Abarbanel S. and Gottlieb D. (1997), ‘A mathematical analysis of the PML method’, J. Comput. Phys. 134, 357–363.
Abramowitz M. and Stegun I., eds (1972), Handbook of Mathematical Functions, Dover, New York.
Alpert B., Greengard L. and Hagstrom T. (1999 a), ‘Accurate solution of the wave equation on unbounded domains’. In preparation.
Alpert B., Greengard L. and Hagstrom T. (1999 b), ‘Rapid evaluation of nonreflecting boundary kernels for time-domain wave propagation’, SIAM J. Numer. Anal. To appear.
Anderson C. R. (1992), ‘An implementation of the fast multipole method without multipoles’, SIAM J. Sci. Statist. Comput. 13, 923–947.
Barry A., Bielak J. and MacCamy R. (1988), ‘On absorbing boundary conditions for wave propagation’, J. Comput. Phys. 79, 449–468.
Bayliss A. and Turkel E. (1980), ‘Radiation boundary conditions for wave-like equations’, Comm. Pure Appl. Math. 33, 707–725.
Berenger J.-P. (1994), ‘A perfectly matched layer for the absorption of electromagnetic waves’, J. Comput. Phys. 114, 185–200.
Bettess P. (1992), Infinite Elements, Penshaw Press, Sunderland, UK.
Chew W. and Weedon W. (1994), ‘A 3-D perfectly matched medium from modified Maxwell's equations with stretched coordinates’, Microwave Optical Technol. Lett. 7, 599–604.
Collino F. (1993), Conditions d'ordre élevé pour des modèles de propagation d'ondes dans des domaines rectangulaires, Technical Report 1790, INRIA.
Collino F. and Monk P. (1998), ‘Optimizing the perfectly matched layer’. Preprint.
Demkowicz L. and Gerdes K. (1999), ‘Convergence of the infinite element methods for the Helmholtz equation in separable domains’, Numer. Math. To appear.
Doetsch G. (1974), Introduction to the Theory and Application of the Laplace Transformation, Springer, New York.
Driscoll J., Healy D. and Rockmore D. (1997), ‘Fast discrete polynomial transforms with applications to data analysis for distance transitive graphs’, SIAM J. Comput. 26, 1066–1099.
Engquist B. and Majda A. (1977), ‘Absorbing boundary conditions for the numerical simulation of waves’, Math. Comput. 31, 629–651.
Engquist B. and Majda A. (1979), ‘Radiation boundary conditions for acoustic and elastic wave calculations’, Comm. Pure Appl. Math. 32, 313–357.
Eringen A. and Şuhubi E. (1975), Elastodynamics, Vol. 2, Academic Press, New York.
Geers T. (1998), Benchmark problems, in Computational Methods for Unbounded Domains (Geers T., ed.), Kluwer Academic Publishers, Dordrecht, Netherlands, pp. 1–10.
Giles M. (1990), ‘Nonreflecting boundary conditions for Euler equation calculations’, AIAA Journal 28, 2050–2058.
Givoli D. (1991), ‘Non-reflecting boundary conditions’, J. Comput. Phys. 94, 1–29.
Givoli D. (1992), Numerical Methods for Problems in Infinite Domains, Vol. 33 of Studies in Applied Mechanics, Elsevier, Amsterdam.
Givoli D. and Kohen D. (1995), ‘Non-reflecting boundary conditions based on Kirchoff-type formulae’, J. Comput. Phys. 117, 102–113.
Goodrich J. and Hagstrom T. (1999), ‘High-order radiation boundary conditions for computational aeroacoustics’. In preparation.
Greengard L. and Lin P. (1998), ‘On the numerical solution of the heat equation on unbounded domains (Part I)’. Preprint.
Greengard L. and Rokhlin V. (1997), A new version of the fast multipole method for the Laplace equation in three dimensions, in Acta Numerica, Vol. 6, Cambridge University Press, pp. 229–269.
Grote M. and Keller J. (1995), ‘Exact nonreflecting boundary conditions for the time dependent wave equation’, SIAM J. Appl. Math. 55, 280–297.
Grote M. and Keller J. (1996), ‘Nonreflecting boundary conditions for time dependent scattering’, J. Comput. Phys. 127, 52–81.
Grote M. and Keller J. (1998), Exact nonreflecting boundary conditions for elastic waves, Technical Report 1998–08, ETH, Zürich.
Grote M. and Keller J. (1999), ‘Nonreflecting boundary conditions for Maxwell's equations’, J. Comput. Phys. To appear.
Gustafsson B. and Kreiss H.-O. (1979), ‘Boundary conditions for time-dependent problems with an artificial boundary’, J. Comput. Phys. 30, 333–351.
Hagstrom T. (1983), Reduction of Unbounded Domains to Bounded Domains for Partial Differential Equation Problems, PhD thesis, California Institute of Technology.
Hagstrom T. (1991a), ‘Asymptotic boundary conditions for dissipative waves: General theory’, Math. Comput. 56, 589–606.
Hagstrom T. (1991b), ‘Conditions at the downstream boundary for simulations of viscous, incompressible flow’, SIAM J. Sci. Statist. Comput. 12, 843–858.
Hagstrom T. (1995), On the convergence of local approximations to pseudodifferential operators with applications, in Proc. 3rd Int. Conf. on Math, and Num. Aspects of Wave Prop. Phen. (Bécache E., Cohen G., Joly P. and Roberts J., eds), SIAM, pp. 474–482.
Hagstrom T. (1996), On high-order radiation boundary conditions, in IMA Volume on Computational Wave Propagation (Engquist B. and Kriegsmann G., eds), Springer, New York, pp. 1–22.
Hagstrom T. and Goodrich J. (1998), ‘Experiments with approximate radiation boundary conditions for computational aeroacoustics’, Appl. Numer. Math. 27, 385–402.
Hagstrom T. and Hariharan S. (1996), Progressive wave expansions and open boundary problems, in IMA Volume on Computational Wave Propagation (Engquist B. and Kriegsmann G., eds), Springer, New York, pp. 23–43.
Hagstrom T. and Hariharan S. (1998), ‘A formulation of asymptotic and exact boundary conditions using local operators’, Appl. Numer. Math. 27, 403–416.
Hagstrom T. and Keller H. B. (1986), ‘Exact boundary conditions at an artificial boundary for partial differential equations in cylinders’, SIAM J. Math. Anal. 17, 322–341.
Hagstrom T. and Lorenz J. (1994), Boundary conditions and the simulation of low Mach number flows, in Proceedings of the First International Conference on Theoretical and Computational Acoustics (Lee D. and Schultz M., eds), World Scientific, Singapore, pp. 657–668.
Hairer E., Lubich C. and Schlichte M. (1985), ‘Fast numerical solution of nonlinear Volterra convolutional equations’, SIAM J. Sci. Statist. Comput. 6, 532–541.
Halpern L. (1986), ‘Artificial boundary conditions for the linear advection diffusion equation’, Math. Comput. 46, 425–438.
Halpern L. (1991), ‘Artificial boundary conditions for incompletely parabolic perturbations of hyperbolic systems’, SIAM J. Math. Anal. 22, 1256–1283.
Halpern L. and Rauch J. (1987), ‘Error analysis for absorbing boundary conditions’, Numer. Math. 51, 459–467.
Halpern L. and Rauch J. (1995), ‘Absorbing boundary conditions for diffusion equations’, Numer. Math. 71, 185–224.
Halpern L. and Schatzman M. (1989), ‘Artificial boundary conditions for viscous incompressible flows’, SIAM J. Math. Anal. 20, 308–353.
He S. and Weston V. (1996), Wave-splitting and absorbing boundary conditions for Maxwell's equations on a curved surface, Technical Report TRITA-TET-96–14, KTH, Stockholm.
Higdon R. (1986), ‘Absorbing boundary conditions for difference approximations to the multidimensional wave equation’, Math. Comput. 47, 437–459.
Higdon R. (1987), ‘Numerical absorbing boundary conditions for the wave equation’, Math. Comput. 49, 65–90.
Higdon R. (1991), ‘Absorbing boundary conditions for elastic waves’, Geophysics 56, 231–254.
Higdon R. (1992), ‘Absorbing boundary conditions for acoustic and elastic waves in stratified media’, J. Comput. Phys. 101, 386–418.
Higdon R. (1994), ‘Radiation boundary conditions for dispersive waves’, SIAM J. Numer. Anal. 31, 64–100.
Holford R. (1999), ‘A multipole expansion for the acoustic field exterior to a prolate or oblate spheroid’. Submitted to J. Acoust. Soc. Amer.
Johansson C. (1993), ‘Boundary conditions for open boundaries for the incompressible Navier-Stokes equations’, J. Comput. Phys. 105, 233–251.
Kato T. (1976), Perturbation Theory for Linear Operators, Springer, New York.
Kreiss H.-O. and Lorenz J. (1989), Initial-Boundary Value Problems and the Navier–Stokes Equations, Academic Press, New York.
Lindman E. (1975), ‘Free space boundary conditions for the time dependent wave equation’, J. Comput. Phys. 18, 66–78.
Lohéac J.-P. (1991), ‘An artificial boundary condition for an advection-diffusion equation’, Math. Meth. Appl. Sci. 14, 155–175.
Ludwig D. (1960), ‘Exact and asymptotic solutions of the Cauchy problem’, Comm. Pure Appl. Math. 13, 473–508.
Mohlenkamp M. (1997), ‘A fast transform for spherical harmonics’. Preprint.
Newton R. (1966), Scattering Theory of Waves and Particles, McGraw-Hill, New York.
Nordström J. (1995), ‘Accurate solutions of the Navier–Stokes equations despite unknown outflow boundary data’, J. Comput. Phys 120, 184–205.
Nordström J. (1997), ‘On extrapolation procedures at artificial outflow boundaries for the time-dependent Navier–Stokes equations’, Appl. Numer. Math. 23, 457–468.
Oberhettinger F. and Badii L. (1970), Tables of Laplace Transforms, Springer, New York.
Olver F. (1954), ‘The asymptotic expansion of Bessel functions of large order’, Philos. Trans. Royal Soc. London A247, 328–368.
Petropoulos P. (1999), ‘Reflectionless sponge layers as absorbing boundary conditions for the numerical solution of Maxwell's equations in rectangular, cylindrical and spherical coordinates’. Submitted to SIAM J. Appl. Math.
Radvogin Y. and Zaitsev N. (1998), Absolutely transparent boundary conditions for time-dependent wave problems, in Seventh International Conference on Hyperbolic Problems.
Ramm A. (1986), Scattering by Obstacles, D. Reidel, Dordrecht, Netherlands.
Rokhlin V. (1990), ‘Rapid solution of integral equations of scattering theory in two dimensions’, J. Comput. Phys. 86, 414–439.
Ryabeńkii V. (1985), ‘Boundary equations with projections’, Russian Math. Surveys 40, 147–183.
Schwartz M. (1987), Principles of Electrodynamics, Dover, New York.
Sofronov I. (1993), ‘Conditions for complete transparency on the sphere for the three-dimensional wave equation’, Russian Acad. Sci. Dokl. Math. 46, 397–401.
Sofronov I. (1999), ‘Artificial boundary conditions of absolute transparency for two-and three-dimensional external time-dependent scattering problems’, Euro. J. Appl. Math. To appear.
Ting L. and Miksis M. (1986), ‘Exact boundary conditions for scattering problems’, J. Acoust. Soc. Amer. 80, 1825–1827.
Trefethen L. and Halpern L. (1986), ‘Well-posedness of one-way wave equations and absorbing boundary conditions’, Math. Comput. 47, 421–435.
Trefethen L. and Halpern L. (1988), ‘Wide-angle one-way wave equations’, J. Acoust. Soc. Amer. 84, 1397–1404.
Tsynkov S. (1998), ‘Numerical solution of problems on unbounded domains. A review’, Appl. Numer. Math. 27, 465–532.
Turkel E. and Yefet A. (1998), ‘Absorbing PML boundary layers for wave-like equations’, Appl. Numer. Math. 27, 533–557.
Vacus O. (1996), Singularités de frontière et conditions limites absorbantes: le problème du coin, Technical Report 2851, INRIA.
Xu L. and Hagstrom T. (1999), ‘On convergent sequences of approximate radiation boundary conditions and reflectionless sponge layers’. In preparation.