versionFindings
  • A. Bayliss, C.I. Goldstein and E. Turkel, The numerical solution of the Helmholtz equation for wave propagation problems in underwater acoustics, Comput. Math. Appl. 11 (1985) 655-665.
    Google ScholarLocate open access versionFindings
  • A. Bayliss, M. Gunzburger and E. Turkel, Boundary conditions for numerical solution of elliptic equations in exterior domains, SIAMJ. Appl. Math. 42 (1982) 430-451.
    Google ScholarLocate open access versionFindings
  • A. Bayliss and E. Turkel, Radiation boundary conditions for wave-like equations, Comm. Pure Appl. Math. 33 (1980) 707-725.
    Google ScholarLocate open access versionFindings
  • A. Bayliss and E. Turkel, Outflow boundary conditions for fluid dynamics, SIAM J. Sci. Statist. Comput. 3 (1982) 250-259.
    Google ScholarLocate open access versionFindings
  • A. Bayliss and E. Turkel, Far-field boundary conditions for compressible flows, J. Comput. Phys. 48 (1982) 182-199.
    Google ScholarLocate open access versionFindings
  • J.-P. Berenger, A perfectly matched layer for the absorption of electromagnetic waves, J. Comput. Phys. 114 (1994) 185-200.
    Google ScholarLocate open access versionFindings
  • J.-P. Berenger, Three-dimensional perfectly matched layer for the absorption of electromagnetic waves, J. Comput. Phys. 127 (1996) 363-379.
    Google ScholarLocate open access versionFindings
  • H. Berger, G. Warnecke and W.L. Wendland, Analysis of a FEM/BEM coupling method for transonic flow computations, Math. Comp. 66 (1997) 1407-1440.
    Google ScholarLocate open access versionFindings
  • J.A. Bettess and P. Bettess, New mapped wave infinite element and diffraction of waves by elliptical cylinders of varying aspect ratio, in: T.L. Geers, ed., Collection of Abstracts oflUTAM Symposium on Computational Methodsfor Unbounded Domains, University of Colorado at Boulder, July 27-31, 1997 (Kluwer Academic, to appear).
    Google ScholarLocate open access versionFindings
  • J. Bielak, L.E Kallivokas and R.C. MacCamy, Absorbing boundaries for acoustic wave propagation problems, in: T.L. Geers, ed., Collection of Abstracts of lUTAM Symposium on Computational Methods for Unbounded Domains, University of Colorado at Boulder, July 27-31, 1997 (Kluwer Academic, to appear).
    Google ScholarLocate open access versionFindings
  • J.G. Blaschak and G.A. Kriegsmann, A comparative study of absorbing boundary conditions, J. Comput. Phys. 77 (1988) 109-139.
    Google ScholarLocate open access versionFindings
  • E Bonnet and E Poupaud, Berenger absorbing boundary condition with time finite-volume scheme for triangular meshes, Appl. Numer. Math. 25 (1997) 333-354.
    Google ScholarLocate open access versionFindings
  • K.V. Brushlinskii, V.S. Ryaben'kii and N.B. Tuzova, The transfer of boundary conditions across a vacuum in axisymmetric problems, Comput. Math. Math. Phys. 32 (1992) 1757-1767.
    Google ScholarLocate open access versionFindings
  • R.H. Burkhart, Asymptotic expansion of the free-space Green's function for the discrete 3-D Poisson equation, SIAMJ. Sci. Comput. 18 (1997) 1142-1162.
    Google ScholarLocate open access versionFindings
  • R.H. Burkhart, J. Bussoletti, ET. Johnson, S.S. Samant and D.P. Young, Solution of the discrete free-space 3-D Poisson equation, Boeing Computer Services Technical Report, BCSTECH-94-015 (April 1994).
    Google ScholarFindings
  • D. Burnett, An ellipsoidal infinite element for 3D radiation and scattering, Presented at IUTAM Symposium on Computational Methods for Unbounded Domains, University of Colorado at Boulder, July 27-31, 1997.
    Google ScholarFindings
  • A.E Calderon, Boundary-value problems for elliptic equations, in: Proceedings of the Soviet-American Conference on Partial Differential Equations at Novosibirsk (Fizmatgiz, Moscow, 1963) 303-304.
    Google ScholarLocate open access versionFindings
  • A. Clement, Coupling of two absorbing boundary conditions for 2D time-domain simulation of free surface gravity waves, J. Comput. Phys. 126 (1996) 139-151.
    Google ScholarLocate open access versionFindings
  • J.D. Cole and L.P. Cook, Transonic Aerodynamics (Elsevier, Amsterdam, 1986).
    Google ScholarFindings
  • E Collino, Perfectly matched absorbing layers for paraxial equations, J. Comput. Phys. 131 (1996) 164-180.
    Google ScholarLocate open access versionFindings
  • T. Colonius, Numerically nonreflecting boundary and interface conditions for compressible flow and aeroacoustic computations, AIAA J. 35 (1197) 1126-1133.
    Google ScholarLocate open access versionFindings
  • J.S. Danowitz, A local far-field non-reflecting boundary condition for viscous two-dimensional external flows, Ph.D. Thesis, Tel-Aviv University, Israel (July 1994).
    Google ScholarFindings
  • A.S. Deakin and H. Rasmussen, Sparse boundary conditions on artificial boundaries for three-dimensional potential problems, J. Comput. Phys. 129 (1996) 111-120.
    Google ScholarLocate open access versionFindings
  • L. Demkowicz and E Ihlenburg, Proof of convergence for the coupled finite/infinite elements methods for Helmholtz exterior boundary-value problems, in: T.L. Geers, ed., Collection of Abstracts of IUTAM Symposium on Computational Methods for Unbounded Domains, University of Colorado at Boulder, July 27-31, 1997 (Kluwer Academic, to appear). S.V.Tsynkov/ AppliedNumericalMathematics27 (1998)465-532
    Google ScholarLocate open access versionFindings
  • J. De Moerloose and D. De Zutter, Surface integral representation radiation boundary conditions for the FDTD method, IEEE Trans. Antennas Propagation 41 (1993) 890-895.
    Google ScholarLocate open access versionFindings
  • K. Dgaygui and P. Joly, Absorbing boundary conditions for linear gravity waves, SlAM J. Appl. Math. 54 (1994) 93-131.
    Google ScholarLocate open access versionFindings
  • M. Drela, Two-dimensional transonic aerodynamic design and analysis using the Euler equations, Massachusetts Institute of Technology, Gas Turbine Laboratory Report No. 187 (February 1986).
    Google ScholarFindings
  • B. Engquist and L. Halpern, Far field boundary conditions for computation over long time, Appl. Numer Math. 4 (1988) 21--45.
    Google ScholarLocate open access versionFindings
  • B. Engquist and A. Majda, Absorbing boundary conditions for the numerical simulation of waves, Math. Comp. 31 (1977) 629-651.
    Google ScholarLocate open access versionFindings
  • B. Engquist and A. Majda, Radiation boundary conditions for acoustic and elastic wave calculations, Comm. PureAppl. Math. 32 (1979) 313-357.
    Google ScholarLocate open access versionFindings
  • B. Engquist and A. Majda, Numerical radiation boundary conditions for unsteady transonic flow, J. Comput. Phys. 40 (1981) 91-103. [431 B. Engquist and H.-K. Zhao, Absorbing boundary conditions for domain decomposition, in: T.L. Geers, ed., Collection of Abstracts of lUTAM Symposium on Computational Methods for Unbounded Domains, University of Colorado at Boulder, July 27-31, 1997 (Kluwer Academic, to appear).
    Google ScholarLocate open access versionFindings
  • [44] B. Engquist and H.-K. Zhao, Absorbing boundary conditions for domain decomposition, AppL Numer. Math. 27 (1998) 341-365 (this issue).
    Google ScholarLocate open access versionFindings
  • [45] L. Ferm, Open boundary conditions for stationary inviscid flow problems, J. Comput. Phys. 78 (1988) 94113. I46] L. Ferm, Open boundary conditions for external flow problems, J. Comput. Phys. 91 (1990) 55-70.
    Google ScholarLocate open access versionFindings
  • [47] L. Ferm, Non-reflecting accurate open boundary conditions for the steady Euler equations, Technical Report No. 143, Department of Scientific Computing, Uppsala University, Uppsala, Sweden (1992).
    Google ScholarFindings
  • [48] L. Ferm, Modified external boundary conditions for the steady Euler equations, Technical Report No. 153, Department of Scientific Computing, Uppsala University, Uppsala, Sweden (1993).
    Google ScholarFindings
  • [49] L. Ferm, Multigrid for external flow problems, Technical Report, Department of Scientific Computing, Uppsala University, Uppsala, Sweden (1993). [501 L. Ferm, Non-reflecting boundary conditions for the steady Euler equations, J. Comput. Phys. 122 (1995)
    Google ScholarFindings
  • 10 (1982) 261-276.
    Google ScholarLocate open access versionFindings
  • [521 G.J. Fix and S.P. Matin, Variational methods for underwater acoustic problems, J. Comput. Phys. 28 (1978)
    Google ScholarLocate open access versionFindings
  • [531 J.B. Freund, Proposed inflow/outflow boundary conditions for direct computation of aerodynamic sound, AIAA J. 35 (1997) 740-742.
    Google ScholarLocate open access versionFindings
  • [54] T.L. Geers, Singly and doubly asymptotic computational boundaries, in: T.L. Geers, ed,, Collection of Abstracts of IUTAM Symposium on Computational Methods for Unbounded Domains, University of Colorado at Boulder, July 27-31, 1997 (Kluwer Academic, to appear).
    Google ScholarLocate open access versionFindings
  • [55] K. Gerdes, Infinite element methods, in: T.L. Geers, ed., Collection of Abstracts oflUTAM Symposium on Computational Methods for Unbounded Domains, University of Colorado at Boulder, July 27-31, 1997 (Kluwer Academic, to appear).
    Google ScholarLocate open access versionFindings
  • [56] M.B. Giles, Nonreflecting boundary conditions for Euler equation calculations, AIAA J. 28 (1990) 20502058.
    Google ScholarLocate open access versionFindings
  • [57] M.B. Giles and M. Drela, Two-dimensional transonic aerodynamicdesign method, AIAA J. 25 (1987) 11991206.
    Google ScholarLocate open access versionFindings
  • [58] D. Givoli, Non-reflecting boundary conditions, J. Comput. Phys. 94 (1991) 1-29. S.V. Tsynkov/ AppliedNumericalMathematics27 (1998) 465-532
    Google ScholarLocate open access versionFindings
  • [59] D. Givoli, A spatially exact non-reflecting boundary condition for time dependent problems, Comput. Methods Appl. Mech. Engrg. 95 (1992)97-113.
    Google ScholarFindings
  • [60] D. Givoli, Numerical Methods for Problems in Infinite Domains (Elsevier, Amsterdam, 1992).
    Google ScholarLocate open access versionFindings
  • [61] D. Givoli and D. Cohen, Nonreflecting boundary conditions based on Kirchhoff-type formulae, J. Comput. Phys. 117 (1995) 102-113.
    Google ScholarLocate open access versionFindings
  • [62] D. Givoli and J.B. Keller, A finite-element method for large domains, Comput. MethodsAppl. Mech. Engrg. 76 (1989) 41-66.
    Google ScholarLocate open access versionFindings
  • [63] D. Givoli and J.B. Keller, Non-reflecting boundary conditions for elastic waves, Wave Motion 12 (1990)
    Google ScholarLocate open access versionFindings
  • [64] D. Givoli and J.B. Keller, Special finite-elements for use with higher-order boundary conditions, Comput. Methods Appl. Mech. Engrg. 119 (1994) 199-213.
    Google ScholarLocate open access versionFindings
  • [65] D. Givoli and I. Patlashenko, Optimal local artificial boundary conditions, in: T.L. Geers, ed., Collection of Abstracts of IUTAM Symposium on Computational Methods for Unbounded Domains, University of Colorado at Boulder, July 27-31, 1997 (Kluwer Academic, to appear).
    Google ScholarLocate open access versionFindings
  • [66] D. Givoli, I. Patlashenko and J.B. Keller, High-order boundary conditions and finite elements for infinite domains, Comput. Methods Appl. Mech. Engrg. 143 (1997) 13-39.
    Google ScholarLocate open access versionFindings
  • [67] D. Givoli and S. Vigdergauz, Artificial boundary conditions for 2D problems in geophysics, Comput. Methods Appl. Mech. Engrg. 110 (1993) 87-101.
    Google ScholarLocate open access versionFindings
  • [68] EE Grinstein, Open boundary conditions in the simulation of subsonic turbulent shear flows, J. Comput. Phys. 115 (1994) 43-55.
    Google ScholarLocate open access versionFindings
  • [69] M.J. Grote and J.B. Keller, On nonreflecting boundary conditions, J. Comput. Phys. 122 (1995) 231-243.
    Google ScholarLocate open access versionFindings
  • [70] M.J. Grote and J.B. Keller, Exact nonreflecting boundary conditions for the time-dependent wave equation, SIAM J. Appl. Math. 55 (1995) 280-297.
    Google ScholarLocate open access versionFindings
  • [71] M.J. Grote and J.B. Keller, Nonreflecting boundary conditions for time-dependent scattering, J. Comput. Phys. 127 (1996) 52-65.
    Google ScholarLocate open access versionFindings
  • [72] M.J. Grote and J.B. Keller, Nonreflecting boundary conditions for Maxwell's equations, J. Comput. Phys. 139 (1998) 327-342.
    Google ScholarLocate open access versionFindings
  • [73] E Guillaume and M. Masmoud, Solution to the time-harmonic Maxwell's equations in a waveguide; use of higher-order derivatives for solving the discrete problem, SIAM J. Numer. Anal. 34 (1997) 1306-1330.
    Google ScholarLocate open access versionFindings
  • [74] B. Gustafsson, The choice of numerical boundary conditions for hyperbolic systems, J. Comput. Phys. 48 (1982) 270-283.
    Google ScholarLocate open access versionFindings
  • [75] B. Gustafsson, Far-field boundary conditions for time-dependent hyperbolic systems, SIAM J. Sci. Statist. Comput. 9 (1988) 812-828.
    Google ScholarLocate open access versionFindings
  • [76] B. Gustafsson, Inhomogeneous conditions at open boundaries for wave propagation problems, Appl. Numer. Math. 4 (1988) 3-19.
    Google ScholarLocate open access versionFindings
  • [77] B. Gustafsson and J. Nordstr6m, Extrapolation procedures at outflow boundaries for the Navier-Stokes equations, in: R. Glowinski and A. Lichnewsky, eds., Computing Methods in Applied Science and Engineering (SIAM, Philadelphia, PA, 1990) pp. 136-151.
    Google ScholarLocate open access versionFindings
  • [78] B. Gustafsson and A. Sundstr6m, Incompletely parabolic problems in fluid dynamics, SlAM J. Appl. Math. 35 (1978) 343-357.
    Google ScholarLocate open access versionFindings
  • [79] D.-J. Guo and Q.-C. Zeng, Open boundary conditions for a numerical shelf sea model, J. Comput. Phys. 116 (1995) 97-102.
    Google ScholarLocate open access versionFindings
  • [80] G.R. Hadley, Transparent boundary condition for beam propagation, Opt. Lett. 16 (1991) 624-626.
    Google ScholarLocate open access versionFindings
  • [81] T.M. Hagstrom, Asymptotic expansions and boundary conditions for time-dependent problems, SIAM J. Numer. Anal 23 (1986) 948-958.
    Google ScholarLocate open access versionFindings
  • [82] T.M. Hagstrom, Boundary conditions at outflow for a problem with transport and diffusion, J. Comput. Phys. 69 (1987) 69-80.
    Google ScholarLocate open access versionFindings
  • [83] T.M. Hagstrom, Asymptotic boundary conditions for dissipative waves: general theory, Math. Comp. 56 (1991) 589-606.
    Google ScholarFindings
  • [84] T.M. Hagstrom, On the convergence of local approximation to pseudodifferential operators with applications, NASA Technical Memorandum No. 106792, ICOMP-94-29, Lewis Research Center (November 1994).
    Google ScholarLocate open access versionFindings
  • [85] T.M. Hagstrom, Exact and high-order boundary conditions in time domain, in: T.L. Geers, ed., Collection of Abstracts of IUTAM Symposium on Computational Methods for Unbounded Domains, University of Colorado at Boulder, July 27-31, 1997 (Kluwer Academic, to appear).
    Google ScholarLocate open access versionFindings
  • [86] T.M. Hagstrom and S.I. Hariharan, Accurate boundary conditions for exterior problems in gas dynamics, Math. Comp. 51 (1988) 581-597.
    Google ScholarLocate open access versionFindings
  • [87] T.M. Hagstrom and S.I. Hariharan, Progressive wave expansions and open boundary problems, in: B. Engquist and G.A. Kriegsmann, eds., Computational Wave Propagation, IMA Volumes in Mathematics and Its Applications, Vol. 86 (Springer, New York, 1996) 23-43.
    Google ScholarLocate open access versionFindings
  • [88] T.M. Hagstrom and H.B. Keller, Exact boundary conditions at an artificial boundary for partial differential equations in cylinders, SIAMJ. Math. Anal. 17 (1986) 322-341.
    Google ScholarLocate open access versionFindings
  • [89] T.M. Hagstrom and H.B. Keller, Asymptotic boundary conditions and numerical methods for nonlinear elliptic problems on unbounded domains, Math. Comp. 48 (1987) 449-470.
    Google ScholarLocate open access versionFindings
  • [90] T. Hagstrom and J. Lorenz, Boundary conditions and the simulation of low Mach number flows, in: D. Lee and M.H. Schultz, eds., Theoretical and Computational Acoustics, Vol. 2, Proceedings of the First International Conference on Theoretical and Computational Acoustics, Mystic, CT, July 5-9, 1993 (World Scientific, 1994) 657-668.
    Google ScholarLocate open access versionFindings
  • [91] L. Halpern, Artificial boundary conditions for the linear advection-diffusion equation, Math. Comp. 46 (1986) 425--438.
    Google ScholarLocate open access versionFindings
  • [92] L. Halpern, Artificial boundary conditions for incompletely parabolic perturbations of hyperbolic systems, SIAM J. Math. Anal. 22 (1991) 1256-1283.
    Google ScholarLocate open access versionFindings
  • [93] H. Han, J. Lu and W. Bao, A discrete artificial boundary condition for steady incompressible viscous flows in a no-slip channel using fast iterative method, J. Comput. Phys. 114 (1994) 201-208.
    Google ScholarLocate open access versionFindings
  • [94] I. Harari, A variational formulation for partitioned exterior problems, in: T.L. Geers, ed., Collection of Abstracts of IUTAM Symposium on Computational Methods for Unbounded Domains, University of Colorado at Boulder, July 27-31, 1997 (Kluwer Academic, to appear).
    Google ScholarLocate open access versionFindings
  • [95] I. Harafi and T.J.R. Hughes, Analysis of continuous formulations underlying the computation of timeharmonic acoustics in exterior domains, Comput. Methods AppL Mech. Engrg. 97 (1992) 103-124.
    Google ScholarLocate open access versionFindings
  • [96] S.I. Hariharan and T.M. Hagstrom, A systematic approach for constructing asymptotic boundary conditions for wave-like equations, in: T.L. Geers, ed., Collection of Abstracts oflUTAM Symposium on Computational Methodsfor Unbounded Domains, University of Colorado at Boulder, July 27-31, 1997 (Kluwer Academic, to appear).
    Google ScholarLocate open access versionFindings
  • [97] A. Harten and I. Yad-Shalom, Fast multiresolution algorithms for matrix-vector multiplication, SlAM J. Numer. Anal. 31 (1994) 1191-1218.
    Google ScholarLocate open access versionFindings
  • [98] E.M. Hayder and H.L. Atkins, Experience with PML boundary conditions in fluid flow computations, in: T.L. Geers, ed., Collection of Abstracts of lUTAM Symposium on Computational Methods for Unbounded Domains, University of Colorado at Boulder, July 27-31, 1997 (Kluwer Academic, to appear).
    Google ScholarLocate open access versionFindings
  • [99] M.E. Hayder and T. Hagstrom, An outflow boundary condition for aeroacoustic computations, in: A.S. Lyrintzis, R.R. Mankbadi, O. Baysal and M. Ikegawa, eds., Computational Aeroacoustics 1995, Proceedings of the 1995 ASME/JSME Fluids Engineering and Laser Anemometry Conference and Exhibition, The Fluids Engineering Division, Hilton Head, SC, August 13-18, 1995, ASME 219 (1995) 41-46.
    Google ScholarLocate open access versionFindings
  • [100] M.E. Hayder, F.Q. Hu and M.Y. Hussaini, Towards perfectly absorbing boundary conditions for Euler equations, AIAA Paper No. 97-2075, in: Proceedings of the 13th AIAA Computational Fluid Dynamics Conference, Snowmass Village, CO, Part 2 (1997) 1150-1160.
    Google ScholarFindings
  • [101] M.E. Hayder and E. Turkel, High order accurate solutions of viscous problems, AIAA Paper No. 93-3074, in: 24th AIAA Fluid Dynamics Conference, Orlando, FL (1993).
    Google ScholarFindings
  • [102] M.E. Hayder and E. Turkel, Nonreflecting boundary conditions for jet flow computations, AIAA J. 33 (1995) 2264-2270.
    Google ScholarLocate open access versionFindings
  • [103] G.W. Hedstrom, Nonreflecting boundary conditions for nonlinear hyperbolic systems, J. Comput. Phys. 30 (1979) 222-237.
    Google ScholarLocate open access versionFindings
  • [104] J.H. Hesthaven and D. Gottlieb, A stable penalty method for the compressible Navier-Stokes equations: I. Open boundary conditions, SlAM J. Sci. Comput. 17 (1996) 579-612. [lO5] R.L. Higdon, Absorbing boundary conditions for difference approximations to the multidimensional wave equation, Math. Comp. 47 (1986) 437-459.
    Google ScholarLocate open access versionFindings
  • [106] R.L. Higdon, Absorbing boundary conditions for acoustic and elastic waves in stratified media, J. Comput. Phys. 101 (1992) 386--418. [1071 R.L. Higdon, Radiation boundary conditions for dispersive waves, SlAM J. Numer. Anal. 31 (1994) 64-100.
    Google ScholarLocate open access versionFindings
  • [108] R.L. Higdon, Absorbing boundary conditions for dispersive waves, in: T.L. Geers, ed., Collection of Abstracts of IUTAM Symposium on Computational Methods for Unbounded Domains, University of Colorado at Boulder, July 27-31, 1997 (Kluwer Academic, to appear). [1091 S.L. Hodge, W.E. Zorumski and W.R. Watson, Solution of the three-dimensional Helmholtz equation with nonlocal boundary conditions, NASA Technical Memorandum No. 110174, Langley Research Center (May 1995).
    Google ScholarLocate open access versionFindings
  • [110] EQ. Hu, On absorbing boundary conditions for linearized Euler equations by a perfectly matched layer, J. Comput. Phys. 129 (1996) 201-219. [lll] M. Israeli and S. Orszag, Approximation of radiation boundary conditions, J. Comput. Phys. 41 (1981) 115135.
    Google ScholarFindings
  • [112] A. Jameson, W. Schmidt and E. Turkel, Numerical solutions of the Euler equations by finite volume methods using Runge-Kutta time-stepping schemes, AIAA Paper No. 81-1259, in: 14th AIAA Fluid and Plasma Dynamics Conference, Palo Alto, CA (1981).
    Google ScholarLocate open access versionFindings
  • [113] H. Jiang and Y.S. Wong, Absorbing boundary conditions for second-order hyperbolic equations, J. Comput. Phys. 88 (1990) 205-231. [114l G. Jin and M. Braza, A nonreflecting outlet boundary condition for incompressible unsteady Navier-Stokes calculations, J. Comput. Phys. 107 (1993) 239-253.
    Google ScholarLocate open access versionFindings
  • [115] J.M. Jin and W.C. Chew, Combining PML and ABC for finite element analysis of scattering problems, Microwave Opt. Tech. Lett. 12 (1996) 192-197. [1161 C. Johansson, Boundary conditions for open boundaries for the incompressible Navier-Stokes equation, J. Comput. Phys. 105 (1993) 233-251. [1171 M. Johnsen and D.R. Lynch, A second-order radiation boundary condition for the shallow water wave equations on two-dimensional unstructured finite element grids, lnternat. J. Numer. Methods Fluids 18 (1994) 575-604.
    Google ScholarLocate open access versionFindings
  • [118] L.F. Kallivokas and J. Bielak, Time-domain analysis of transient structural acoustics problems based on the finite-element method and a novel absorbing boundary element, J. Acoust. Soc. Amer. 94 (1993[)3480-3492.
    Google ScholarLocate open access versionFindings
  • [119] L.F. Kallivokas, J. Bielak and R.C. MacCamy, A simple impedance-infinite element for the finite element solution of the three-dimensional wave equation in unbounded domains, Comput. Methods Appl. Mech. Engrg. 147 (1997) 235-262. [1201 L.E Kallivokas, J. Bielak and R.C. MacCamy, Absorbing boundary conditions of arbitrary shape for the three-dimensional wave equation, in: T.L. Geers, ed., Collection of Abstracts of IUTAM Symposium on Computational Methods for Unbounded Domains, University of Colorado at Boulder, July 27-31, 1997 (Kluwer Academic, to appear). [1211 L.E Kallivokas, A. Tsikas and J. Bielak, On transient three-dimensional absorbing boundary conditions for the modeling of acoustic scattering from near-surface obstacles, J. Comput. Acoust. 5 (1997) 117-136. S.V. Tsynkov~AppliedNumericalMathematics27 (1998) 465-532
    Google ScholarLocate open access versionFindings
  • [122] E Kang, Finite element method and natural boundary reduction, in: Proceedings of the International Congress of Mathematicians, Warszawa, August 16-24 (1983) 1439-1453.
    Google ScholarLocate open access versionFindings
  • [123] N.V. Kantartzis and T.D. Tsiboukis, A comparative study of the Berenger PML, the superabsorption technique and several high-order ABCS for the FD-TD algorithm in two and three dimensional problems, IEEE Trans. Magnetics 33 (1997) 1460--1463.
    Google ScholarLocate open access versionFindings
  • [124] S. Kami, Far-field filtering operators for suppression of reflections from artificial boundaries, SlAM J. Numer. Anal, 33 (1996) 1014-1047.
    Google ScholarLocate open access versionFindings
  • [125] J.B. Keller and D. Givoli, Exact non-reflecting boundary conditions, J. Comput. Phys. 82 (1989) 172-192.
    Google ScholarFindings
  • [126] E.B. Klunker, Contribution to methods for calculating the flow about thin lifting wings at transonic speeds--analytic expressions for the far field, NASA Technical Note No. D-6530, Langley Research Center (November 1971).
    Google ScholarLocate open access versionFindings
  • [127] R. Kosloffand D. Kosloff, Absorbing boundaries for wave propagation problems, J. Comput. Phys. 63 (1986) 363-376.
    Google ScholarLocate open access versionFindings
  • [128] H.-O. Kreiss and B. Gustafsson, Boundary conditions for time-dependent problems with artificial boundary, J. Comput. Phys. 30 (1979) 333-351.
    Google ScholarLocate open access versionFindings
  • [129] D. Krrner, Absorbing boundary conditions for the linearized Euler equations, Math. Comp. 57 (1991) 153167.
    Google ScholarFindings
  • [130] H. Lamb, Hydrodynamics (Dover, New York, 1945).
    Google ScholarFindings
  • [131] L.D. Landau and E.M. Lifshitz, Fluid Mechanics (Pergamon Press, Oxford, 1986).
    Google ScholarLocate open access versionFindings
  • [132] J. Lon~arir, Sensor/actuator placement via optimal distributed control of exterior Stokes flow, in: J.T. Borggaard, J. Burns, E. Cliff and S. Schreck, eds., Computational Methods in Optimal Design and Control (Birkh~iuser, Boston, MA, 1998).
    Google ScholarLocate open access versionFindings
  • [133] P. Luchini and R. Tognaccini, Direction-adaptive nonreflecting boundary conditions, J. Comput. Phys. 128 (1996) 121-133.
    Google ScholarLocate open access versionFindings
  • [134] G.S.S. Ludford, The behavior at infinity of the potential function of a two-dimensional subsonic compressible flow, J. Math. Phys. 30 (1951) 117-130. [1351 R.C. MacCamy, Variational procedure for a class of exterior interface problems, J. Math. Anal, Appl. 78 (1980) 248-266.
    Google ScholarLocate open access versionFindings
  • [136] I.C. Mathews and S. Newhouse, A comparison between time and frequency domain approaches for rigid body scattering problems, in: T.L. Geers, ed., Collection of Abstracts of IUTAM Symposium on Computational Methods for Unbounded Domains, University of Colorado at Boulder, July 27-31, 1997 (Kluwer Academic, to appear).
    Google ScholarLocate open access versionFindings
  • [137] T. Matsushima and P.S. Marcus, A spectral method for unbounded domains, J. Comput. Phys. 137 (1997) 321-345.
    Google ScholarFindings
  • [138] K. Mazaheri and P. Roe, Numerical wave propagation and steady-state solutions: soft wall and outer boundary conditions, AIAA J. 36 (1997) 965-975.
    Google ScholarFindings
  • [139] S.G. Mikhlin, N.E Morozov and M.V. Paukshto, The Integral Equations of the Theory of Elasticity (Teubner, Stuttgart, 1995).
    Google ScholarLocate open access versionFindings
  • [140] M.N. Mishkov and V.S. Ryaben'kii, Artificial boundary conditions for the Helmholtz equation in a stratified medium, Keldysh Inst. Appl. Math., Russian Acad. Sci., Preprint No. 70, Moscow (1992) (in Russian).
    Google ScholarLocate open access versionFindings
  • [141] M.N. Mishkov and V.S. Ryaben'kii, A study of one technique for constructing artificial boundary conditions, Part I, Keldysh Inst. Appl. Math., Russian Acad. Sci., Preprint No. 55, Moscow (1997) (in Russian).
    Google ScholarLocate open access versionFindings
  • [142] M.N. Mishkov and V.S. Ryaben'kii, A study of one technique for constructing artificial boundary conditions, Part II, Keldysh Inst. Appl. Math., Russian Acad. Sci., Preprint No. 56, Moscow (1997) (in Russian).
    Google ScholarLocate open access versionFindings
  • [143] R. Mittra, O. Ramahi, A. Khebir, R. Gordon and A. Kouki, A review of absorbing boundary conditions for two and three-dimensional electromagnetic scattering problems, IEEE Trans. Magnetics 25 (1989) 30343039. S.V. Tsynkov/ Applied NumericaI Mathematics27 (1998)465-532
    Google ScholarLocate open access versionFindings
  • [1441 P. Monk and E Collino, Optimizing the perfectly matched layer, in: T.L. Geers, ed., Collection ofAbstracts of IUTAM Symposium on Computational Methodsfor Unbounded Domains, University of Colorado at Boulder, July 27-31, 1997 (Kluwer Academic, to appear).
    Google ScholarLocate open access versionFindings
  • I145] G. Mur, Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic-field equations, IEEE Trans. Electromagn. Compatibility 23 (1981) 377-382.
    Google ScholarLocate open access versionFindings
  • [146] E Nataf, An open boundary condition for the computation of the incompressible Navier-Stokes equations, J. Comput. Phys. 85 (1989) 104-129.
    Google ScholarFindings
  • [147] J.-C. Nedelec, On the use of retarded potentials in different wave equations, Presented at IUTAM Symposium on Computational Methods for Unbounded Domains, University of Colorado at Boulder, July 27-31, 1997.
    Google ScholarFindings
  • [148] A.I. Nesterov, A.S. Shamaev and S.I. Shamaev, eds., Methods, Algorithms, and Facilities fi)r Aerospace Computer Radar Tomography of Earth Surface Regions (Scientific World, Moscow, 1996).
    Google ScholarFindings
  • [149] N. Nordin and J. NordstrOm, Improved far-field boundary conditions in EURANUS, The Aeronautical Research Institute of Sweden, FFA TN 1995-26, Bromma, Sweden (April 1995).
    Google ScholarLocate open access versionFindings
  • [150] J. Nordstrtim, The influence of open boundary conditions on the convergence to steady state for the NavierStokes equations, J. Comput. Phys. 85 (1989) 210-244.
    Google ScholarFindings
  • [151] J. Nordstrrm, Accurate solutions of the timed-dependent Navier-Stokes equations despite erroneous outflow boundary data, Technical Report No. 150, Department of Scientific Computing, Uppsala University, Uppsala, Sweden (1993).
    Google ScholarFindings
  • [152] J. Nordstrt~m, Accuracy and stability of extrapolation procedures at artificial outflow boundaries for the time-dependent Navier-Stokes equations, Technical Report No. 151, Department of Scientific Computing, Uppsala University, Uppsala, Sweden (1993).
    Google ScholarLocate open access versionFindings
  • [153] J. Nordstrrm, Accurate solution of the Navier-Stokes equations despite unknown outflow boundary data, J. Comput. Phys. 120 (1995) 184-205. [1541 J. Nordstrrm, The use of characteristic boundary conditions for the Navier-Stokes equations, Comput. & Fluids 24 (1995) 609-623.
    Google ScholarLocate open access versionFindings
  • [1551 A.A. Oberai, M. Malhorta and P.M. Pinsky, Implementing highly accurate non-reflecting boundary conditions for large scale problems in structural acoustics, in: T.L. Geers, ed., Collection of Abstracts of IUTAM Symposium on Computational Methodsfor Unbounded Domains, University of Colorado at Boulder, July 27-31, 1997 (Kluwer Academic, to appear).
    Google ScholarLocate open access versionFindings
  • [156] I. Patlashenko and D. Givoli, Local non-reflecting finite-element schemes for acoustic wave guides, in: J.-A. Drsid6ri, P. Le Tallec, E. Ofiate, J. Prriaux and E. Stain, eds., Numerical Methods in Engineering '96, Proceedings of the Second ECCOMAS Conference on Numerical Methods in Engineering, Paris, France, September 9-13, 1996 (Wiley, New York, 1996) 337-343.
    Google ScholarLocate open access versionFindings
  • [157] I. Patlashenko and D. Givoli, Non-reflecting finite-element schemes for three-dimensional acoustic waves, J. Comput. Acoust. 5 (1997) 95-115.
    Google ScholarLocate open access versionFindings
  • [158] A.E Peterson, Absorbing boundary conditions for the vector wave equation, Microwave Optical Tech. Lett. 1 (1988) 62-64.
    Google ScholarLocate open access versionFindings
  • [159] EG. Petropoulos, Analysis of exponential time-differencing for FD-TD in lossy dielectrics, IEEE Trans. Antennas Propagation 45 (1997) 1054-1057. [1601 P.G. Petropoulos, On the termination of the perfectly matched layer with local absorbing boundary conditions, J. Comput. Phys. 143 (1998) 1-9.
    Google ScholarLocate open access versionFindings
  • [162] P.G. Petropoulos, N.V. Kantartzis and T.D. Tsiboukis, A comparison of the Grote-Keller ABC and the unsplit PML for Maxwell's equations in spherical coordinates, in: Proceedings of the 14th Annual Review of Progress in Applied Computational Electromagnetics, Vol. II, Monterey, CA (1998) 623-630. s.v. Tsynkov/Applied NumericalMathematics27 (1998)465-532
    Google ScholarLocate open access versionFindings
  • [163] EG. Petropoulos, L. Zhao and A.C. Cangellaris, A reflectionless sponge layer absorbing boundary condition for the solution of Maxwell's equations with high-order staggered finite difference schemes, J. Comput. Phys. 139 (1998) 184-208. [1641 EM. Pinsky and N.N. Abboud, Finite element solution of the transient exterior structural acoustics problem based on the use of radially asymptotic operators, Comput. MethodsAppl. Mech. Engrg. 85 (1991) 311-348.
    Google ScholarLocate open access versionFindings
  • [165] A.D. Poezd and S.A. Yakunin, Unsteady non-local in time boundary conditions for semi-opened cylindrical systems, Vestnik Moskov. Univ., Ser. X V Vychisl. Mat. Kibernet. 3 (1988) 16-21 (in Russian). [1661 T.J. Poinsot and S.K. Lele, Boundary conditions for direct simulations of compressible viscous flows, J. Comput. Phys. 101 (1992) 104-129.
    Google ScholarFindings
  • I167] Yu.B. Radvogin and N.A. Zaitsev, Adequate boundary conditions for unsteady aeroacoustic problems, in: C.K.W. Tam and J.C. Hardin, eds., Proceedings of the Second Computational Aeroacoustics Workshop on Benchmark Problems (NASA CP No. 3352, June 1997) 179-190.
    Google ScholarFindings
  • [168] A.A. Reznik, Approximation of the surface potentials of elliptic operators by difference potentials and the solution of boundary value problems, Ph.D. Thesis, Moscow Institute of Physics and Technology, Moscow (1983) (in Russian). [1691 D. Rudy and J. Strikwerda, A non-reflecting outflow boundary condition for subsonic Navier-Stokes calculations, J. Comput. Phys. 36 (1980) 55-70. [1701 D. Rudy and J. Strikwerda, Boundary conditions for subsonic compressible Navier-Stokes calculations, Comput. & Fluids 9 (1981) 327-338.
    Google ScholarLocate open access versionFindings
  • [171] V.S. Ryaben'kii, Boundary equations with projections, Russian Math. Surveys 40 (1985) 147-183.
    Google ScholarFindings
  • [172] V.S. Ryaben'kii, Difference Potentials Methodfor Some Problems of Continuous Media Mechanics (Nauka, Moscow, 1987) (in Russian).
    Google ScholarLocate open access versionFindings
  • [173] V.S. Ryaben'kii, Exact transfer of difference boundary conditions, Functional Anal. AppL 24 (3) (1990) 251-253.
    Google ScholarFindings
  • [174] V.S. Ryaben'kii, Exact transfer of boundary conditions, Comput. Mech. 1 (1990) 129-145 (in Russian).
    Google ScholarLocate open access versionFindings
  • [175] V.S. Ryaben'kii, Difference potentials method and its applications, Math. Nachr. 177 (1996) 251-264.
    Google ScholarLocate open access versionFindings
  • [176] V.S. Ryaben'kii and I.L. Sofronov, Difference spherical functions, Keldysh Inst. Appl. Math., U.S.S.R. Acad. Sci., Preprint No. 75, Moscow (1983) (in Russian).
    Google ScholarFindings
  • [177] V.S. Ryaben'kii and I.L. Sofronov, Numerical solution of the three-dimensional external problems for Helmholtz's equation by means of the difference potentials method, in: Numerical Simulation in Aerodynamics (Nauka, Moscow, 1986) 187-201 (in Russian).
    Google ScholarLocate open access versionFindings
  • [178] V.S. Ryaben'kii and S.V. Tsynkov, Artificial boundary conditions for the numerical solution of external viscous flow problems, SIAMJ. Numer. Anal. 32 (1995) 1355-1389.
    Google ScholarLocate open access versionFindings
  • [179] V.S. Ryaben'kii and S.V. Tsynkov, An effective numerical technique for solving a special class of ordinary difference equations, Appl. Numer. Math. 18 (1995) 489-501.
    Google ScholarFindings
  • [180] V.S. Ryaben'kii and S.V. Tsynkov, An application of the difference potentials method to solving external problems in CFD, NASA Technical Memorandum No. 110338, Langley Research Center (March 1997); also in: M. Hafez and K. Oshima, eds., CFD Review 1997, to appear. [1811 J.-Y. Sa and K.S. Chang, Far-field stream function condition for two-dimensional incompressible flows, J. Comput. Phys. 91 (1990) 398--412.
    Google ScholarLocate open access versionFindings
  • [182] A. Safjan, Progress on highly accurate non-reflecting boundary conditions for finite-element formulations of transient acoustic problems, in: T.L. Geers, ed., Collection of Abstracts of IUTAM Symposium on Computational Methods for Unbounded Domains, University of Colorado at Boulder, July 27-31, 1997 (Kluwer Academic, to appear).
    Google ScholarFindings
  • [183] H. Schlichting, Boundary Layer Theory (McGraw-Hill, New York, 1968).
    Google ScholarLocate open access versionFindings
  • [184] E Schmidt and P. Deuflhard, Discrete transparent boundary conditions for Fresnel's equation, in: Proceedings of the Integrated Photonic Research Conference (IPR), Vol. 3 (1994) 45-47.
    Google ScholarFindings
  • [185] J.N. Scott, R.R. Mankbadi, M.E. Hayder and S.I. Hariharan, Outflow boundary conditions for the computational analysis of jet noise, AIAA Paper No. 93-4366, in: 15th AIAA Aeroacoustics Conference, Long Beach, CA (1993).
    Google ScholarLocate open access versionFindings
  • [186] R.T. Seeley, Singular integrals and boundary value problems, Amer. J. Math. 88 (1966) 781-809.
    Google ScholarFindings
  • [187] A. Seifert, A. Daraby, B. Nishri and I. Wygnanski, The effects of forced oscillations on the performance of airfoils, AIAA Paper No. 93-3264, in: AIAA Shear Flow Conference, Orlando, FL (1993). I188] I.L. Sofronov, Expansion of the difference potentials method and its application to solving the steady diffraction problems, Ph.D. Thesis, Moscow Institute of Physics and Technology, Moscow (1984) (in Russian). [1891 I.L. Sofronov, Difference potentials method for diffraction problems governed by the Maxwell equations, Comput. Mech. 2 (1990) 158-177 (in Russian).
    Google ScholarLocate open access versionFindings
  • [190] I.L. Sofronov, A rapidly converging method for solving the Euler equation, Comput. Math. Math. Phys. 31 (4) (1991) 66-78. [1911 I.L. Sofronov, Artificial boundary conditions which are adequate to the wave equation outside the sphere, Keldysh Inst. Appl. Math., Russian Acad. Sci., Preprint No. 42, Moscow (1992) (in Russian).
    Google ScholarLocate open access versionFindings
  • [192] I.L. Sofronov, Conditions of complete transparency on the sphere for the three-dimensional wave equation, Russian Acad. Sci. Dokl. Math. 46 (1993) 397-401.
    Google ScholarLocate open access versionFindings
  • [193] I.L. Sofronov, Condition of absolute transparency on sphere for wave equation, in: K. Morgan, E.Ofiate, J. Ptriaux, J. Peraire and O.C. Zienkiewicz, eds., Finite Elements in Fluids: New Trends and Applications, CIMNE, Barcelona, 1993 (Pineridge Press, 1993) 1387-1396.
    Google ScholarLocate open access versionFindings
  • [194] I.L. Sofronov, Transparent boundary conditions for unsteady transonic flow problems in wind tunnel, Mathematical Institute A, Stuttgart University, Preprint No. 95-21, Stuttgart (1995). [1951 I.L. Sofronov, Generation of 2D and 3D artificial boundary conditions transparent for waves outgoing to infinity, Mathematical Institute A, Stuttgart University, Preprint No. 96-09, Stuttgart (1996). [1961 I.L. Sofronov, Artificial boundary conditions of absolute transparency for 3D and 3D external timedependent scattering problems, European J. Appl. Math., to appear.
    Google ScholarLocate open access versionFindings
  • [197] I.L. Sofronov, Non-reflecting inflow and outflow in wind tunnel for transonic time-accurate simulation, £ Math. Anal. Appl., to appear.
    Google ScholarLocate open access versionFindings
  • [198] I.L. Sofronov and S.V. Tsynkov, An implementation of the potential flow model in setting the external boundary conditions for the Euler equations. Part II, Keldysh Inst. Appl. Math., U.S.S.R. Acad. Sci., Preprint No. 41, Moscow (1991) (in Russian).
    Google ScholarLocate open access versionFindings
  • [199] J. Strikwerda, Initial boundary value problems for incompletely parabolic systems, Comm. Pure Appl. Math. 30 (1977) 797-822. [2001 R.C. Swanson and E. Turkel, A multistage time-stepping scheme for the Navier-Stokes equations, AIAA Paper No. 85-0035, in: 23rd AIAA Aerospace Sciences Meeting, Reno, NV (1985). [2011 R.C. Swanson and E. Turkel, Artificial dissipation and central difference schemes for the Euler and NavierStokes equations, AIAA Paper No. 87-1107-CP, in: 8th AIAA Computational Fluid Dynamics Conference, Honolulu, HI (1987).
    Google ScholarFindings
  • [202] R.C. Swanson and E. Turkel, Multistage schemes with multigrid for the Euler and Navier-Stokes equations. Components and analysis, NASA Technical Paper No. 3631, Langley Research Center (August 1997).
    Google ScholarFindings
  • [203] A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Boston, 1995).
    Google ScholarLocate open access versionFindings
  • [204] C.K.W. Tam and J.C. Webb, Dispersion-relation-preserving finite difference schemes for computational acoustics, J. Comput. Phys. 107 (1993) 262-281.
    Google ScholarLocate open access versionFindings
  • [205] C.K.W. Tam and J.C. Webb, Radiation boundary condition and anisotropy correction for finite-difference solutions of the Helmholtz equation, J. Comput. Phys. 113 (1994) 122-133.
    Google ScholarLocate open access versionFindings
  • [206] Y. Tang and R. Grimshaw, Radiation boundary conditions in barotropic coastal ocean numerical model, J. Comput. Phys. 123 (1996)96-110. [2071 J.L. Thomas and M.D. Salas, Far-field boundary conditions for transonic lifting solutions to the Euler equations, AIAA Paper No. 85-0020, in: 23rd AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV (1985).
    Google ScholarLocate open access versionFindings
  • [208] K.W. Thompson, Time-dependent boundary conditions for hyperbolic systems, J. Comput. Phys. 68 (1987) 1-24.
    Google ScholarLocate open access versionFindings
  • [209] K.W. Thompson, Time-dependent boundary conditions for hyperbolic systems, II, J. Comput. Phys. 89 (1990) 439-461. [2101 L. Ting and M.J. Miksis, Exact boundary conditions for scattering problems, J. Acoust. Soc. Amer. 80 (1986) 1825-1827.
    Google ScholarLocate open access versionFindings
  • [2111 L. Tourrette, Artificial boundary conditions for the linearized compressible Navier-Stokes equations, J. Comput. Phys. 137 (1997) 1-37.
    Google ScholarLocate open access versionFindings
  • [212] L.N. Trefethen and L. Halpem, Well-posedness of one-way wave equations and absorbing boundary conditions, Math. Comp. 47 (1986) 421-435.
    Google ScholarLocate open access versionFindings
  • [213] S.V. Tsynkov, Boundary conditions at the external boundary of the computational domain for subsonic problems in computational fluid dynamics, Keldysh Inst. Appl. Math., U.S.S.R. Acad. Sci., Preprint No. 108, Moscow (1990) (in Russian).
    Google ScholarFindings
  • [214] S.V. Tsynkov, An implementation of the potential flow model in setting the external boundary conditions for the Euler equations. Part I, Keldysh Inst. Appl. Math., U.S.S.R. Acad. Sci., Preprint No. 40, Moscow (1991) (in Russian).
    Google ScholarLocate open access versionFindings
  • [215] S.V. Tsynkov, An application of nonlocal external conditions to viscous flow computations, J. Comput. Phys. 116 (1995) 212-225.
    Google ScholarLocate open access versionFindings
  • [216] S.V. Tsynkov, Nonlocal artificial boundary conditions for computation of external viscous flows, in: S.N. Atluri, G. Yagawa and T.A. Cruse, eds., Computational Mechanics '95 (Springer, Berlin, 1995) 10651070.
    Google ScholarFindings
  • [217] S.V. Tsynkov, Nonlocal artificial boundary conditions based on the difference potentials method, in: Sixth International Symposium on Computational Fluid Dynamics, Collection of Technical Papers, Vol. IV, Lake Tahoe, NV (September 4-8, 1995) 114-119.
    Google ScholarFindings
  • [218] S.V. Tsynkov, Artificial boundary conditions based on the difference potentials method, NASA Technical Memorandum No. 110265, Langley Research Center (July 1996).
    Google ScholarLocate open access versionFindings
  • [219] S.V. Tsynkov, Nonlocal artificial boundary conditions for computation of external viscous flows, in: J.-A. Desideri, C. Hirsch, E Le Tallec, M. Pandolfi and J. Ptriaux, eds., Computational Fluid Dynamics '96, Proceedings of the Third ECCOMAS CFD Conference, Pads, France, September 9-13, 1996 (Wiley, New York, 1996) 512-518. [22ol S.V. Tsynkov, Artificial boundary conditions for infinite-domain problems, in: V. Venkatakrishnan, M.D. Salas and S. Chakravarthy, eds., Barriers and Challenges in Computational Fluid Dynamics (Kluwer Academic, Dordrecht, 1998) 119-138.
    Google ScholarLocate open access versionFindings
  • [221] S.V. Tsynkov, Artificial boundary conditions for computation of oscillating external flows, SlAM J. Sci. Comput. 18 (1997) 1612-1656.
    Google ScholarLocate open access versionFindings
  • [222] S.V. Tsynkov, External boundary conditions for three-dimensional problems of computational aerodynamics, NASA Technical Memorandum No. 110337, Langley Research Center, March 1997; also SlAM J. Sci. Comput., submitted.
    Google ScholarLocate open access versionFindings
  • [223] S.V. Tsynkov, On the combined implementation of global boundary conditions with central-difference multigrid flow solvers, in: T.L. Geers, ed., Collection of Abstracts of lUTAM Symposium on Computational Methodsfor Unbounded Domains, University of Colorado at Boulder, July 27-31, 1997 (Kluwer Academic, to appear). [2241 S.V. Tsynkov, E. Turkel and S. Abarbanel, External flow computations using global boundary conditions, AIAA J. 34 (1996) 700-706.
    Google ScholarLocate open access versionFindings
  • [2251 S.V. Tsynkov and V.N. Vatsa, An improved treatment of external boundary for three-dimensional flow computations, AIAA Paper No. 97-2074, in: Proceedings of the 13th AIAA Computational Fluid Dynamics Conference, Part 2, Snowmass Village, CO (1997), 1139-1149; also AIAA J., submitted.
    Google ScholarFindings
  • [226] E. Turkel, V.N. Vatsa and R. Radespiel, Preconditioning methods for low-speed flows, AIAA Paper No. 962460-CP, in: 14th AIAA Applied Aerodynamics Conference, New Orleans, LA (1996).
    Google ScholarLocate open access versionFindings
  • [227] E. Turkel and A. Yefet, Absorbing PML boundary layers for wave-like equations, Appl. Numer. Math. 27 (1998) 533-557 (this issue).
    Google ScholarLocate open access versionFindings
  • [228] T.C. Vanajakshi, K.W. Thompson and D.C. Black, Boundary value problems is magnetohydrodynamics (and fluid dynamics). I. Radiation boundary condition, J. Comput. Phys. 84 (1989) 343-359.
    Google ScholarLocate open access versionFindings
  • [229] V.N. Vatsa, M.D. Sanetrik and E.B. Parlette, Development of a flexible and efficient multigrid-based multiblock flow solver, AIAA Paper No. 93-0677, in: 31st AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV (1993).
    Google ScholarLocate open access versionFindings
  • [230] A. Verhoff, First-order far-field computational boundary conditions for O-grid topologies, AIAA Paper No. 95-0563, in: 33rd AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV (1995).
    Google ScholarFindings
  • [231] A. Verhoff, Global far-field computational boundary conditions for C-grid topologies, AIAA Paper No. 952184, in: 26th Fluid Dynamics Conference, San Diego, CA (1995).
    Google ScholarLocate open access versionFindings
  • [233] A. Verhoff, Global far-field computational boundary conditions for C- and O-grid topologies, AIAA J. 36 (1998) 148-156.
    Google ScholarFindings
  • [234] A. Verhoff and D. Stookesberry, Second-order far-field computational boundary conditions for inviscid duct flow problems, AIAA J. 30 (1992) 1268-1276.
    Google ScholarLocate open access versionFindings
  • [235] A. Verhoff, D. Stookesberry and S. Agrawal, Far-field computational boundary conditions for twodimensional external flow problems, AIAA J. 30 (1992) 2585-2594.
    Google ScholarLocate open access versionFindings
  • [236] V.S. Vladimirov, Equations of Mathematical Physics (Dekker, New York, 1971).
    Google ScholarFindings
  • [237] E. Watanabe and T. Utsunomiya, A response analysis of very large floating structure under airplane landing by FEM and a sponge layer for unbounded domain, in: T.L. Geers, ed., Collection of Abstracts oflUTAM Symposium on Computational Methods for Unbounded Domains, University of Colorado at Boulder, July 27-31, 1997 (Kluwer Academic, to appear).
    Google ScholarLocate open access versionFindings
  • [238] W.R. Watson and M.K. Myers, Inflow-outflow boundary conditions for two-dimensional acoustic waves in channels with flow, AIAA J. 29 (1991) 1383-1389.
    Google ScholarLocate open access versionFindings
  • [239] W.R. Watson and M.K. Myers, Two-step method for evolving nonlinear acoustic systems to a steady state, AIAA J. 30 (1992) 1724-1730.
    Google ScholarLocate open access versionFindings
  • [240] W.R. Watson, W.E. Zorumski and S.L. Hodge, Evaluation of several nonreflecting computational boundary conditions for duct acoustics, J. Comput. Acoust. 3 (1995) 327-342.
    Google ScholarLocate open access versionFindings
  • [241] W.R. Watson and W.E. Zorumski, Periodic time domain nonlocal nonreflecting boundary conditions for duct acoustics, NASA Technical Memorandum No. 110230, Langley Research Center (March 1996).
    Google ScholarFindings
  • [242] R.J. Weizman and E.V. Zinoviev, Sound energy flow caused by plates and shells vibrations, Akusticheskii J. 41 (1995) 567-575.
    Google ScholarLocate open access versionFindings
  • [243] F.W. Wubs, J.W. Boerstoel and A.J. Van der Wees, Grid size reduction in flow calculations on infinite domains by higher-order far-field asymptotics in numerical boundary conditions, J. Engrg. Math. 18 (1984) 157-177. [2441 K.S. Yee, Numerical solution of initial boundary value problem involving Maxwell's equations in isotropic media, IEEE Trans. Antennas Propagation 14 (1966) 302-307.
    Google ScholarLocate open access versionFindings
  • [245] V.Yu. Zavadsky, Finite-Difference Methods for the Wave Problems in Acoustics (Nauka, Moscow, 1982) (in Russian).
    Google ScholarFindings
  • [246] X. Zeng, L.F. Kallivokas and J. Bielak, Stable localized symmetric integral equation method for acoustic scattering problems, J. Acoust. Soc. Amer. 91 (1992) 2510-2518. S.V.Tsynkov/ Applied Numerical Mathematics 27 (1998) 465-532
    Google ScholarLocate open access versionFindings
  • [247] L. Zhao and A.C. Cangellaris, GT-PML: generalized theory of perfectly matched layers and its application to the reflectionless truncation of finite-difference time-domain grids, IEEE Trans. Microwave Theory Tech. 44 (1996) 2555-2563.
    Google ScholarLocate open access versionFindings
  • [248] W.E. Zorumski, W.R. Watson and S.L. Hodge, A non-local computational boundary condition for duct acoustics, NASA Technical Memorandum No. 109091, Langley Research Center (March 1994).
    Google ScholarFindings
  • [249] W.E. Zorumski, W.R, Watson and S.L. Hodge, A non-local computational boundary condition for duct acoustics, J. Comput. Acoust. 3 (1995) 15-26.
    Google ScholarLocate open access versionFindings
  • [250] N.M. Zueva, M.S. Mikhailova and V.S. Ryaben'kii, Transfer of boundary conditions from infinity to an artificial boundary for the difference analogue of the Laplace equation, Keldysh Inst. Appl. Math., U.S.S.R. Acad. Sci., Preprint No. 110, Moscow (1991) (in Russian).
    Google ScholarLocate open access versionFindings
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