Publications

You can also visit my Zotero profile, my Google Scholar profile, my arXiv author page, or download a bibliography file.

Journal articles

 

Driscoll, T. A., Nakatsukasa, Y., & Trefethen, L. N. (2024). AAA Rational Approximation on a Continuum. SIAM Journal on Scientific Computing, 46(2), A929–A952. https://doi.org/10.1137/23M1570508

Driscoll, T. A., Braun, R. J., Luke, R. A., Sinopoli, D., Phatak, A., Dorsch, J., Begley, C. G., & Awisi-Gyau, D. (2023). Fitting ODE models of tear film breakup. Modeling and Artificial Intelligence in Ophthalmology, 5(1), 1–36. 10.35119/maio.v5i1.128

Taranchuk, M. J., Cummings, L. J., Driscoll, T. A., & Braun, R. J. (2023). Extensional flow of a free film of nematic liquid crystal with moderate elasticity. Physics of Fluids, 35(6), 062113. 10.1063/5.0151809

Driscoll, T., Braun, R. J., & Begley, C. G. (2021). Automatic detection of the cornea location in video captures of fluorescence. Modeling and Artificial Intelligence in Ophthalmology, 3(1), Article 1. 10.35119/maio.v3i1.113

Luke, R. A., Braun, R. J., Driscoll, T. A., Awisi-Gyau, D., & Begley, C. G. (2021). Parameter Estimation for Mixed-Mechanism Tear Film Thinning. Bulletin of Mathematical Biology, 83(5), 56. 10.1007/s11538-021-00871-x

Braun, R. J., Luke, R. A., Driscoll, T. A., & Begley, C. G. (2021). Dynamics and mechanisms for tear breakup (TBU) on the ocular surface. Mathematical Biosciences and Engineering, 18(5), Article mbe-18-05-262. 10.3934/mbe.2021262

Luke, R. A., Braun, R. J., Driscoll, T. A., Begley, C. G., & Awisi-Gyau, D. (2020). Parameter Estimation for Evaporation-Driven Tear Film Thinning. Bulletin of Mathematical Biology, 82(6), 71. 10.1007/s11538-020-00745-8

Aiton, K. W., & Driscoll, T. A. (2020). Preconditioned Nonlinear Iterations for Overlapping Chebyshev Discretizations with Independent Grids. SIAM Journal on Scientific Computing, 42(4), A2360–A2370. 10.1137/19m1242483

Driscoll, T. (2019). ComplexRegions.jl: A Julia package for regions in the complex plane. Journal of Open Source Software, 4(44), 1811. 10.21105/joss.01811

Aiton, K. W., & Driscoll, T. A. (2019). An Adaptive Partition of Unity Method for Multivariate Chebyshev Polynomial Approximations. SIAM Journal on Scientific Computing, 41(5), A3230–A3245. 10.1137/18m1184904

Maki, K. L., Henshaw, W. D., McManus, A., Braun, R. J., Chapp, D. M., & Driscoll, T. A. (2019). A model for tear film dynamics during a realistic blink. Journal for Modeling in Ophthalmology, 3, 21–27. 10.35119/maio.v2i3.91

Braun, R. J., Driscoll, T. A., Begley, C. G., King-Smith, P. E., & Siddique, J. I. (2018). On tear film breakup (TBU): Dynamics and imaging. Mathematical Medicine and Biology, 35(2), 145–180. 10.1093/imammb/dqw023

Aiton, K. W., & Driscoll, T. A. (2018). An adaptive partition of unity method for Chebyshev polynomial interpolation. SIAM Journal on Scientific Computing, 40(1), A251–A265. 10.1137/17m112052x

Driscoll, T. A., Braun, R. J., & Brosch, J. K. (2018). Simulation of parabolic flow on an eye-shaped domain with moving boundary. Journal of Engineering Mathematics, 111(1), 111–126. 10.1007/s10665-018-9957-7

Brosch, J. K., Wu, Z., Begley, C. G., Driscoll, T. A., & Braun, R. J. (2017). Blink characterization using curve fitting and clustering algorithms. Journal for Modeling in Ophthalmology, 1(3), 60–81. 10.35119/maio.v1i3.38

Li, L., Braun, R. J., Driscoll, T. A., Henshaw, W. D., Banks, J. W., & King-Smith, P. E. (2016). Computed tear film and osmolarity dynamics on an eye-shaped domain. Mathematical Medicine and Biology, 33(2), 123–157. 10.1093/imammb/dqv013

Driscoll, T. A., Süli, E., & Townsend, A. (2016). New directions in numerical computation. Notices of the American Mathematical Society, 63(4), 398–400. 10.1090/noti1363

Driscoll, T. A., & Hale, N. (2015). Rectangular spectral collocation. IMA Journal of Numerical Analysis, 36(1), 108–132. 10.1093/imanum/dru062

Deng, Q., Braun, R., & Driscoll, T. A. (2014). Heat transfer and tear film dynamics over multiple blink cycles. Physics of Fluids, 26(7), 071901. 10.1063/1.4887341

Driscoll, T. A., & Weideman, J. (2014). Optimal domain splitting for interpolation by Chebyshev polynomials. SIAM Journal on Numerical Analysis, 52(4), 1913–1927. 10.1137/130919428

Deng, Q., Braun, R. J., Driscoll, T. A., & King-Smith, P. E. (2013). A model for the tear film and ocular surface temperature for partial blinks. Interfacial Phenomena and Heat Transfer, 1(4), 357–381. 10.1615/interfacphenomheattransfer.v1.i4.40

Birkisson, A., & Driscoll, T. A. (2012). Automatic Fréchet Differentiation for the Numerical Solution of Boundary-Value Problems. ACM Transactions on Mathematical Software, 38(4), 1–29. 10.1145/2331130.2331134

Deng, Q., & Driscoll, T. A. (2012). A Fast Treecode for Multiquadric Interpolation with Varying Shape Parameters. SIAM Journal on Scientific Computing, 34(2), A1126–A1140. 10.1137/110836225

Braun, R., Usha, R., McFadden, G., Driscoll, T. A., Cook, L., & King-Smith, P. E. (2012). Thin film dynamics on a prolate spheroid with application to the cornea. Journal of Engineering Mathematics, 73(1), 121–138. 10.1007/s10665-011-9482-4

Reid, W. M., Driscoll, T. A., & Doty, M. F. (2012). Forming delocalized intermediate states with realistic quantum dots. Journal of Applied Physics, 111, 056102. 10.1063/1.3691113

Neves, A. M. A., Driscoll, T. A., Heryudono, A. R. H., Ferreira, A. J. M., Soares, C. M. M., & Jorge, R. M. N. (2011). Adaptive Methods for Analysis of Composite Plates with Radial Basis Functions. Mechanics of Advanced Materials and Structures, 18(6), 420–430. 10.1080/15376494.2010.528155

Driscoll, T. A. (2010). Automatic spectral collocation for integral, integro-differential, and integrally reformulated differential equations. Journal of Computational Physics, 229(17), 5980–5998. 10.1016/j.jcp.2010.04.029

Heryudono, A. R. H., & Driscoll, T. A. (2010). Radial Basis Function Interpolation on Irregular Domain through Conformal Transplantation. Journal of Scientific Computing, 44(3), 286–300. 10.1007/s10915-010-9380-3

Usher, D. C., Driscoll, T. A., Dhurjati, P., Pelesko, J. A., Rossi, L. F., Schleiniger, G., Pusecker, K., & White, H. B. (2010). A transformative model for undergraduate quantitative biology education. CBE Life Sciences Education, 9(3), 181–188. 10.1187/cbe.10-03-0029

DeLillo, T. K., Driscoll, T. A., Elcrat, A. R., & Pfaltzgraff, J. A. (2008). Radial and circular slit maps of unbounded multiply connected circle domains. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 464(2095), 1719–1737. 10.1098/rspa.2008.0006

Driscoll, T. A., Bornemann, F., & Trefethen, L. N. (2008). The chebop system for automatic solution of differential equations. BIT Numerical Mathematics, 48(4), 701–723. 10.1007/s10543-008-0198-4

Maki, K. L., Braun, R. J., Driscoll, T. A., & King-Smith, P. E. (2008). An overset grid method for the study of reflex tearing. Math. Med. Biol., 25, 187–214. 10.1093/imammb/dqn013

Driscoll, T. A., & Heryudono, A. R. H. (2007). Adaptive residual subsampling methods for radial basis function interpolation and collocation problems. Computers & Mathematics with Applications, 53(6), 927–939. 10.1016/j.camwa.2006.06.005

Driscoll, T. A., & Maki, K. L. (2007). Searching for Rare Growth Factors Using Multicanonical Monte Carlo Methods. SIAM Review, 49(4), 673–692. 10.1137/050637662

Heryudono, A., Braun, R. J., Driscoll, T. A., Maki, K. L., Cook, Lp., & PE, K.-S. (2007). Single-equation models for the tear film in a blink cycle: Realistic lid motion. Mathematical Medicine and Biology-a Journal of The Ima, 24(4), 347–377. 10.1093/imammb/dqm004

DeLillo, T. K., Driscoll, T. A., Elcrat, A. R., & Pfaltzgraff, J. A. (2006). Computation of Multiply Connected Schwarz-Christoffel Maps for Exterior Domains. Computational Methods and Function Theory, 6(2), 301–315. 10.1007/BF03321616

Pelesko, J. A., & Driscoll, T. A. (2006). The effect of the small-aspect-ratio approximation on canonical electrostatic MEMS models. Journal of Engineering Mathematics, 53(3–4), 239–252. 10.1007/s10665-005-9013-2

Platte, R. B., & Driscoll, T. A. (2006). Eigenvalue stability of radial basis function discretizations for time-dependent problems. Computers & Mathematics with Applications, 51(8), 1251–1268. 10.1016/j.camwa.2006.04.007

Driscoll, T. A. (2005). Algorithm 843: Improvements to the Schwarz-Christoffel toolbox for MATLAB. ACM Transactions on Mathematical Software (TOMS), 31(2), 239–251. 10.1145/1067967.1067971

Platte, R. B., & Driscoll, T. A. (2005). Polynomials and Potential Theory for Gaussian Radial Basis Function Interpolation. SIAM Journal on Numerical Analysis, 43(2), 750–766. 10.1137/040610143

Collins, C. R., Driscoll, T. A., & Stephenson, K. (2004). Curvature flow in conformal mapping. Computational Methods and Function Theory, 3(1), 325–347. 10.1007/bf03321041

Driscoll, T. (2004). Book Review: A Practical Guide to Boundary Element Methods With the Software Library BEMLIB. By C. P OZRIKIDIS. CRC Press, 2002. Journal of Fluid Mechanics, 505, 378–379. 10.1017/s0022112004008201

Platte, R. B., & Driscoll, T. A. (2004). Computing eigenmodes of elliptic operators using radial basis functions. Computers & Mathematics with Applications, 48(3–4), 561–576. 10.1016/j.camwa.2003.08.007

Driscoll, T. A., & Gottlieb, H. (2003). Isospectral shapes with Neumann and alternating boundary conditions. Physical Review E, 68(1), 016702. 10.1103/physreve.68.016702

Driscoll, T. A. (2002). A Composite Runge–Kutta Method for the Spectral Solution of Semilinear PDEs. Journal of Computational Physics, 182(2), 357–367. 10.1006/jcph.2002.7127

Driscoll, T. A., & Fornberg, B. (2002). Interpolation in the limit of increasingly flat radial basis functions. Computers & Mathematics with Applications, 43(3–5), 413–422. 10.1016/s0898-1221(01)00295-4

Fornberg, B., Driscoll, T. A., Wright, G., & Charles, R. (2002). Observations on the behavior of radial basis function approximations near boundaries. Computers & Mathematics with Applications, 43(3–5), 473–490. 10.1016/s0898-1221(01)00299-1

Driscoll, T. A., & Fornberg, B. (2001). A Padé-based algorithm for overcoming the Gibbs phenomenon. Numerical Algorithms, 26(1), 77–92. 10.1023/A:1016648530648

Goano, M., Bertazzi, F., Caravelli, P., Ghione, G., & Driscoll, T. A. (2001). A general conformal-mapping approach to the optimum electrode design of coplanar waveguides with arbitrary cross section. IEEE Transactions on Microwave Theory and Techniques, 49(9), 1573–1580. 10.1109/22.942569

Driscoll, T. A., & Fornberg, B. (2000). Note on nonsymmetric finite differences for Maxwell’s equations. Journal of Computational Physics, 161(2), 723–727. 10.1006/jcph.2000.6524

Ghrist, M., Fornberg, B., & Driscoll, T. A. (2000). Staggered time integrators for wave equations. SIAM Journal on Numerical Analysis, 38(3), 718–741. 10.1137/s0036142999351777

Driscoll, T. A. (1999). A Nonoverlapping Domain Decomposition Method for Symm’s Equation for Conformal Mapping. SIAM Journal on Numerical Analysis, 36(3), 922–934. 10.1137/S0036142997324162

Driscoll, T. A. (1999). Computational Conformal Mapping (book review). SIAM Review, 41(4), 832–834.

Driscoll, T. A., & Fornberg, B. (1999). Block pseudospectral methods for Maxwell’s equations II: Two-dimensional, discontinuous-coefficient case. SIAM Journal on Scientific Computing, 21(3), 1146–1167. 10.1137/s106482759833320x

Fornberg, B., & Driscoll, T. A. (1999). A fast spectral algorithm for nonlinear wave equations with linear dispersion. Journal of Computational Physics, 155(2), 456–467. 10.1006/jcph.1999.6351

Driscoll, T. A., Toh, K.-C., & Trefethen, L. N. (1998). From Potential Theory to Matrix Iterations in Six Steps. SIAM Review, 40(3), 547–578. 10.1137/S0036144596305582

Driscoll, T. A., & Fornberg, B. (1998). A Block Pseudospectral Method for Maxwell’s Equations: I. One-Dimensional Case. J. Comput. Phys., 140, 1–19. 10.1006/jcph.1998.5883

Driscoll, T. A., & Vavasis, S. A. (1998). Numerical conformal mapping using cross-ratios and Delaunay triangulation. SIAM Journal on Scientific Computing, 19(6), 1783–1803. 10.1137/s1064827596298580

Driscoll, T. A. (1997). Eigenmodes of Isospectral Drums. SIAM Review, 39(1), 1–17. 10.1137/S0036144595285069

Driscoll, T. A., & Trefethen, L. N. (1996). Pseudospectra for the wave equation with an absorbing boundary. Journal of Computational and Applied Mathematics, 69(1), 125–142. 10.1016/0377-0427(95)00021-6

Driscoll, T. A. (1996). Algorithm 756: A MATLAB toolbox for Schwarz-Christoffel mapping. ACM Transactions on Mathematical Software (TOMS), 22(2), 168–186. 10.1145/229473.229475

Baggett, J. S., Driscoll, T. A., & Trefethen, L. N. (1995). A mostly linear model of transition to turbulence. Physics of Fluids, 7(4), 833–838. 10.1063/1.868606

Dzielski, J. E., & Driscoll, T. A. (1993). Error bound on the solution of a linear differential equation in Chebyshev series. International Journal of Systems Science, 24(7), 1317–1327. 10.1080/00207729308949562

Trefethen, L. N., Trefethen, A. E., Reddy, S. C., & Driscoll, T. A. (1993). Hydrodynamic stability without eigenvalues. Science, 261(5121), 578–584. 10.1126/science.261.5121.578

Books

 

Driscoll, T. A., & Braun, R. J. (2018). Fundamentals of Numerical Computation. Society for Industrial and Applied Mathematics.

Trefethen, L. N., Birkisson, Á., & Driscoll, T. A. (2017). Exploring ODEs. SIAM. 10.1137/1.9781611975161

Driscoll, T. A., Hale, N., & Trefethen, L. N. (2014). Chebfun guide. Pafnuty Publications, Oxford.

Driscoll, T. A. (2009). Learning MATLAB. Society for Industrial and Applied Mathematics.

Driscoll, T. A., & Trefethen, L. N. (2002). Schwarz–Christoffel Mapping. Cambridge University Press.

Book chapters

 

Braun, R. J., Driscoll, T. A., & Begley, C. G. (2019). Mathematical Models of the Tear Film. In Ocular Fluid Dynamics: Anatomy, Physiology, Imaging Techniques, and Mathematical Modeling (pp. 387–432). Springer-Birkhauser. https://www.springer.com/gp/book/9783030258856

Driscoll, T. A., & Fornberg, B. (2007). Pade-based interpretation and correction of the Gibbs phenomenon. In Advances in the Gibbs Phenomenon, ed. By A. Jerri. Sigma Sampling Publishing.

Conference papers

 

Braun, R. J., Driscoll, T., Begley, C., Situ, P., Tichenor, A., & Luke, R. (2023). Tear Breakup (TBU) Analysis with Fluorescence (FL) and Thermal (TH) imaging. Investigative Ophthalmology & Visual Science, 64(8), 186–186.

Braun, R. J., Driscoll, T. A., Sinopoli, D., Dorsch, J., Hammond, C., Luke, R. A., & Begley, C. G. (2022). Data and Analysis from Tear Breakup (TBU) in Normal Subjects. Investigative Ophthalmology & Visual Science, 63(7), 3950-A0230.

Luke, R. A., Braun, R. J., Driscoll, T., Sinopoli, D., Yawatkar, V., You, L., Phatak, A., & Begley, C. (2021). Fitting Simplified Models to Machine Learning-Identified Tear Film Breakup. Investigative Ophthalmology & Visual Science, 62(8), 1315–1315.

Braun, R. J., Zhong, L., Driscoll, T. A., Begley, C. G., Antwi, D., & King-Smith, P. E. (2018, June). Models for Tear Break Up Dynamics and Imaging. 7th European Conference on Computational Fluid Dynamics.

Brosch, J., Driscoll, T., & Braun, R. (2016). Simulation of Thin Film Equations on an Eye-Shaped Domain with Moving Boundary. APS March Meeting Abstracts.

Maki, K., Henshaw, W., Barron, G., Chapp, D., Braun, R. J., & Driscoll, T. A. (2016). A theoretical investigation of the influence of a blink on the tear film dynamics. Investigative Ophthalmology & Visual Science, 57(12), 6173–6173.

Zhong, L., Ketelaar, C. F., Braun, R. J., Driscoll, T. A., King-Smith, P. E., & Begley, C. G. (2016). Mathematical Modeling of Glob-Driven Tear Film Breakup. Investigative Ophthalmology & Visual Science, 57.

Braun, R., Li, L., Henshaw, W., Driscoll, T., & King-Smith, P. (2015). Solute Dynamics and Imaging in the Tear Film on an Eye-shaped Domain. APS Meeting Abstracts.

Ketelaar, C., Zhong, L., Braun, R., Driscoll, T., King-Smith, P., & Begley, C. (2015). Tear Film Dynamics Around a Rigid Model Blob. APS Meeting Abstracts.

Stapf, M., Braun, R., Begley, C., Driscoll, T., & King-Smith, P. E. (2015). Modeling Tear Film Evaporation and Breakup with Duplex Films. APS Meeting Abstracts.

McCulloch, M., Chen, L., Schleiniger, G., & Driscoll, T. (2014). DATA DRIVEN MATHEMATICAL MODELING OF THE SINGLE VENTRICLE ANATOMY AND PHYSIOLOGY. Critical Care Medicine, 42, A1414.

Li, L., Braun, R., Driscoll, T., Henshaw, W., Banks, J., & King-Smith, P. (2013). Coupling Osmolarity Dynamics within Human Tear Film on an Eye-Shaped Domain. APS Meeting Abstracts.

Deng, Q., Driscoll, T., & Braun, R. (2012). A Model Problem for Tear Film Distribution on a Moving Rectangular Domain. APS Meeting Abstracts.

Braun, R., McFadden, J., Ranganathan, U., Driscoll, T., & King-Smith, E. (2008). Recent progress on Modeling the Human Tear Film. APS Division of Fluid Dynamics Meeting Abstracts.

Maki, K. L., Braun, R., Driscoll, T., Heryudono, A., King-Smith, P., & Fast, P. (2007). A Overset Grid Method for Fourth Order Evolution Equations of Human Tear Film. APS Division of Fluid Dynamics Meeting Abstracts.

Driscoll, T., & Rossi, L. (2003). Numerical examination of a model of thermo-acoustic instabilites in lean, pre-mixed combustors. APS Division of Fluid Dynamics Meeting Abstracts.

Driscoll, T. A., & Fornberg, B. (1998). Uses of the Berenger PML in Pseudospectral Methods for Maxwell’s Equations. IUTAM Symposium on Computational Methods for Unbounded Domains, 95–102. https://doi.org/10.1007/978-94-015-9095-2_10

Trefethen, L. N., & Driscoll, T. A. (1998). Schwarz-Christoffel mapping in the computer era. Proceedings of the International Congress of Mathematicians, 3, 533–542.

Wojcik, G., Fomberg, B., Waag, R., Carcione, L., Mould, J., Nikodym, L., & Driscoll, T. A. (1997). Pseudospectral methods for large-scale bioacoustic models. 1997 IEEE Ultrasonics Symposium Proceedings. An International Symposium (Cat. No. 97CH36118), 2, 1501–1506. https://doi.org/10.1109/ultsym.1997.661861

Driscoll, T., & Dzielski, J. (1992). Computational efficiency of a functional expansion algorithm for linear quadratic optimal control. Proceedings of the 31st IEEE Conference on Decision and Control, 143–144. https://doi.org/10.1109/cdc.1992.371773

Software

 

Driscoll, T. A. (2023). RationalFunctionApproximation.jl: Rational function approximatoin in Julia (0.1.0) [Computer software]. Zenodo. 10.5281/ZENODO.8355790

Driscoll, T. A. (2021). Cornea detection software package for Julia (0.1.0) [Computer software]. On GitHub

Driscoll, T. A. (2019). ComplexRegions.jl: A Julia package for regions in the complex plane (Computer software). 10.5281/zenodo.3548866

Trefethen, L., Hale, N., Platte, R., Driscoll, T., & Pachón, R. (2009). Chebfun version 2 (Computer software). chebfun.org

Driscoll, T. A. (1994). Schwarz-Christoffel Toolbox for MATLAB (Computer software). [On GitHub[(https://github.com/tobydriscoll/sc-toolbox)