Publications of J. Thomas Beale

Papers Published

  1. J. T. Beale, A proof that a discrete delta function is second-order accurate, J. Comput. Phys., vol. 227 (2008), pp. 2195-97
  2. J. T. Beale and J. Strain, Locally corrected semi-Lagrangian methods for Stokes flow with moving elastic interfaces, J. Comput. Phys., vol. 227 (2008), pp. 3896-3920
  3. J. T. Beale and A. T. Layton, On the accuracy of finite difference methods for elliptic problems with interfaces, Commun. Appl. Math. Comput. Sci., vol. 1 (2006), pp. 91-119
  4. G. R. Baker and J. T. Beale, Vortex blob methods applied to interfacial motion, J. Comput. Phys., vol. 196 (2004), pp. 233-58
  5. J. T. Beale, A grid-based boundary integral method for elliptic problems in three dimensions, SIAM J. Numer. Anal., vol. 42 (2004), pp. 599-620
  6. J. T. Beale, Methods for computing singular and nearly singular integrals, J. Turbulence, vol. 3, (2002), article 041 (4 pp.)
  7. J. T. Beale, Discretization of Layer Potentials and Numerical Methods for Water Waves, Proc. of Workshop on Kato's Method and Principle for Evolution Equations in Mathematical Physics, H. Fujita, S. T. Kuroda, H.Okamoto, eds., Univ. of Tokyo Press, pp. 18-26.
  8. J. T. Beale, M.-C. Lai, A Method for Computing Nearly Singular Integrals, SIAM J. Numer. Anal., 38 (2001), 1902-25
  9. J. T. Beale, A Convergent Boundary Integral Method for Three-Dimensional Water Waves, Math. Comp. 70 (2001), 977-1029
  10. J. T. Beale, Boundary Integral Methods for Three-Dimensional Water Waves, Equadiff 99, Proceedings of the International Conference on Differential Equations, Vol. 2, pp. 1369-78
  11. J. T. Beale, T.Y. Hou, J.S. Lowengrub, Stability of Boundary Integral Methods for Water Waves, Nonlinear Evolutionary Partial Differential Equations, X. X. Ding and T.P. Liu eds., A.M.S., 1997, 107-27.
  12. J. T. Beale, T. Y. Hou and J. S. Lowengrub, Convergence of a Boundary Integral Method for Water Waves, SIAM J. Numer. Anal. 33 (1996), 1797-1843.
  13. J. T. Beale, A. Lifschitz, W.H. Suters, The Onset of Instability in Exact Vortex Rings with Swirl, J. Comput. Phys. 129 (1996) 8-29
  14. J. T. Beale, T.Y. Hou, J.S. Lowengrub, Stability of Boundary Integral Methods for Water Waves, Advances in Multi-Fluid Flows, Y. Renardy et al., ed., pp. 241-45, SIAM, Philadelphia, 1996.
  15. J. T. Beale, A. Lifschitz, W.H. Suters, A Numerical and Analytical Study of Vortex Rings with Swirl, Vortex Flows and Related Numerical Methods, II, ESAIM Proc. 1, 565-75, Soc. Math. Appl. Indust., Paris, 1996.
  16. J. T. Beale, Analytical and Numerical Aspects of Fluid Interfaces, Proc. International Congress of Mathematicians 1994, S. Chatterji, ed., Vol. II, pp. 1055-64, Birkhauser, Basel, 1995.
  17. J. T. Beale, C. Greengard, Convergence of Euler-Stokes Splitting of the Navier-Stokes Equations, Comm. Pure Appl. Math. 47 (1994), 1083-1115.
  18. J. T. Beale, T. Y. Hou, J. S. Lowengrub, and M. Shelley, Spatial and Temporal Stability Issues for Interfacial Flows with Surface Tension, Mathl. Comput. Modeling 20 (1994), No. 10/11, 1-27
  19. A. Bourgeois, J. T. Beale, Validity of the Quasigeostrophic Model for Large Scale Flow in the Atmosphere and Ocean, SIAM J. Math. Anal. 25 (1994), 1023-68.
  20. J. T. Beale, T. Y. Hou, J. S. Lowengrub, Growth rates for the linearized motion of fluid interfaces away from equilibrium, Comm. Pure Appl. Math. 46 (1993), 1269-1301.
  21. J. T. Beale, T. Y. Hou, J. S. Lowengrub, On the well-posedness of two-fluid interfacial flows with surface tension, Singularities in Fluids, Plasmas, and Optics, R. Caflisch et al., ed., pp. 11-38, NATO ASI Series, Kluwer, 1993.
  22. J. T. Beale, E. Thomann, C. Greengard, Operator splitting for Navier-Stokes and the Chorin-Marsden product formula, Vortex Flows and Related Numerical Methods, J. T. Beale et al., ed., pp. 27-38, NATO ASI Series, Kluwer, 1993.
  23. J. T. Beale, The approximation of weak solutions to the Euler equations by vortex elements, Multidimensional Hyperbolic Problems and Computations, J. Glimm et al., ed., pp. 23-37, Springer-Verlag, New York, 1991.
  24. J. T. Beale, Exact solitary water waves with capillary ripples at infinity, Comm. Pure Appl. Math. 44 (1991), 211-257.
  25. J. T. Beale, A. Eydeland, B. Turkington, Numerical tests of 3-D vortex methods using a vortex ring with swirl, Vortex Dynamics and Vortex Methods, C. Anderson and C. Greengard, ed., pp. 1-9, A.M.S., 1991.
  26. J. T. Beale, Solitary water waves with ripples beyond all orders, Asymptotics beyond All Orders, H. Segur et al., ed., pp. 293-98, NATO ASI Series, Plenum, 1991.
  27. J. T. Beale, Large-time behavior of model gases with a discrete set of velocities, Mathematics Applied to Science, J. Goldstein et al., ed. pp. 1-12, Academic Press, Orlando, 1988.
  28. J. T. Beale, On the accuracy of vortex methods at large times, Computational Fluid Dynamics and Reacting Gas Flows, B. Engquist et al., ed., pp. 19-32, Springer-Verlag, New York, 1988.
  29. J. T. Beale, D. Schaeffer, Nonlinear behavior of model equations which are linearly ill-posed, Comm. P. D. E. 13 (1988), 423-67.
  30. J. T. Beale, Existence, regularity, and decay of viscous surface waves, Nonlinear Systems of Partial Differential Equations in Applied Mathematics, Part 2, Lectures in Applied Mathematics, Vol. 23, A.M.S., Providence, 1986, 137-48.
  31. J. T. Beale, A convergent three-dimensional vortex method with grid-free stretching, Math. Comp. 46 (1986), 401-24 and S15-S20.
  32. J. T. Beale, Large-time behavior of discrete velocity Boltzmann equations, Comm. Math. Phys. 106 (1986), 659-78.
  33. J. T. Beale, A. Majda, High order accurate vortex methods with explicit velocity kernels, J. Comp. Phys. 58 (1985), 188-208.
  34. J. T. Beale, T. Nishida, Large-time behavior of viscous surface waves, North-Holland Mathematics Studies, 128 (1985), 1-14.
  35. J. T. Beale, Large-time behavior of the Broadwell model of a discrete velocity gas, Comm. Math. Phys. 102 (1985), 217-35.
  36. J. T. Beale, Large-time regularity of viscous surface waves, Arch. Rational Mech. Anal. 84 (1984), 307-52.
  37. J. T. Beale, T. Kato, A. Majda, Remarks on the breakdown of smooth solutions for the 3-D Euler equations, Comm. Math. Phys. 94 (1984), 61-66.
  38. J. T. Beale, A. Majda, Vortex methods for fluid flow in two or three dimensions, Contemp. Math. 28 (1984), 221-29.
  39. J. T. Beale, Large-time regularity of viscous surface waves, Contemp. Math. 17 (1983), 31-33.
  40. J. T. Beale, A. Majda, Vortex methods I: Convergence in three dimensions, Math. Comp. 39 (1982), 1-27.
  41. J. T. Beale, A. Majda, Vortex methods II: Higher order accuracy in two and three dimensions, Math. Comp. 39 (1982), 29-52.
  42. J. T. Beale, A. Majda, The design and numerical analysis of vortex methods, Transonic, Shock, and Multidimensional Flows, R. E. Meyer, ed., Academic Press, New York, 1982.
  43. J. T. Beale, The initial value problem for the Navier-Stokes equations with a free surface, Comm. Pure Appl. Math. 34 (1981), 359-392.
  44. J. T. Beale, A. Majda, Rates of convergence for viscous splitting of the Navier-Stokes equations, Math. Comp. 37 (1981), 243-259.
  45. J. T. Beale, Water waves generated by a pressure disturbance on a steady stream, Duke Math. J. 47 (1980), 297-323.
  46. J. T. Beale, The existence of cnoidal water waves with surface tension, J. Differential Eqns. 31(1979), 230-263.
  47. J. T. Beale, Acoustic scattering from locally reacting surfaces, Indiana Univ. Math. J. 26 (1977), 199-222.
  48. J. T. Beale, Eigenfunction expansions for objects floating in an open sea, Comm. Pure Appl. Math. 30 (1977), 283-313.
  49. J. T. Beale, The existence of solitary water waves, Comm. Pure Appl. Math. 30 (1977), 373-389.
  50. J. T. Beale, Spectral properties of an acoustic boundary condition, Indiana Univ. Math. J. 25 (1976), 895-917.
  51. J. T. Beale, Purely imaginary scattering frequencies for exterior domains, Duke Math. J. 41 (1974), 607-637.
  52. J. T. Beale, S. I. Rosencrans, Acoustic boundary conditions, Bull. Amer. Math. Soc. 80 (1974), 1276-1278.
  53. J. T. Beale, Scattering frequencies of resonators, Comm. Pure Appl. Math. 26 (1973), 549-563.