Curriculum Vitae

J. Thomas Beale

Box 90320, Durham, NC 27708-0320 +1 919 660 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

Fellow, American Mathematical Society
Invited Lecture, International Congress of Mathematicians, August, 1994
Alfred P. Sloan Fellowship, 1978
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, Solving partial differential equations on closed surfaces with planar cartesian grids, SIAM Journal on Scientific Computing, vol. 42 no. 2 (January, 2020), pp. A1052-A1070
  2. 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
  3. 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
  4. 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. 3 (September, 2016), pp. 733-753, Global Science Press
  5. 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 (January, 2015), pp. 2097-2111, Society for Industrial & Applied Mathematics (SIAM), ISSN 0036-1429
  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. 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, Global Science Press, ISSN 1815-2406
  8. 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 (June, 2012), pp. 1139-1153, American Institute of Mathematical Sciences (AIMS), ISSN 1531-3492
  9. 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
  10. 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 (July, 2009), pp. 2476-2495, Society for Industrial & Applied Mathematics (SIAM), ISSN 0036-1429
  11. Beale, JT; Layton, AT, A velocity decomposition approach for moving interfaces in viscous fluids, Journal of Computational Physics, vol. 228 no. 9 (May, 2009), pp. 3358-3367, Elsevier BV, ISSN 0021-9991
  12. 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 (August, 2008), pp. 95-100, Mathematical Sciences Publishers
  13. Beale, JT; Strain, J, Locally corrected semi-Lagrangian methods for Stokes flow with moving elastic interfaces, Journal of Computational Physics, vol. 227 no. 8 (April, 2008), pp. 3896-3920, Elsevier BV, ISSN 0021-9991
  14. Beale, JT, A proof that a discrete delta function is second-order accurate, Journal of Computational Physics, vol. 227 no. 4 (February, 2008), pp. 2195-2197, Elsevier BV, ISSN 0021-9991
  15. Beale, JT; Layton, AT, On the accuracy of finite difference methods for elliptic problems with interfaces, Commun. Appl. Math. Comput. Sci., vol. 1 no. 1 (2006), pp. 91-119, Mathematical Sciences Publishers
  16. Beale, JT, A grid-based boundary integral method for elliptic problems in three dimensions, SIAM Journal on Numerical Analysis, vol. 42 no. 2 (December, 2004), pp. 599-620, Society for Industrial & Applied Mathematics (SIAM), ISSN 0036-1429
  17. Baker, GR; Beale, JT, Vortex blob methods applied to interfacial motion, J. Comput. Phys., vol. 196 no. 1 (2004), pp. 233-258, Elsevier BV
  18. 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)
  19. 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
  20. 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)
  21. 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
  22. 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)
  23. 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
  24. 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 (November, 1994), pp. 1-27, Elsevier BV, ISSN 0895-7177
  25. 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
  26. 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
  27. 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 (January, 1993), pp. 1269-1301, WILEY, ISSN 0010-3640
  28. 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
  29. 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
  30. 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
  31. 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
  32. 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
  33. Beale, JT, Convergent 3-D vortex method with grid-free stretching., vol. 46 no. 174 (January, 1986), pp. 401-401, JSTOR
  34. Beale, JT, Convergent 3-D vortex method with grid-free stretching. (January, 1986)
  35. 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
  36. 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
  37. 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
  38. 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
  39. 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 (March, 1984), pp. 61-66, Springer Nature, ISSN 0010-3616
  40. Beale, JT; Majda, AJ, Explicit smooth velocity kernels for vortex methods. (January, 1983)
  41. Beale, JT; Majda, A, Vortex methods. ii: Higher order accuracy in two and three dimensions, Mathematics of Computation, vol. 39 no. 159 (January, 1982), pp. 29-52, American Mathematical Society (AMS)
  42. 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, JSTOR, ISSN 0025-5718
  43. 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
  44. Beale, JT, The initial value problem for the navier‐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; MAJDA, A, Rates of Convergence for Viscous Splitting of the Navier-Stokes Equations, MATHEMATICS OF COMPUTATION, vol. 37 no. 156 (1981), pp. 243-259, JSTOR, ISSN 0025-5718
  46. 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
  47. 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
  48. Beale, JT, 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
  49. Beale, JT, 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
  50. BEALE, JT, ACOUSTIC SCATTERING FROM LOCALLY REACTING SURFACES, INDIANA UNIVERSITY MATHEMATICS JOURNAL, vol. 26 no. 2 (1977), pp. 199-222
  51. Beale, JT, Spectral Properties of an Acoustic Boundary Condition, Indiana University Mathematics Journal, vol. 25 no. 9 (1976), pp. 895-917
  52. 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
  53. 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
  54. Beale, JT, Scattering frequencies of resonators, Communications on Pure and Applied Mathematics, vol. 26 no. 4 (January, 1973), pp. 549-563, WILEY, ISSN 0010-3640
  55. J. T. Beale, Methods for computing singular and nearly singular integrals, J. Turbulence, vol. 3, (2002), article 041 (4 pp.)
  56. 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.
  57. 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
  58. 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.
  59. 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.
  60. 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.
  61. 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.
  62. 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.
  63. 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.
  64. 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.
  65. 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.
  66. 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.
  67. 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.
  68. J. T. Beale, A convergent three-dimensional vortex method with grid-free stretching, Math. Comp. 46 (1986), 401-24 and S15-S20.
  69. J. T. Beale, Large-time regularity of viscous surface waves, Arch. Rational Mech. Anal. 84 (1984), 307-52.
  70. J. T. Beale, A. Majda, Vortex methods for fluid flow in two or three dimensions, Contemp. Math. 28 (1984), 221-29.
  71. J. T. Beale, Large-time regularity of viscous surface waves, Contemp. Math. 17 (1983), 31-33.
  72. J. T. Beale, A. Majda, Vortex methods I: Convergence in three dimensions, Math. Comp. 39 (1982), 1-27.
  73. 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: 2024/04/19