• R.J. Astley (1996), “Transient Wave Envelope Elements for Wave Problems,” J. Sound Vib., 192, 245–261.

  Article  Google Scholar 

• A. Bayliss and E. Turkel (1980), “Radiation Boundary Conditions for Wave-Like Equations,” Comm. Pure Appl. Math., 33, 707–725.

  Google Scholar 

• J.P. Bérenger (1994), “A Perfectly Matched Layer for the Absorption of Electromagnetic Waves,” J. Comput. Phys., 114, 185–200.

  Google Scholar 

• P. Bettess (1977), “Infinite Elements,” Int. J. Numer. Meth. Engng., 11, 53–64.

  Google Scholar 

• D.S. Burnett (1994), “A Three-Dimensional Acoustic Infinite Element Based on a Prolate Spheroidal Multipole Expansion,” J. Acoust. Soc. Am., 96, 2798–2816.

  Google Scholar 

• F. Collino (1993), “High Order Absorbing Boundary Conditions for Wave Propagation Models. Straight Line Boundary and Corner Cases,” in Proc. 2nd Int. Conf. on Mathematical & Numerical Aspects of Wave Propagation, R. Kleinman et al., Eds., SIAM, Delaware, pp. 161–171.

  Google Scholar 

• B. Engquist and A. Majda (1979), “Radiation Boundary Conditions for Acoustic and Elastic Calculations,” Comm. Pure Appl. Math., 32, 313–357.

  Google Scholar 

• D. Givoli (1991), “Non-Reflecting Boundary Conditions: A Review,” J. Comput. Phys., 94, 1–29.

  Google Scholar 

• D. Givoli (1999), “Exact Representations on Artificial Interfaces and Applications in Mechanics,” Appl. Mech. Rev., 52, 333–349.

  Google Scholar 

• D. Givoli (2001), “High-Order Non-Reflecting Boundary Conditions Without High-Order Derivatives,” J. Comput. Phys., 170, 849–870.

  Google Scholar 

• D. Givoli and J.B. Keller (1989), “A Finite Element Method for Large Domains,” Comput. Meth. Appl. Mech. Engng., 76, 41–66.

  Google Scholar 

• D. Givoli and B. Neta (2003), “High-Order Non-Reflecting Boundary Scheme for Time-Dependent Waves,” J. Comput. Phys., 186, 24–46.

  Google Scholar 

• D. Givoli and I. Patlashenko (2002), “An Optimal High-Order Non-Reflecting Finite Element Scheme for Wave Scattering Problems,” Int. J. Numer. Meth. Engng., 53, 2389–2411.

  Google Scholar 

• M.J. Grote and J.B. Keller (1995), “Exact Nonreflecting Boundary Conditions for the Time Dependent Wave Equation,” SIAM J. of Appl. Math., 55, 280–297.

  Article MathSciNet MATH  Google Scholar 

• M.J. Grote and J.B. Keller (1996), “Nonreflecting Boundary Conditions for Time Dependent Scattering,” J. Comput. Phys., 127, 52–65.

  Google Scholar 

• M.J. Grote and J.B. Keller (2000), “Nonreflecting Boundary Conditions for Elastic Waves,” SIAM J. Appl. Math., 60, 803–819.

  Google Scholar 

• M.N. Guddati and J.L. Tassoulas (2000), “Continued-Fraction Absorbing Boundary Conditions for the Wave Equation,” J. Comput. Acoust., 8, 139–156.

  Google Scholar 

• T. Hagstrom (1999), “Radiation Boundary Conditions for the Numerical Simulation of Waves,” Acta Numerica, 8, 47–106.

  Article MathSciNet  Google Scholar 

• T. Hagstrom and S.I. Hariharan (1998), “A Formulation of Asymptotic and Exact Boundary Conditions Using Local Operators,” Appl. Nu-mer. Math., 27, 403–416.

  Google Scholar 

• T. Hagstrom and H.B. Keller (1986), “Exact Boundary Conditions at an Artificial Boundary for Partial Differential Equations in Cylinders,” SIAM J. Math. Anal., 17, 322–341.

  Google Scholar 

• R.L. Higdon (1994), “Radiation Boundary Conditions for Dispersive Waves,” SIAM J. Numer. Anal., 31, 64–100.

  Google Scholar 

• H.B. Keller (1976), Numerical Solution of Two Point Boundary Value Problems, No. 24, CBMS/NSF Regional Conference Series on Applied Mathematics, SIAM, Philadelphia, PA.

  Book  Google Scholar 

• H.B. Keller and M. Lentini (1980), “Boundary Value Problems on Semi-Infinite Intervals and Their Numerical Solution,” SIAM J. Numer. Anal., 17, 577–604.

  Google Scholar 

• J.B. Keller and D. Givoli (1989). Givoli (1989), “Exact Non-Reflecting Boundary Conditions,” J. Comput. Phys., 82, 172–192, 1989.

  Article MathSciNet MATH  Google Scholar 

• F.J. Rizzo (1989), The Boundary Element Method — Some Early History: A Personal View, in Boundary Elements in Structural Analysis, D.E. Beskos, Ed., 1–16, ASCE, New York.

  Google Scholar 

• V.S. Ryaben’kii and S.V. Tsynkov (1995), “Artificial Boundary Conditions for the Numerical Solution of External Viscous Flow Problems,” SIAM J. Numer. Anal., 32, 1355–1389.

  Google Scholar 

• L. Ting and M.J. Miksis (1986), “Exact Boundary Conditions for Scattering Problems,” J. Acoust. Soc. Am., 80, 1825–1827.

  Google Scholar 

• S.V. Tsynkov (1998), “Numerical Solution of Problems on Unbounded Domains, A Review,” Appl. Numer. Math., 27, 465–532.

  Google Scholar 

• V.J. van Joolen (2003), Application of Higdon Non-Reflecting Boundary Conditions to Shallow Water Models, PhD thesis, Dept. of Applied Math., Naval Postgraduate School, Monterey, CA, USA.

  Google Scholar 

Download references