Publications of J. Thomas Beale

Papers Published

  1. Tlupova, S; Beale, JT, Regularized single and double layer integrals in 3D Stokes flow, Journal of Computational Physics, vol. 386 (June, 2019), pp. 568-584
  2. Beale, JT; Ying, W, Solution of the Dirichlet problem by a finite difference analog of the boundary integral equation, Numerische Mathematik, vol. 141 no. 3 (March, 2019), pp. 605-626
  3. Beale, JT; Ying, W; Wilson, JR, A Simple Method for Computing Singular or Nearly Singular Integrals on Closed Surfaces, Communications in Computational Physics, vol. 20 no. 03 (September, 2016), pp. 733-753, Global Science Press
  4. Beale, JT, Uniform Error Estimates for Navier--Stokes Flow with an Exact Moving Boundary Using the Immersed Interface Method, Siam Journal on Numerical Analysis, vol. 53 no. 4 (2015), pp. 2097-2111, Society for Industrial & Applied Mathematics (SIAM), ISSN 0036-1429
  5. Ying, W; Beale, JT, A Fast Accurate Boundary Integral Method for Potentials on Closely Packed Cells, Communications in Computational Physics, vol. 14 no. 04 (2013), pp. 1073-1093, Global Science Press, ISSN 1815-2406
  6. Tlupova, S; Beale, JT, Nearly singular integrals in 3D stokes flow, Communications in Computational Physics, vol. 14 no. 5 (2013), pp. 1207-1227, Global Science Press, ISSN 1815-2406
  7. Layton, AT; Beale, JT, A partially implicit hybrid method for computing interface motion in stokes flow, Discrete and Continuous Dynamical Systems Series B, vol. 17 no. 4 (2012), pp. 1139-1153, American Institute of Mathematical Sciences (AIMS), ISSN 1531-3492
  8. Beale, JT, Partially implicit motion of a sharp interface in Navier-Stokes flow, J. Comput. Phys., vol. 231 no. 18 (2012), pp. 6159-6172, Elsevier BV
  9. Beale, JT, Smoothing properties of implicit finite difference methods for a diffusion equation in maximum norm, Siam Journal on Numerical Analysis, vol. 47 no. 4 (2009), pp. 2476-2495, Society for Industrial & Applied Mathematics (SIAM), ISSN 0036-1429
  10. Beale, JT; Layton, AT, A velocity decomposition approach for moving interfaces in viscous fluids, Journal of Computational Physics, vol. 228 no. 9 (2009), pp. 3358-3367, Elsevier BV, ISSN 0021-9991
  11. Beale, JT; Chopp, D; LeVeque, R; Li, Z, Correction to the article A comparison of the extended finite element method with the immersed interface method for elliptic equations with discontinuous coefficients and singular sources by Vaughan et al., Commun. Appl. Math. Comput. Sci., vol. 3 no. 1 (2008), pp. 95-100, Mathematical Sciences Publishers
  12. Beale, JT; Strain, J, Locally corrected semi-Lagrangian methods for Stokes flow with moving elastic interfaces, Journal of Computational Physics, vol. 227 no. 8 (2008), pp. 3896-3920, Elsevier BV, ISSN 0021-9991
  13. Beale, JT, A proof that a discrete delta function is second-order accurate, Journal of Computational Physics, vol. 227 no. 4 (2008), pp. 2195-2197, Elsevier BV, ISSN 0021-9991
  14. Thomas Beale, J; Layton, AT, On the accuracy of finite difference methods for elliptic problems with interfaces, Communications in Applied Mathematics and Computational Science, vol. 1 no. 1 (2006), pp. 91-119, Mathematical Sciences Publishers
  15. Beale, JT, A grid-based boundary integral method for elliptic problems in three dimensions, Siam Journal on Numerical Analysis, vol. 42 no. 2 (2004), pp. 599-620, Society for Industrial & Applied Mathematics (SIAM), ISSN 0036-1429
  16. Baker, GR; Beale, JT, Vortex blob methods applied to interfacial motion, Journal of Computational Physics, vol. 196 no. 1 (2004), pp. 233-258, Elsevier BV
  17. Beale, JT; Lai, MC, A method for computing nearly singular integrals, Siam Journal on Numerical Analysis, vol. 38 no. 6 (December, 2001), pp. 1902-1925, Society for Industrial & Applied Mathematics (SIAM)
  18. Beale, JT, Discretization of Layer Potentials and Numerical Methods for Water Waves (Tosio Kato's Method and Principle for Evolution Equations in Mathematical Physics), Rims Kokyuroku, vol. 1234 (October, 2001), pp. 18-26, Kyoto University, ISSN 1880-2818
  19. Beale, JT, A convergent boundary integral method for three-dimensional water waves, Mathematics of Computation, vol. 70 no. 235 (July, 2001), pp. 977-1029, American Mathematical Society (AMS)
  20. Beale, JT; Hou, TY; Lowengrub, J, Stability of boundary integral methods for water waves, Ams Ims Siam Joint Summer Research Conference (January, 1996), pp. 241-245
  21. Beale, JT; Hou, TY; Lowengrub, J, Convergence of a boundary integral method for water waves, Siam Journal on Numerical Analysis, vol. 33 no. 5 (January, 1996), pp. 1797-1843, Society for Industrial & Applied Mathematics (SIAM)
  22. Lifschitz, A; Suters, WH; Beale, JT, The onset of instability in exact vortex rings with swirl, Journal of Computational Physics, vol. 129 no. 1 (January, 1996), pp. 8-29, Elsevier BV
  23. Beale, JT; Greengard, C, Convergence of euler-stokes splitting of the navier-stokes equations, Communications on Pure and Applied Mathematics, vol. 47 no. 8 (August, 1994), pp. 1083-1115, WILEY, ISSN 0010-3640
  24. Bourgeois, AJ; Beale, JT, Validity of the Quasigeostrophic Model for Large-Scale Flow in the Atmosphere and Ocean, Siam Journal on Mathematical Analysis, vol. 25 no. 4 (July, 1994), pp. 1023-1068, Society for Industrial & Applied Mathematics (SIAM), ISSN 0036-1410
  25. Beale, JT; Hou, TY; Lowengrub, JS; Shelley, MJ, Spatial and temporal stability issues for interfacial flows with surface tension, Mathematical and Computer Modelling, vol. 20 no. 10-11 (January, 1994), pp. 1-27, Elsevier BV, ISSN 0895-7177
  26. Beale, JT; Hou, TY; Lowengrub, JS, Growth rates for the linearized motion of fluid interfaces away from equilibrium, Communications on Pure and Applied Mathematics, vol. 46 no. 9 (1993), pp. 1269-1301, WILEY, ISSN 0010-3640
  27. 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., NATO ASI Series, Kluwer (1993), pp. 11-38
  28. Beale, JT, Exact solitary water waves with capillary ripples at infinity, Communications on Pure and Applied Mathematics, vol. 44 no. 2 (March, 1991), pp. 211-257, WILEY, ISSN 0010-3640
  29. Beale, JT; Schaeffer, DG, Nonlinear behavior of model equations which are linearly ill-posed, Communications in Partial Differential Equations, vol. 13 no. 4 (January, 1988), pp. 423-467, Informa UK Limited, ISSN 0360-5302
  30. Beale, JT, Large-time behavior of discrete velocity boltzmann equations, Communications in Mathematical Physics, vol. 106 no. 4 (December, 1986), pp. 659-678, Springer Nature, ISSN 0010-3616
  31. BEALE, JT, ANALYSIS OF VORTEX METHODS FOR INCOMPRESSIBLE-FLOW, Journal of Statistical Physics, vol. 44 no. 5-6 (September, 1986), pp. 1009-1011, ISSN 0022-4715
  32. Beale, JT, A Convergent 3-D Vortex Method With Grid-Free Stretching, Mathematics of Computation, vol. 46 no. 174 (April, 1986), pp. 401-401, JSTOR
  33. Beale, JT, Convergent 3-D vortex method with grid-free stretching. (January, 1986)
  34. Beale, JT, Large-time behavior of the Broadwell model of a discrete velocity gas, Communications in Mathematical Physics, vol. 102 no. 2 (June, 1985), pp. 217-235, Springer Nature, ISSN 0010-3616
  35. Beale, JT; Nishida, T, Large-Time Behavior of Viscous Surface Waves, North-Holland Mathematics Studies, vol. 128 no. C (January, 1985), pp. 1-14, Elsevier, ISSN 0304-0208
  36. Beale, JT; Majda, A, High order accurate vortex methods with explicit velocity kernels, Journal of Computational Physics, vol. 58 no. 2 (January, 1985), pp. 188-208, Elsevier BV, ISSN 0021-9991
  37. Beale, JT, Large-time regularity of viscous surface waves, Archive for Rational Mechanics and Analysis, vol. 84 no. 4 (December, 1984), pp. 307-352, Springer Nature, ISSN 0003-9527
  38. Beale, JT; Kato, T; Majda, A, Remarks on the breakdown of smooth solutions for the 3-D Euler equations, Communications in Mathematical Physics, vol. 94 no. 1 (1984), pp. 61-66, Springer Nature, ISSN 0010-3616
  39. Beale, JT; Majda, AJ, Explicit smooth velocity kernels for vortex methods. (January, 1983)
  40. Beale, JT; Majda, A, Vortex methods. II. Higher order accuracy in two and three dimensions, Mathematics of Computation, vol. 39 no. 159 (September, 1982), pp. 29-29, American Mathematical Society (AMS)
  41. Beale, JT; Majda, A, Vortex Methods. II: Higher Order Accuracy in Two and Three Dimensions, Mathematics of Computation, vol. 39 no. 159 (July, 1982), pp. 29-29, JSTOR, ISSN 0025-5718
  42. Beale, JT; MAJDA, A, Vortex Methods 1: Convergence in 3 Dimensions, Mathematics of Computation, vol. 39 no. 159 (1982), pp. 1-27, American Mathematical Society (AMS), ISSN 0025-5718
  43. Beale, JT; Majda, A, Rates of Convergence for Viscous Splitting of the Navier-Stokes Equations, Mathematics of Computation, vol. 37 no. 156 (October, 1981), pp. 243-243, JSTOR, ISSN 0025-5718
  44. Beale, JT, The initial value problem for the navierā€stokes equations with a free surface, Communications on Pure and Applied Mathematics, vol. 34 no. 3 (January, 1981), pp. 359-392, WILEY, ISSN 0010-3640
  45. Beale, JT, Water-Waves Generated by a Pressure Disturbance on a Steady Stream, Duke Mathematical Journal, vol. 47 no. 2 (1980), pp. 297-323, Duke University Press, ISSN 0012-7094
  46. Beale, JT, The existence of cnoidal water waves with surface tension, Journal of Differential Equations, vol. 31 no. 2 (January, 1979), pp. 230-263, Elsevier BV, ISSN 0022-0396
  47. Thomas Beale, J, The existence of solitary water waves, Communications on Pure and Applied Mathematics, vol. 30 no. 4 (July, 1977), pp. 373-389, WILEY, ISSN 0010-3640
  48. Thomas Beale, J, Eigenfunction expansions for objects floating in an open sea, Communications on Pure and Applied Mathematics, vol. 30 no. 3 (May, 1977), pp. 283-313, WILEY, ISSN 0010-3640
  49. BEALE, JT, ACOUSTIC SCATTERING FROM LOCALLY REACTING SURFACES, Indiana University Mathematics Journal, vol. 26 no. 2 (1977), pp. 199-222
  50. Beale, JT, Spectral Properties of an Acoustic Boundary Condition, Indiana University Mathematics Journal, vol. 25 no. 9 (1976), pp. 895-917
  51. Beale, JT, Purely imaginary scattering frequencies for exterior domains, Duke Mathematical Journal, vol. 41 no. 3 (September, 1974), pp. 607-637, Duke University Press, ISSN 0012-7094
  52. Beale, JT; Rosencrans, SI, Acoustic boundary conditions, Bulletin of the American Mathematical Society, vol. 80 no. 6 (January, 1974), pp. 1276-1278, American Mathematical Society (AMS), ISSN 0002-9904
  53. Beale, JT, Scattering frequencies of resonators, Communications on Pure and Applied Mathematics, vol. 26 no. 4 (July, 1973), pp. 549-563, WILEY, ISSN 0010-3640
  54. J. T. Beale, Methods for computing singular and nearly singular integrals, J. Turbulence, vol. 3, (2002), article 041 (4 pp.)
  55. 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.
  56. 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
  57. 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.
  58. 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.
  59. 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.
  60. 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.
  61. 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.
  62. 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.
  63. 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.
  64. 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.
  65. 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.
  66. 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.
  67. J. T. Beale, A convergent three-dimensional vortex method with grid-free stretching, Math. Comp. 46 (1986), 401-24 and S15-S20.
  68. J. T. Beale, Large-time regularity of viscous surface waves, Arch. Rational Mech. Anal. 84 (1984), 307-52.
  69. J. T. Beale, A. Majda, Vortex methods for fluid flow in two or three dimensions, Contemp. Math. 28 (1984), 221-29.
  70. J. T. Beale, Large-time regularity of viscous surface waves, Contemp. Math. 17 (1983), 31-33.
  71. J. T. Beale, A. Majda, Vortex methods I: Convergence in three dimensions, Math. Comp. 39 (1982), 1-27.
  72. 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.

Papers Submitted

  1. J. t. Beale, W. YIng, and J. R. Wilson, A simple method for computing singular or nearly singular integrals on closed surfaces, Commun. Comput. Phys. (August, 2015)