Math @ Duke

Papers Published
 J. T. Beale, A. Majda, Vortex methods I: Convergence in three dimensions,
Math. Comp. 39 (1982), 127.
 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.
 J. T. Beale, Largetime regularity of viscous surface waves,
Contemp. Math.
17 (1983), 3133.
 J. T. Beale, Largetime regularity of viscous surface waves,
Arch. Rational
Mech. Anal. 84 (1984), 30752.
 J. T. Beale, A. Majda, Vortex methods for fluid flow in two or three dimensions,
Contemp. Math. 28 (1984), 22129.
 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, 13748.
 J. T. Beale, A convergent threedimensional vortex method with gridfree
stretching,
Math. Comp. 46 (1986), 40124 and S15S20.
 J. T. Beale, Largetime behavior of model gases with a discrete set of
velocities,
Mathematics Applied to Science, J. Goldstein
et al., ed. pp. 112, Academic Press, Orlando, 1988.
 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. 1932,
SpringerVerlag, New York, 1988.
 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. 2337, SpringerVerlag,
New York, 1991.
 J. T. Beale, A. Eydeland, B. Turkington, Numerical tests of 3D vortex
methods using a vortex ring with swirl,
Vortex Dynamics and Vortex Methods, C. Anderson and C. Greengard, ed., pp. 19, A.M.S., 1991.
 J. T. Beale, Solitary water waves with ripples beyond all orders,
Asymptotics beyond All Orders, H. Segur et al., ed., pp. 29398, NATO ASI Series, Plenum, 1991.
 J. T. Beale, E. Thomann, C. Greengard, Operator splitting
for NavierStokes and the ChorinMarsden product formula,
Vortex Flows and Related Numerical Methods, J. T. Beale et al.,
ed., pp. 2738, NATO ASI Series, Kluwer, 1993.
 J. T. Beale, T.Y. Hou, J.S. Lowengrub, Stability of Boundary Integral Methods for Water Waves,
Advances in MultiFluid Flows, Y. Renardy et al., ed., pp. 24145, SIAM, Philadelphia, 1996.
 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, 56575, Soc. Math. Appl. Indust., Paris, 1996.
 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, 10727.
 J. T. Beale, Boundary Integral Methods for ThreeDimensional Water Waves,
Equadiff 99, Proceedings of the International Conference on Differential Equations, Vol. 2, pp. 136978
[ps]
 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. 1826.
 J. T. Beale, Methods for computing singular and nearly singular integrals,
J. Turbulence, vol. 3, (2002), article 041 (4 pp.)
[pdf]
 Beale, JT, Scattering frequencies of resonators,
Communications on Pure and Applied Mathematics, vol. 26 no. 4
(July, 1973),
pp. 549563, WILEY, ISSN 00103640 [doi]
 Beale, JT; Rosencrans, SI, Acoustic boundary conditions,
Bulletin of the American Mathematical Society, vol. 80 no. 6
(January, 1974),
pp. 12761278, American Mathematical Society (AMS), ISSN 00029904 [doi]
 Beale, JT, Purely imaginary scattering frequencies for exterior domains,
Duke Mathematical Journal, vol. 41 no. 3
(September, 1974),
pp. 607637, Duke University Press, ISSN 00127094 [doi]
 Beale, JT, Spectral Properties of an Acoustic Boundary Condition,
Indiana University Mathematics Journal, vol. 25 no. 9
(1976),
pp. 895917 [abs]
 BEALE, JT, ACOUSTIC SCATTERING FROM LOCALLY REACTING SURFACES,
Indiana University Mathematics Journal, vol. 26 no. 2
(1977),
pp. 199222 [doi] [abs]
 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. 283313, WILEY, ISSN 00103640 [doi]
 Thomas Beale, J, The existence of solitary water waves,
Communications on Pure and Applied Mathematics, vol. 30 no. 4
(July, 1977),
pp. 373389, WILEY, ISSN 00103640 [doi]
 Beale, JT, The existence of cnoidal water waves with surface tension,
Journal of Differential Equations, vol. 31 no. 2
(January, 1979),
pp. 230263, Elsevier BV, ISSN 00220396 [doi]
 Beale, JT, WaterWaves Generated by a Pressure Disturbance on a Steady Stream,
Duke Mathematical Journal, vol. 47 no. 2
(1980),
pp. 297323, Duke University Press, ISSN 00127094 [Gateway.cgi], [doi]
 Beale, JT, The initial value problem for the navierāstokes equations with a free surface,
Communications on Pure and Applied Mathematics, vol. 34 no. 3
(January, 1981),
pp. 359392, WILEY, ISSN 00103640 [doi]
 Beale, JT; Majda, A, Rates of Convergence for Viscous Splitting of the NavierStokes Equations,
Mathematics of Computation, vol. 37 no. 156
(October, 1981),
pp. 243243, JSTOR, ISSN 00255718 [Gateway.cgi], [doi]
 Beale, JT; MAJDA, A, Vortex Methods 1: Convergence in 3 Dimensions,
Mathematics of Computation, vol. 39 no. 159
(1982),
pp. 127, American Mathematical Society (AMS), ISSN 00255718 [Gateway.cgi], [doi]
 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. 2929, JSTOR, ISSN 00255718 [Gateway.cgi], [doi]
 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. 2929, American Mathematical Society (AMS) [doi]
 Beale, JT; Majda, AJ, Explicit smooth velocity kernels for vortex methods.
(January, 1983) [abs]
 Beale, JT; Kato, T; Majda, A, Remarks on the breakdown of smooth solutions for the 3D Euler equations,
Communications in Mathematical Physics, vol. 94 no. 1
(March, 1984),
pp. 6166, Springer Nature, ISSN 00103616 [doi] [abs]
 Beale, JT, Largetime regularity of viscous surface waves,
Archive for Rational Mechanics and Analysis, vol. 84 no. 4
(December, 1984),
pp. 307352, Springer Nature, ISSN 00039527 [doi]
 Beale, JT; Nishida, T, LargeTime Behavior of Viscous Surface Waves,
NorthHolland Mathematics Studies, vol. 128 no. C
(January, 1985),
pp. 114, Elsevier, ISSN 03040208 [doi] [abs]
 Beale, JT; Majda, A, High order accurate vortex methods with explicit velocity kernels,
Journal of Computational Physics, vol. 58 no. 2
(January, 1985),
pp. 188208, Elsevier BV, ISSN 00219991 [doi] [abs]
 Beale, JT, Largetime behavior of the Broadwell model of a discrete velocity gas,
Communications in Mathematical Physics, vol. 102 no. 2
(June, 1985),
pp. 217235, Springer Nature, ISSN 00103616 [doi] [abs]
 Beale, JT, Convergent 3D vortex method with gridfree stretching.
(January, 1986) [abs]
 Beale, JT, A Convergent 3D Vortex Method With GridFree Stretching,
Mathematics of Computation, vol. 46 no. 174
(April, 1986),
pp. 401401, JSTOR [doi] [abs]
 BEALE, JT, ANALYSIS OF VORTEX METHODS FOR INCOMPRESSIBLEFLOW,
Journal of Statistical Physics, vol. 44 no. 56
(September, 1986),
pp. 10091011, ISSN 00224715 [Gateway.cgi]
 Beale, JT, Largetime behavior of discrete velocity boltzmann equations,
Communications in Mathematical Physics, vol. 106 no. 4
(December, 1986),
pp. 659678, Springer Nature, ISSN 00103616 [doi] [abs]
 Beale, JT; Schaeffer, DG, Nonlinear behavior of model equations which are linearly illposed,
Communications in Partial Differential Equations, vol. 13 no. 4
(January, 1988),
pp. 423467, Informa UK Limited, ISSN 03605302 [doi]
 Beale, JT, Exact solitary water waves with capillary ripples at infinity,
Communications on Pure and Applied Mathematics, vol. 44 no. 2
(March, 1991),
pp. 211257, WILEY, ISSN 00103640 [doi]
 J. T. Beale, T. Y. Hou, J. S. Lowengrub, On the wellposedness of twofluid interfacial flows with surface tension,
Singularities in Fluids, Plasmas, and Optics, R. Caflisch et al., ed., NATO ASI Series, Kluwer
(1993),
pp. 1138
 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
(October, 1993),
pp. 12691301, WILEY, ISSN 00103640 [doi]
 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. 1011
(January, 1994),
pp. 127, Elsevier BV, ISSN 08957177 [doi] [abs]
 Bourgeois, AJ; Beale, JT, Validity of the Quasigeostrophic Model for LargeScale Flow in the Atmosphere and Ocean,
Siam Journal on Mathematical Analysis, vol. 25 no. 4
(July, 1994),
pp. 10231068, Society for Industrial & Applied Mathematics (SIAM), ISSN 00361410 [doi]
 Beale, JT; Greengard, C, Convergence of eulerstokes splitting of the navierstokes equations,
Communications on Pure and Applied Mathematics, vol. 47 no. 8
(August, 1994),
pp. 10831115, WILEY, ISSN 00103640 [doi]
 Beale, JT; Hou, TY; Lowengrub, J, Stability of boundary integral methods for water waves,
Ams Ims Siam Joint Summer Research Conference
(January, 1996),
pp. 241245 [abs]
 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. 17971843, Society for Industrial & Applied Mathematics (SIAM) [doi] [abs]
 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. 829, Elsevier BV [doi] [abs]
 Beale, JT, A convergent boundary integral method for threedimensional water waves,
Mathematics of Computation, vol. 70 no. 235
(July, 2001),
pp. 9771029, American Mathematical Society (AMS) [ps], [doi] [abs]
 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. 1826, Kyoto University, ISSN 18802818
 Beale, JT; Lai, MC, A method for computing nearly singular integrals,
Siam Journal on Numerical Analysis, vol. 38 no. 6
(December, 2001),
pp. 19021925, Society for Industrial & Applied Mathematics (SIAM) [ps], [doi] [abs]
 Baker, GR; Beale, JT, Vortex blob methods applied to interfacial motion,
Journal of Computational Physics, vol. 196 no. 1
(May, 2004),
pp. 233258, Elsevier BV [pdf], [doi] [abs]
 Beale, JT, A gridbased boundary integral method for elliptic problems in three dimensions,
Siam Journal on Numerical Analysis, vol. 42 no. 2
(December, 2004),
pp. 599620, Society for Industrial & Applied Mathematics (SIAM), ISSN 00361429 [pdf], [doi] [abs]
 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
(January, 2006),
pp. 91119, Mathematical Sciences Publishers [pdf], [doi] [abs]
 Beale, JT, A proof that a discrete delta function is secondorder accurate,
Journal of Computational Physics, vol. 227 no. 4
(February, 2008),
pp. 21952197, Elsevier BV, ISSN 00219991 [pdf], [doi] [abs]
 Beale, JT; Strain, J, Locally corrected semiLagrangian methods for Stokes flow with moving elastic interfaces,
Journal of Computational Physics, vol. 227 no. 8
(April, 2008),
pp. 38963920, Elsevier BV, ISSN 00219991 [repository], [doi] [abs]
 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. 95100, Mathematical Sciences Publishers [pdf], [doi]
 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. 33583367, Elsevier BV, ISSN 00219991 [pdf], [doi] [abs]
 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. 24762495, Society for Industrial & Applied Mathematics (SIAM), ISSN 00361429 [pdf], [doi] [abs]
 Beale, JT, Partially implicit motion of a sharp interface in NavierStokes flow,
J. Comput. Phys., vol. 231 no. 18
(2012),
pp. 61596172, Elsevier BV [pdf], [doi]
 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. 11391153, American Institute of Mathematical Sciences (AIMS), ISSN 15313492 [pdf], [doi] [abs]
 Tlupova, S; Beale, JT, Nearly singular integrals in 3D stokes flow,
Communications in Computational Physics, vol. 14 no. 5
(2013),
pp. 12071227, Global Science Press, ISSN 18152406 [pdf], [doi] [abs]
 Ying, W; Beale, JT, A Fast Accurate Boundary Integral Method for Potentials on Closely Packed Cells,
Communications in Computational Physics, vol. 14 no. 04
(October, 2013),
pp. 10731093, Global Science Press, ISSN 18152406 [pdf], [doi] [abs]
 Beale, JT, Uniform Error Estimates for NavierStokes Flow with an Exact Moving Boundary Using the Immersed Interface Method,
Siam Journal on Numerical Analysis, vol. 53 no. 4
(January, 2015),
pp. 20972111, Society for Industrial & Applied Mathematics (SIAM), ISSN 00361429 [pdf], [doi]
 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. 733753, Global Science Press [doi] [abs]
 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. 605626 [doi] [abs]
 Tlupova, S; Beale, JT, Regularized single and double layer integrals in 3D Stokes flow,
Journal of Computational Physics, vol. 386
(June, 2019),
pp. 568584 [doi] [abs]
Papers Submitted
 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) [pdf]


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Mathematics Department
Duke University, Box 90320
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