Far field boundary conditions for computation over long time

A new class of computational far field boundary conditions for hyperbolic partial differential equations is developed. These boundary conditions combine properties of absorbing boundary conditions for transient solutions and properties of far field boundary conditions for steady-state problems. The conditions can be used to limit the computational domain when both traveling waves and evanescent waves are present. Boundary conditions for scalar wave equations are derived and analyzed. Extensions to systems of equations are discussed and results from numerical experiments are presented.

[1]  M. Gunzburger,et al.  Boundary conditions for the numerical solution of elliptic equations in exterior regions , 1982 .

[2]  Björn Engquist,et al.  Absorbing boundary conditions for wave-equation migration , 1980 .

[3]  L. Trefethen,et al.  Well-Posedness of one-way wave equations and absorbing boundary conditions , 1986 .

[4]  A. Bayliss,et al.  Radiation boundary conditions for wave-like equations , 1980 .

[5]  J. Sochacki.  Absorbing boundary conditions for the elastic wave equations , 1988 .

[6]  Bertil Gustafsson,et al.  A down-stream boundary procedure for the euler equations , 1982 .

[7]  David H. Rudy,et al.  A nonreflecting outflow boundary condition for subsonic navier-stokes calculations , 1980 .

[8]  O. Zienkiewicz,et al.  The coupling of the finite element method and boundary solution procedures , 1977 .

[9]  J. Lions.  Exact controllability, stabilization and perturbations for distributed systems , 1988 .

[10]  Laurence Halpern,et al.  Error analysis for absorbing boundary conditions , 1987 .

[11]  Cathleen S. Morawetz,et al.  Notes on Time Decay and Scattering for Some Hyperbolic Problems , 1987 .

[12]  Marc Lenoir,et al.  The Localized Finite Element Method and Its Application to the Two-Dimensional Sea-Keeping Problem , 1988 .

[13]  R. Higdon.  Absorbing boundary conditions for difference approximations to the multi-dimensional wave equation , 1986 .

[14]  A. Majda,et al.  Absorbing boundary conditions for the numerical simulation of waves , 1977 .

[15]  Goong Chen,et al.  Control and Stabilization for the Wave Equation in a Bounded Domain, Part II , 1979 .

[16]  J. Lions,et al.  Problèmes aux limites non homogènes et applications , 1968 .

[17]  F. Brezzi,et al.  On the coupling of boundary integral and finite element methods , 1979 .

[18]  A. Majda,et al.  Radiation boundary conditions for acoustic and elastic wave calculations , 1979 .