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Bibliography

  • [1] R. J. Braun, R. Usha, G. B. McFadden, T. A. Driscoll, Cook, L. P., and P. E. King-Smith, “On the effect of the ellipsoidal cornea on the tear film,” AIMS J. Discrete Cont. Dynamical Systems, vol. submitted.

  • [2] T. A. Driscoll and J. E. Dzielski, “Error bound on the solution of a linear-differential equation in Chebyshev series,” Int. J. Systems Sci., vol. 24, pp. 1317–1327, 1993.

  • [3] L. N. Trefethen, A. Trefethen, S. C. Reddy, and T. A. Driscoll, “Hydrodynamic Stability Without Eigenvalues,” Science, vol. 261, no. 5121, pp. 578–584, 1993.

  • [4] T. A. Driscoll, “Conformal mapping and convergence of Krylov iterations,” 1994.

  • [5] J. S. Baggett, T. A. Driscoll, and L. N. Trefethen, “A mostly linear model of transition to turbulence,” vol. 7, no. 4, p. 833, 1995.

  • [6] T. A. Driscoll and B. Land, “Vibrations of Isospectral Drums,” 1995.

  • [7] T. A. Driscoll and L. N. Trefethen, “Pseudospectra for the wave operator with an absorbing boundary,” J. Comput. Appl. Math., vol. 69, no. 1, pp. 125–142, 1996.

  • [8] T. A. Driscoll and S. A. Vavasis, “Numerical Conformal Mapping Using Cross-Ratios and Delaunay Triangulation,” Cornell Theory Center, 1996.

  • [9] T. A. Driscoll, “Algorithm 756: A MATLAB toolbox for Schwarz-Christoffel mapping,” vol. 22, no. 2, pp. 168–186, Jun. 1996.

  • [10] T. A. Driscoll, “Eigenmodes of Isospectral Drums,” SIAM Rev., vol. 39, no. 1, pp. 1–17, 1997.

  • [11] T. A. Driscoll and S. A. Vavasis, “Numerical Conformal Mapping Using Cross-Ratios and Delaunay Triangulation,” SIAM J. Sci. Comput., vol. 19, pp. 1783–1803, 1998.

  • [12] L. N. Trefethen, T. A. Driscoll, and K. C. Toh, “From potential theory to matrix iterations in six steps,” pp. 547–578, 1998.

  • [13] T. A. Driscoll and B. Fornberg, “A Block Pseudospectral Method for Maxwell's Equations I. One-Dimensional Case,” vol. 140, no. 1, pp. 47–65, Feb. 1998.

  • [14] B. Fornberg and T. A. Driscoll, “Block pseudospectral methods for Maxwell's equations. II. Two-dimensional, discontinuous-coefficient case,” SIAM J. Sci. Comput., vol. 21, pp. 1146–1167, 1999.

  • [15] B. Fornberg and T. A. Driscoll, “Note on nonsymmetric finite differences for Maxwell's equations,” J. Comput. Phys., vol. 161, pp. 723–727, 2000.

  • [16] M. Ghrist, B. Fornberg, and T. A. Driscoll, “Staggered time integrators for wave equations,” SIAM J. Numer. Anal., vol. 38, pp. 718–741, 2000.

  • [17] M. Goano, F. Bertazzi, P. Caravelli, G. Ghione, and T. A. Driscoll, “A general conformal-mapping approach to the optimum electrode design of coplanar waveguides with arbitrary cross section,” Microwave Theory …, 2001.

  • [18] T. A. Driscoll and B. Fornberg, “A Padé-based algorithm for overcoming the Gibbs phenomenon,” vol. 26, no. 1, pp. 77–92, 2001.

  • [19] T. A. Driscoll and B. Fornberg, “Interpolation in the limit of increasingly flat radial basis functions,” Comput. Math. Appl., vol. 43, pp. 413–422, 2002.

  • [20] T. A. Driscoll, “A composite Runge--Kutta method for the spectral solution of semilinear PDE,” J. Comput. Phys., vol. 182, no. 2, pp. 357–367, 2002.

  • [21] T. A. Driscoll and L. N. Trefethen, Schwarz--Christoffel Mapping. Cambridge Univ. Press, 2002.

  • [22] B. Fornberg, T. A. Driscoll, G. Wright, and R. Charles, “Observations on the behavior of radial basis function approximations near boundaries,” Comput. Math. Appl., vol. 43, pp. 473–490, 2002.

  • [23] C. R. Collins, T. A. Driscoll, and K. Stephenson, “Curvature flow in conformal mapping,” Comput. Meth. Function Theory, vol. 3, pp. 325–347, 2003.

  • [24] T. A. Driscoll and H. P. W. Gottlieb, “Isospectral shapes with Neumann and alternating boundary conditions,” Phys. Rev. E, vol. 68, no. 1, p. 016702, Jul. 2003.

  • [25] R. B. Platte and T. A. Driscoll, “Computing eigenmodes of elliptic operators using radial basis functions,” Computers Math. Appl., vol. 48, no. 3, pp. 561–576, 2004.

  • [26] J. Pelesko and T. A. Driscoll, “The effect of the small-aspect-ratio approximation on canonical electrostatic MEMS models,” vol. 53, no. 3, pp. 239–252, 2005.

  • [27] R. B. Platte and T. A. Driscoll, “Polynomials and Potential Theory for Gaussian Radial Basis Function Interpolation,” SIAM J. Numer. Anal., vol. 43, no. 2, pp. 750–766, 2005.

  • [28] T. A. Driscoll, “Algorithm 843: Improvements to the Schwarz--Christoffel toolbox for MATLAB,” vol. 31, no. 2, pp. 239–251, Jun. 2005.

  • [29] R. B. Platte and T. A. Driscoll, “Eigenvalue stability of radial basis function discretizations for time-dependent problems,” Comput. Math. Appl., vol. 51, no. 8, pp. 1251–1268, 2006.

  • [30] T. K. DeLillo, T. A. Driscoll, A. R. Elcrat, and J. A. Pfaltzgraff, “Computation of Multiply Connected Schwarz-Christoffel Maps for Exterior Domains,” vol. 6, no. 2, 2006.

  • [31] A. Heryudono, R. J. Braun, T. A. Driscoll, K. L. Maki, L. P. Cook, and P. K. Smith, “Single-equation models for the tear film in a blink cycle: realistic lid motion,” vol. 24, no. 4, 2007.

  • [32] T. A. Driscoll and A. R. H. Heryudono, “Adaptive residual subsampling methods for radial basis function interpolation and collocation problems,” vol. 53, no. 6, pp. 927–939, Mar. 2007.

  • [33] T. K. DeLillo, T. A. Driscoll, A. R. Elcrat, and J. A. Pfaltzgraff, “Radial and circular slit maps of unbounded multiply connected circle domains,” vol. 464, no. 2095, pp. 1719–1737, Jul. 2008.

  • [34] K. L. Maki, R. J. Braun, T. A. Driscoll, and P. E. King-Smith, “An overset grid method for the study of reflex tearing,” Mathematical Medicine and Biology, vol. 25, no. 3, pp. 187–214, Jul. 2008.

  • [35] T. A. Driscoll, F. Bornemann, and L. N. Trefethen, “The chebop system for automatic solution of differential equations,” vol. 48, no. 4, pp. 701–723, Nov. 2008.

  • [36] T. A. Driscoll, Learning MATLAB. Philadelphia: Society for Industrial and Applied Mathematics, 2009.

  • [37] T. A. Driscoll, “Automatic spectral collocation for integral, integro-differential, and integrally reformulated differential equations,” vol. 229, no. 17, pp. 5980–5998, 2010.

  • [38] A. R. H. Heryudono and T. A. Driscoll, “Radial Basis Function Interpolation on Irregular Domain through Conformal Transplantation,” vol. 44, no. 3, pp. 286–300, Jun. 2010.

  • [39] D. C. Usher, T. A. Driscoll, P. Dhurjati, J. A. Pelesko, L. F. Rossi, G. Schleiniger, K. Pusecker, H. B. White, and T. A. Driscoll, “A Transformative Model for Undergraduate Quantitative Biology Education,” CBE Life Sci Educ, vol. 9, no. 3, pp. 181–188, Sep. 2010.

  • [40] A. Neves, T. A. Driscoll, and A. Heryudono, “Adaptive methods for analysis of composite plates with radial basis functions,” Mechanics of …, vol. 18, no. 6, pp. 420–430, 2011.

  • [41] R. J. Braun, R. Usha, G. B. McFadden, T. A. Driscoll, Cook, L. P., and P. E. King-Smith, “Thin film dynamics on a prolate spheroid with application to the cornea,” vol. 73, no. 1, pp. 121–138, Jun. 2011.

  • [42] A. Birkisson and T. A. Driscoll, “Automatic Fréchet differentiation for the numerical solution of boundary-value problems,” vol. 38, no. 4, pp. 1–29, 2012.

  • [43] W. M. Reid, T. Driscoll, and M. F. Doty, “Forming delocalized intermediate states with realistic quantum dots,” vol. 111, no. 5, p. 056102, 2012.

  • [44] Q. Deng and T. A. Driscoll, “A Fast Treecode for Multiquadric Interpolation with Varying Shape Parameters,” vol. 34, no. 2, pp. A1126–A1140, Jan. 2012.

  • [45] Q. Deng, R. J. Braun, T. A. Driscoll, and P. E. King-Smith, “A model for the tear film and ocular surface temperature for partial blinks,” Interfacial Phenom Heat Transf, vol. 1, no. 4, pp. 357–381, 2013.

  • [46] Q. Deng, R. J. Braun, and T. A. Driscoll, “Heat transfer and tear film dynamics over multiple blink cycles,” vol. 26, no. 7, p. 071901, Jul. 2014.

  • [47] T. A. Driscoll and J. A. C. Weideman, “Optimal Domain Splitting for Interpolation by Chebyshev Polynomials,” vol. 52, no. 4, pp. 1913–1927, Jul. 2014.

  • [48] M. Stapf, R. Braun, C. Begley, T. Driscoll, and P. E. King-Smith, “Modeling Tear Film Evaporation and Breakup with Duplex Films,” presented at the Bulletin of the American Physical Society, 2015, vol. 60.

  • [49] C. Ketelaar, L. Zhong, R. J. Braun, T. A. Driscoll, P. E. King-Smith, and C. G. Begley, “Tear Film Dynamics Around a Rigid Model Blob,” presented at the Bulletin of the American Physical Society, 2015, vol. 60.

  • [50] R. J. Braun, L. Li, W. Henshaw, T. Driscoll, and P. E. King-Smith, “Solute Dynamics and Imaging in the Tear Film on an Eye-shaped Domain,” presented at the Bulletin of the American Physical Society, 2015, vol. 60.

  • [51] L. Zhong, C. F. Ketelaar, R. J. Braun, T. A. Driscoll, P. E. King-Smith, and C. G. Begley, “A Model Problem for Blob-Driven Tear Film Breakup (TBU),” presented at the Bulletin of the American Physical Society, 2015, vol. 60.

  • [52] T. A. Driscoll, A. Townsend, and E. Süli, Eds., “New directions in numerical computation,” Notices of the American Mathematical Society, vol. 63, no. 4, pp. 398–400, 2016.

  • [53] K. L. Maki, W. D. Henshaw, G. Barron, D. Chapp, R. J. Braun, and T. A. Driscoll, “A theoretical investigation of the influence of a blink on the tear film dynamics,” Invest. Ophthalmol. Vis. Sci, vol. 57, p. 6173, 2016.

  • [54] L. Li, R. J. Braun, T. A. Driscoll, W. D. Henshaw, J. W. Banks, and P. E. King-Smith, “Computed tear film and osmolarity dynamics on an eye-shaped domain,” Mathematical Medicine and Biology, vol. 33, no. 2, pp. 123–157, 2016.

  • [55] T. A. Driscoll and N. Hale, “Rectangular spectral collocation,” vol. 36, no. 1, pp. 108–132, 2016.

  • [56] L. Zhong, C. F. Ketelaar, R. J. Braun, and T. A. Driscoll, “Mathematical modeling of glob-driven tear film breakup.,” Invest. Ophthalmol. Vis. Sci, vol. 57, p. 6171, 2016.

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