Curriculum Vitae

J. Thomas Beale

Box 90320, Durham, NC 27708-0320 (919) 660-2814 (office)
(email)
Areas of Research

Partial Differential Equations, Fluid Mechanics, Numerical Methods

Professional Experience / Employment History

Duke University
Professor, Mathematics, 1983 - present
Tulane University
Professor, Mathematics, 1982 - 1983
Associate Professor, Mathematics, 1977 - 1982
Assistant Professor, Mathematics, 1973 - 1977
Awards, Honors, and Distinctions

Invited Lecture, International Congress of Mathematicians, August, 1994
Alfred P. Sloan Fellowship, 1978
Recent Grant Support

Selected Recent Invited Talks

Applied Math Seminar, UNC-Chapel Hill, October 4, 2013  
Workshop on Fluid-Structure Interaction Problems, Shanghai Jiao Tong Univ., Shanghai, China, July 26, 2013  
Water waves: computational approaches for complex problems, BIRS, Banff, Canada, July 01, 2013  
Applied Math Colloquium, Penn State Univ., March 15, 2013  
Applied Math Seminar, Penn State Univ., March 14, 2013  
Conference on Partial Differential Equations, U.N.C., Chapel Hill, N.C., July 18, 2012  
Colloquium, Drexel University, Philadelphia, April 26, 2012  
Seminar, Beijing University of Posts and Telecommunications, Beijing, China, March 06, 2012  
Colloquium, Peking University, Beijing, China, March 05, 2012  
Seminar, Tsinghua University, Beijing, China, March 01, 2012  
Seminar, Zhejiang University, Hangzhou, China, February 27, 2012  
Seminar, Shanghai Jiao Tong University, Shanghai, China, February 24, 2012  
NCTS Workshop on Fluid-Structure Interaction Problems, Hsinchu, Taiwan, May 27, 2011  
Workshop on Fluid Motion Driven by Immersed Structures, Fields Inst., Toronto, CA, August 10, 2010  
Analysis and Computation of Incompressible Fluid Flow, I.M.A. Workshop, Minneapolis, MN, February 25, 2010  
Modern Perspectives in Applied Mathematics, Courant Institute, New York Univ., May 19, 2009  
Frontiers in Applied and Computational Mathematics, New Jersey Inst. Tech., May 19, 2008  
Interface Problems Workshop, S.A.M.S.I., R.T.P., NC, November 15, 2007  
Workshop on high-order methods for computational wave propagation and scattering, American Institute of Mathematics, Palo Alto, CA, September 11, 2007  
Minisymposium, Sixth International Congress on Industrial and Applied Mathematics, Zurich, Switzerland, July 18, 2007  
Special Session on Microlocal Analysis and P.D.E., A.M.S. Sectional Meeting, Davidson, N.C., March 03, 2007  
Workshop on the Mathematical Theory of Water Waves, Oberwolfach, Germany, November 13, 2006  
Kyoto Conference on the Navier-Stokes Equations and their Applications, Kyoto, Japan, January 6, 2006  
Doctoral Theses Directed

Michael Pruitt, Maximum norm regularity of implicit difference methods for parabolic equations, (August, 2011)  
Jason R. Wilson, On computing smooth, singular, and nearly singular integrals on implicitly defined surfaces, (August, 2010)  
Matthew W. Surles, Numerical Approximation of Layer Potentials along Curve Segments, (August, 2008)  
Michael Nicholas, A third order numerical method for 3D doubly periodic electromagnetic scattering problems, (August, 2007)  
David Ambrose, Well-posedness of Vortex Sheets with Surface Tension, (2002)  
Henry Suters, Ph.D., (1994)  
Andrew Ferrari, Ph.D., (1992)  
Alfred Bourgeois, Ph.D., (1991)  
Tien-Yu Sun, Ph.D., (1991)  
Donna Gates Sylvester, Ph.D., (1988)  

Publications

Papers Published

  1. 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
  2. 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, ISSN 0036-1429
  3. Tlupova, S; Beale, JT, Nearly singular integrals in 3D stokes flow, Communications in computational physics, vol. 14 no. 5 (2013), pp. 1207-1227, ISSN 1815-2406
  4. Ying, W; Beale, JT, A fast accurate boundary integral method for potentials on closely packed cells, Communications in computational physics, vol. 14 no. 4 (2013), pp. 1073-1093, ISSN 1815-2406
  5. Beale, JT, Partially implicit motion of a sharp interface in Navier-Stokes flow, J. Comput. Phys., vol. 231 (2012), pp. 6159-6172
  6. 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, ISSN 1531-3492
  7. 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, ISSN 0021-9991
  8. 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, ISSN 0036-1429
  9. 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 (2008), pp. 95-100
  10. 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, ISSN 0021-9991
  11. 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, ISSN 0021-9991
  12. Beale, JT; Layton, AT, On the accuracy of finite difference methods for elliptic problems with interfaces, Commun. Appl. Math. Comput. Sci., vol. 1 (2006), pp. 91-119
  13. Baker, GR; Beale, JT, Vortex blob methods applied to interfacial motion, Journal of Computational Physics, vol. 196 no. 1 (2004), pp. 233-258
  14. 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, ISSN 0036-1429
  15. Beale, JT, Discretization of Layer Potentials and Numerical Methods for Water Waves (Tosio Kato's Method and Principle for Evolution Equations in Mathematical Physics), vol. 1234 (October, 2001), pp. 18-26, Kyoto University, ISSN 1880-2818
  16. Beale, JT, A convergent boundary integral method for three-dimensional water waves, Mathematics of Computation, vol. 70 no. 235 (2001), pp. 977-1029
  17. Beale, JT; Lai, M-C, A method for computing nearly singular integrals, SIAM Journal on Numerical Analysis, vol. 38 no. 6 (2001), pp. 1902-1925
  18. Beale, JT; Hou, TY; Lowengrub, J, Stability of boundary integral methods for water waves, AMS-IMS-SIAM Joint Summer Research Conference (1996), pp. 241-245
  19. Beale, JT; Hou, TY; Lowengrub, J, Convergence of a boundary integral method for water waves, SIAM Journal on Numerical Analysis, vol. 33 no. 5 (1996), pp. 1797-1843
  20. Lifschitz, A; Suters, WH; Beale, JT, The onset of instability in exact vortex rings with swirl, Journal of Computational Physics, vol. 129 no. 1 (1996), pp. 8-29
  21. Beale, JT; Greengard, C, Convergence of euler-stokes splitting of the navier-stokes equations, Communications on Pure & Applied Mathematics, vol. 47 no. 8 (August, 1994), pp. 1083-1115, ISSN 0010-3640
  22. 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, ISSN 0036-1410
  23. 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 (1994), pp. 1-27, ISSN 0895-7177
  24. Beale, JT; Hou, TY; Lowengrub, JS, Growth rates for the linearized motion of fluid interfaces away from equilibrium, Communications on Pure & Applied Mathematics, vol. 46 no. 9 (1993), pp. 1269-1301, ISSN 0010-3640
  25. 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
  26. Beale, JT, Exact solitary water waves with capillary ripples at infinity, Communications on Pure & Applied Mathematics, vol. 44 no. 2 (March, 1991), pp. 211-257, ISSN 0010-3640
  27. 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, ISSN 0360-5302
  28. 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
  29. Beale, JT, Convergent 3-D vortex method with grid-free stretching. (1986)
  30. Beale, JT, Large-time behavior of discrete velocity boltzmann equations, Communications in Mathematical Physics, vol. 106 no. 4 (1986), pp. 659-678, ISSN 0010-3616
  31. Beale, JT; Nishida, T, Large-Time Behavior of Viscous Surface Waves, North-Holland Mathematics Studies, vol. 128 no. C (1985), pp. 1-14, ISSN 0304-0208
  32. Beale, JT; Majda, A, High order accurate vortex methods with explicit velocity kernels, Journal of Computational Physics, vol. 58 no. 2 (1985), pp. 188-208, ISSN 0021-9991
  33. Beale, JT, Large-time behavior of the Broadwell model of a discrete velocity gas, Communications in Mathematical Physics, vol. 102 no. 2 (1985), pp. 217-235, ISSN 0010-3616
  34. 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, ISSN 0010-3616
  35. Beale, JT, Large-time regularity of viscous surface waves, Archive for Rational Mechanics and Analysis, vol. 84 no. 4 (1984), pp. 307-352, ISSN 0003-9527
  36. 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
  37. Beale, JT; MAJDA, A, Vortex Methods 2: Higher-Order Accuracy in 2 and 3 Dimensions, Mathematics of Computation, vol. 39 no. 159 (1982), pp. 29-52, ISSN 0025-5718
  38. Beale, JT; MAJDA, A, Vortex Methods 1: Convergence in 3 Dimensions, Mathematics of Computation, vol. 39 no. 159 (1982), pp. 1-27, ISSN 0025-5718
  39. Beale, JT, The initial value problem for the navier-stokes equations with a free surface, Communications on Pure & Applied Mathematics, vol. 34 no. 3 (May, 1981), pp. 359-392, ISSN 0010-3640
  40. Beale, JT; MAJDA, A, Rates of Convergence for Viscous Splitting of the Navier-Stokes Equations, Mathematics of Computation, vol. 37 no. 156 (1981), pp. 243-259, ISSN 0025-5718
  41. Beale, JT, Water-Waves Generated by a Pressure Disturbance on a Steady Stream, Duke Mathematical Journal, vol. 47 no. 2 (1980), pp. 297-323, ISSN 0012-7094
  42. Beale, JT, The existence of cnoidal water waves with surface tension, Journal of Differential Equations, vol. 31 no. 2 (1979), pp. 230-263, ISSN 0022-0396
  43. Beale, JT, The existence of solitary water waves, Communications on Pure & Applied Mathematics, vol. 30 no. 4 (July, 1977), pp. 373-389, ISSN 0010-3640
  44. Beale, JT, Eigenfunction expansions for objects floating in an open sea, Communications on Pure & Applied Mathematics, vol. 30 no. 3 (May, 1977), pp. 283-313, ISSN 0010-3640
  45. Beale, JT, Acoustic Scattering From Locally Reacting Surfaces, Indiana University Mathematics Journal, vol. 26 no. 2 (1977), pp. 199-222
  46. Beale, JT, Spectral Properties of an Acoustic Boundary Condition, Indiana University Mathematics Journal, vol. 25 no. 9 (1976), pp. 895-917
  47. Beale, JT; Rosencrans, SI, Acoustic boundary conditions, vol. 80 no. 6 (November, 1974), pp. 1276-1279, ISSN 0002-9904
  48. Beale, JT, Purely imaginary scattering frequencies for exterior domains, Duke Mathematical Journal, vol. 41 no. 3 (September, 1974), pp. 607-637, ISSN 0012-7094
  49. Beale, JT, Scattering frequencies of resonators, Communications on Pure & Applied Mathematics, vol. 26 no. 4 (July, 1973), pp. 549-563, ISSN 0010-3640
  50. J. T. Beale, Methods for computing singular and nearly singular integrals, J. Turbulence, vol. 3, (2002), article 041 (4 pp.)
  51. 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.
  52. 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
  53. 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.
  54. 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.
  55. 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.
  56. 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.
  57. 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.
  58. 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.
  59. 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.
  60. 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.
  61. 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.
  62. 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.
  63. J. T. Beale, A convergent three-dimensional vortex method with grid-free stretching, Math. Comp. 46 (1986), 401-24 and S15-S20.
  64. J. T. Beale, Large-time regularity of viscous surface waves, Arch. Rational Mech. Anal. 84 (1984), 307-52.
  65. J. T. Beale, A. Majda, Vortex methods for fluid flow in two or three dimensions, Contemp. Math. 28 (1984), 221-29.
  66. J. T. Beale, Large-time regularity of viscous surface waves, Contemp. Math. 17 (1983), 31-33.
  67. J. T. Beale, A. Majda, Vortex methods I: Convergence in three dimensions, Math. Comp. 39 (1982), 1-27.
  68. 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)

Last modified: 2017/12/12