Tobin A. Driscoll

Research interests

Education

1996 Cornell University

1993 Cornell University

1991 Pennsylvania State University

Professional experience

2010–present University of Delaware

2004–2010 University of Delaware

2000–2004 University of Delaware

1996–2000 University of Colorado at Boulder

Honors and awards

2014 Outstanding Scholar Award, College of Arts & Sciences, University of Delaware (sole winner for year)

2002 Winner, 100 Digit Challenge (SIAM)

1999–2000 NSF VIGRE Postdoctoral Fellow

1996–1999 NSF Mathematical Sciences Postdoctoral Research Fellow

1999 SIAM Outstanding Paper Prize

1998 Runner-up, Richard C. DiPrima Dissertation Prize

1997 Second Prize, Leslie Fox Competition

1995 SIAM Student Paper Prize Honorable Mention

1991–1994 NSF Graduate Fellow

1991–1994 A. D. White Fellow (Cornell graduate study)

1987–1991 Braddock Scholar (Penn State undergraduate study)

Grants

2014–2017 R. J. Braun (PI), T. A. Driscoll, and K. L. Maki (co-PIs). Collaborative Research: Tear Film Dynamics: Modeling, Blinking, and Computation. NSF DMS-1412085 $375,003

2014–2016 M. McCulloch (PI), T. A. Driscoll, and G. Schleiniger (co-PIs). Data driven mathematical modeling of the hypoplastic left heart syndrome circulation. NIH Delaware INBRE III, $60,724

2013–2015 T. A. Driscoll. Special support from The MathWorks, Inc.

2013–2014 M. McCulloch (PI), T. A. Driscoll, and G. Schleiniger (co-PIs). Computer simulation of the single ventricle anatomy and physiology explaining mechanisms for sudden cardiac death. NIH Delaware INBRE Grant, $44,182

2012–2015 T. A. Driscoll (PI) with 5 other key personnel. Meeting the need in mathematics at the University of Delaware. U.S. Department of Education Graduate Assistance in Areas of National Need, $527,700

2010–2013 R. J. Braun (PI) and T. A. Driscoll (co-PI), Modeling tear film dynamics. NSF DMS-1022706, $444,000

2007 L. F. Rossi, T. Driscoll, and R. Luke (co-PIs), Strengthening mathematics instruction with automated algorithmic mastery activities. Center for Teaching Effectiveness (UD), $20,000

2006–2009 R. Braun (PI), L. P. Cook, and T. A. Driscoll (co-PIs), Modeling the blink cycle and lipid dynamics in the tear film. NSF DMS-0616483, $325,000

2006–2010 H. B. White et al. (co-PIs), with T. A. Driscoll and others as senior personnel. Howard Hughes Medical Institute Undergraduate Science Education grant, $1,500,000

2003 R. Braun, T. A. Driscoll, P. Monk, L. F. Rossi (co-PIs). NSF Scientific Computing Research Environments for the Mathematical Sciences. NSF DMS-0322583, $68,460

2003 University of Delaware International Travel Award

2001–2004 T. A. Driscoll (PI). Novel fast and accurate methods for partial differential equations. NSF DMS-0104229, $88,407

2001–2002 T. A. Driscoll (PI). Fast time stepping for the computational simulation of differential equations. University of Delaware Research Foundation, $21,042

1996–1999 T. A. Driscoll (PI). NSF Mathematical Sciences Postdoctoral Research Fellowship (University of Colorado). NSF DMS-9627677, $75,000

Publications

For a filterable list with live links, go to my web site. Or you can visit my Google Scholar site.

Books

2018 L. N. Trefethen, A. Birkisson, and T. A. Driscoll. Exploring ODEs, SIAM

2017 T. A. Driscoll and R. J. Braun. Fundamentals of Numerical Computation, SIAM

2014 T. A. Driscoll, N. Hale, and L. N. Trefethen, eds. Chebfun Guide, 1st edition. Oxford, UK.

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

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

Book chapters

2007 T. A. Driscoll and B. Fornberg. Padé-based interpretation and correction of the Gibbs phenomenon. In Advances in the Gibbs Phenomenon, ed. by A. Jerri, Sigma Sampling Publishing, Potsdam, NY.

2002 T. A. Driscoll and L. N. Trefethen. Numerical construction of conformal maps. Appendix to Fundamentals of Complex Analysis with Applications to Engineering, Science, and Mathematics, 3rd edition, by E. D. Saff and A. D. Snider, Prentice Hall.

Journal articles

2018 T. A. Driscoll, R. J. Braun, and J. K. Brosch. Simulation of parabolic flow on an eye-shaped domain with moving boundary. J. Eng. Math. 111 (1): 111–126.

K. Aiton, T. A. Driscoll. An adaptive partition of unity method for Chebyshev polynomial interpolation. SIAM J. Sci. Comput. 40 (1): A251–A265.

R. J. Braun, T. A. Driscoll, C. G. Begley, P. E. King-Smith, and J. I. Siddique. On tear film breakup (TBU): dynamics and imaging.* Math. Med. Biol.* 35 (2): 145–180.

2017 J. K. Brosch, Z. Wu, C. G. Begley, T. A. Driscoll, R. J. Braun. Blink characterization using curve fitting and clustering algorithms. J. Modeling Ophthalmology 1: 60–81.

2016 T. A. Driscoll, E. Süli, and A. Townsend, eds., New Directions in Numerical Computation. Notices of the Amer. Math. Soc. 63 (4): 398–400, 2016.

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. Math. Med. Biol. 33 (2): 123–157. DOI: 10.1093/imammb/dqv013.

T. A. Driscoll and N. Hale, Rectangular spectral collocation. IMA J. Num. Analy. 36 (1): 108–132. DOI: 10.1093/imanum/dru062.

K. Maki, W. Henshaw, G. Barron, D. Chapp, R. J. Braun, T. A. Driscoll. A theoretical investigation of the influence of a blink on the tear film dynamics. Invest. Ophthamology Visual Sci. 57: 6173.

L. Zhong, C. F. Ketelaar, R. J. Braun, T. A. Driscoll, P. E. King-Smith, C. G. Begley. Mathematical modeling of glob-driven tear film breakup. Invest. Ophthamology Visual Sci. 57: 6171.

2014 Q. Deng, R. J. Braun and T. A. Driscoll, Heat transfer and tear film dynamics over multiple blink cycles. Phys. Fluids 26, 071901 (2014); DOI: 10.1063/1.4887341

T. A. Driscoll and J. A. C. Weideman. Optimal domain splitting for interpolation by Chebyshev polynomials. SIAM J. Numer. Anal. 52, 1913–1927. DOI: 10.1137/130919428.

2013 L. Li, R. J. Braun, T. A. Driscoll, W. D. Henshaw, J. W. Banks, and P. E. King–Smith. Coupling osmolarity dynamics within human tear film on an eye-shaped domain. Bull. Amer. Phys. Soc. 58 (18) (refereed abstract for Annual Meeting).

2012 Q. Deng and T. A. Driscoll. A fast treecode for multiquadric interpolation with varying shape parameters. SIAM J. Sci. Comput. 34(2), A1126–A1140. DOI: 10.1137/110836225

W. M. Reid, T. A. Driscoll, M. F. Doty. Forming delocalized intermediate states with realistic quantum dots. J. Applied Phys. 111, 056102. DOI: 10.1063/1.3691113

A. Birkisson and T. A. Driscoll. Automatic Fréchet differentiation for the numerical solution of boundary-value problems. ACM Trans. Math. Soft. 38, Article 26. DOI: 10.1145/2331130.2331134

R. J. Braun, R. Usha, G. B. McFadden, T. A. Driscoll, L. P. Cook, and P. E. King–Smith. Thin film dynamics on a prolate spheroid with application to the cornea. J. Eng. Math. 73(1), 121–138. DOI: 10.1007/s10665-011-9482-4

2011 A. M. Neves, T. A. Driscoll, A. R. H. Heryudono, A. J. Ferreira, C. M. Soares, and R. M. Jorge. Adaptive methods for analysis of composite plates with radial basis functions. Mech. Adv. Materials Struct. 18, 420–430. DOI: 10.1080/15376494.2010.528155

2010 D. C. Usher, T. A. Driscoll, P. Dhurjati, J. A. Pelesko, L. F. Rossi, G. Schleiniger, K. Pusecker, and H. B. White. A transformative model for undergraduate quantitative biology education. CBE Life Sci. Educ. 9, 181–188. DOI: 10.1187/cbe.10-03-0029

A. R. H. Heryudono and T. A. Driscoll. Radial basis function interpolation on irregular domain through conformal transplantation. J. Sci. Comput. 44, 286–300. DOI: 10.1007/s10915-010-9380-3

T. A. Driscoll. Automatic spectral collocation for integral, integro-differential, and integrally reformulated differential equations. J. Comput. Phys. 229, 5980–5998. DOI: 10.1016/j.jcp.2010.04.029

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

K. L. Maki, R. J. Braun, T. A. Driscoll, and P. E. King-Smith. An overset grid method for the study of reflex tearing. Math. Medicine and Biology 25, 187–214. DOI: 10.1093/imammb/dqn013

T. DeLillo, T. Driscoll, A. Elcrat, and J. Pfaltzgraff. Radial and circular slit maps of unbounded multiply connected circle domains. Proc. Roy. Soc. A 464, 1719–1737.

2007 A. Heryudono, R. J. Braun, T. A. Driscoll, K. L. Maki and L. P. Cook. Single-equation models for the tear film in a blink cycle: realistic lid motion. Mathematical Medicine and Biology 24, 347–377. DOI: 10.1093/imammb/dqm004

T. A. Driscoll and K. Maki. Searching for rare growth factors using multicanonical Monte Carlo methods. SIAM Review 49, 673–692.

T. A. Driscoll and A. Heryudono. Adaptive residual subsampling methods for radial basis function interpolation and collocation problems. Computers Math. Appl. 53, 927–939. DOI: 10.1016/j.camwa.2006.06.005

2006 R. Platte and T. A. Driscoll. Eigenvalue stability of radial basis function discretizations for time-dependent problems. Computers Math. Appl. 51, 1251–1268. DOI: 10.1016/j.camwa.2006.04.007

T. DeLillo, T. A. Driscoll, A. Elcrat, and J. Pfaltzgraff. Computation of multiply connected Schwarz–Christoffel maps for exterior domains. Comput. Meth. Function Theory 6, 301–315.

2005 J. A. Pelesko and T. A. Driscoll. The effect of the small-aspect-ratio approximation on canonical electrostatic {MEMS} models. J. Engng. Math. 53, 239–252. DOI: 10.1007/s10665-005-9013-2

R. Platte and T. A. Driscoll. Polynomials and potential theory for Gaussian radial basis function interpolation.} SIAM J. Num. Analy. 43, 750–766. DOI: 10.1137/040610143

T. A. Driscoll. Algorithm 843: Improvements to the MATLAB toolbox for Schwarz–Christoffel mapping. ACM Trans. Math. Soft. 31, 239–251. DOI: 10.1145/1067967.1067971

2004 R. Platte and T. A. Driscoll. Computing eigenmodes of elliptic operators using radial basis functions. Computers Math. Appl. 48, 561–576. DOI: 10.1016/j.camwa.2003.08.007

2003 C. R. Collins, T. A. Driscoll, and K. Stephenson. Curvature flow in conformal mapping. Comput. Meth. Function Theory 3, 325–347.

T. A. Driscoll and H. P. W. Gottlieb. Isospectral shapes with Neumann and alternating boundary conditions. Phys. Rev. E 68, 016702.

2002 T. A. Driscoll. A composite Runge-Kutta method for the spectral solution of semilinear PDE. J. Comp. Phys. 182, 357–367.

T. A. Driscoll and B. Fornberg. Interpolation in the limit of increasingly flat radial basis functions. Computers Math. Appl. 43, 413–422.

B. Fornberg, T. A. Driscoll, G. Wright, and R. Charles. Observations on the behavior of radial basis function approximations near boundaries. Computers Math. Appl. 43, 473–490.

2001 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. IEEE Microw. Theory Tech. 49, 1573-1580.

T. A. Driscoll and B. Fornberg. A Padé-based algorithm for overcoming the Gibbs phenomenon. Numerical Algorithms 26, 77–92.

2000 T. A. Driscoll and B. Fornberg. Note on nonsymmetric finite differences for Maxwell’s equations. J. Comput. Phys. 161, 723–727.

M. Ghrist, T. A. Driscoll, and B. Fornberg. Staggered time integrators for wave equations. SIAM J. Num. Analy. 38, 718–741.

1999 B. Fornberg and T. A. Driscoll. A fast spectral algorithm for nonlinear wave equations with linear dispersion. J. Comput. Phys. 155, 456–467.

T. A. Driscoll and B. Fornberg. Block pseudospectral methods for Maxwell’s equations: II. Two-dimensional, discontinuous-coefficient case. SIAM J. Sci. Comput. 21, 1146–1167.

T. A. Driscoll. A nonoverlapping domain decomposition method for Symm’s equation for conformal mapping. SIAM J. Num. Analy. 36, 922–934.

1998 T. A. Driscoll and B. Fornberg. A block pseudospectral method for Maxwell’s equations: I. One-dimensional case. J. Comput. Phys. 140, 47–65.

T. A. Driscoll, K.-C. Toh, and L. N. Trefethen. From potential theory to matrix iterations in six steps.}
SIAM Review 40, 547–578.

T. A. Driscoll and S. A. Vavasis. Numerical conformal mapping using cross-ratios and Delaunay triangulation.} SIAM Sci. Comp. 19, 1783–1803.

1997 T. A. Driscoll. Eigenmodes of isospectral drums. SIAM Review 39, 1–17.

1996 T. A. Driscoll. A MATLAB Toolbox for Schwarz–Christoffel mapping. ACM Trans. Math. Soft. 22, 168–186.

T. A. Driscoll and L. N. Trefethen. Pseudospectra for the wave equation with an absorbing boundary. J. Comp. Appl. Math. 69, 125–142.

1995 J. S. Baggett, T. A. Driscoll, and L. N. Trefethen. A mostly linear model of transition to turbulence. Physics of Fluids A 7, 833–838.

1993 L. N. Trefethen, A. E. Trefethen, S. C. Reddy, and T. A. Driscoll. Hydrodynamic stability without eigenvalues. Science 261, 578–584.

J. E. Dzielski and T. A. Driscoll. Error bound on the solution of a linear-differential equation in Chebyshev series. Int. J. Systems Sci. 24, 1317–1327.

Refereed proceedings and posters

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

2016 Joseph Brosch, T. A. Driscoll, Richard Braun. Simulation of Thin Film Equations on an Eye-Shaped Domain with Moving Boundary. APS March Meeting Abstracts.

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

2015 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). Bull. Amer. Physical Soc. 60: 68th Annual Meeting of the APS Division of Fluid Dynamics, Boston, 2015.

M. Stapf, R. J. Braun, C. G. Begley, T. A. Driscoll, and P. E. King-Smith. Modeling Tear Film Evaporation and Breakup with Duplex Films. Bull. Amer. Physical Soc. 60: 68th Annual Meeting of the APS Division of Fluid Dynamics Boston, 2015.

R. J. Braun, L. Li, W. Henshaw, T. A. Driscoll, and P. E. King-Smith. Solute Dynamics and Imaging in the Tear Film on an Eye-shaped Domain, Bull. Amer. Physical Soc. 60: 68th Annual Meeting of the APS Division of Fluid Dynamics, Boston, MA, 2015.

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, Bull. Amer. Physical Soc. 60: 68th Annual Meeting of the APS Division of Fluid Dynamics, Boston, 2015.

2014
M. McCulloch, G. Schleiniger, L. Chen, S. Gidding, and T. A. Driscoll. Data driven mathematical modeling of the single ventricle anatomy and physiology. Highlighted Poster (refereed), NISBRE IDeA Conference, 2014.

1998 L. N. Trefethen and T. A. Driscoll. Schwarz–Christoffel mapping in the computer era. Proceedings of the International Congress of Mathematicians, Vol. III (Berlin, 1998). Doc. Math. 1998, Extra Vol. III, 533–542 (electronic).

1997 G. Wojcik, B. Fornberg, R. Waag, J. Mould, T. A. Driscoll, and L. Nikodym. Pseudospectral methods for large-scale bioacoustic models. Proceedings of the 1997 IEEE Ultrasonics Symposium.

Other works

Software

Presentations

2018 “Preconditioning nonlinear equations with domain decomposition,” AMS Eastern Sectional Meeting, University of Delaware, September 2018.

“Exploring differential equations using Chebfun,” SIAM Annual Meeting Minisymposium, Portland, OR, July 2018.

“Dynamics on a model blinking eye-shaped domain,” SIAM Annual Meeting Minisymposium, Portland, OR, July 2018.

2017 “Mathematical and computational modeling of the tear film,” Center for Bioinformatics & Computational Biology Seminar, University of Delaware, 2017.

2016 “Dynamics on a model blinking eye-shaped domain,” SIAM Annual Meeting Minisymposium, Boston, July 2016.

2015 “Data-driven systemic modeling of infant hypoplastic left heart syndrome,” Center for Cardiovascular Health Symposium, University of Delaware, October 2015.

“Flipping the classroom for numerical computation,” MathWorks Research Summit, Natick, MA, June 2015.

“Automatic multivariate approximation,” SIAM Computational Science and Engineering Conference Minisymposium, Salt Lake City, AZ, April 2015.

“An open-source software project for numerical conformal mapping,” BIRS Workshop on Modern Applications of Complex Variables, Banff, AL, January 2015.

2014 “New directions in spectral methods,” Numerical Analysis Seminar, Cornell University, November 2014.

2013 “Optimal splitting in spectral collocation,” Numerical Analysis Group Seminar, Oxford University, November 2013.

“Numerical computing with functions,” Colloquium, Wichita State University, September 2013.

“Reflections on flipping a math classroom,” Summer Faculty Institute, University of Delaware, June 2013.

“Optimal splitting in spectral collocation,” Seminar, Arizona State, April 2013.

“Numerical computing with functions,” Colloquium, Arizona State, April 2013.

2012 “Numerical computing with functions,” Colloquium, Temple University, December 2012.

“Chebfun beyond the ordinary (DE),” http://www2.maths.ox.ac.uk/chebfun/and_beyond/ Workshop, Oxford University, September 2012.

“Spectral deferred correction for time-dependent PDEs in Chebfun,” http://www.siam.org/meetings/an12/, Minneapolis, July 2012. \end{mylist}

“Chebfun for PDE,” http://www.birs.ca/events/2012/5-day-workshops/12w5021, Banff International Research Station, June 2012.

“Optimal splitting in spectral collocation,” Del-Mar Numerical Analysis Day, University of Delaware, April 2012.

2011 “Differential equations in Chebfun,” http://www.iciam2011.com, Vancouver, July 2011 (minisymposium).

“Rectangular projections for reliable spectral collocation,” http://www.iciam2011.com, Vancouver, July 2011 (minisymposium).

“Chebfun: A software system for interacting with functions,” NSF-CBMS Conference on Radial Basis Functions, Dartmouth, MA, June 2011.

“Approximation Theory, Spectral Methods, and Chebfun” (with L. N. Trefethen), [http://www.dmi.units.it/dobbiaco11/index.php?section=page&action=inc&name=aims](Fifth annual Dobbiaco Summer School), Dobbiaco, Italy, June 12-17, 2011.

2010 “Automatic Fréchet differentiation for the spectral solution of boundary-value problems,” SIAM Annual Meeting, July 2010 (minisymposium).

2009 “Automatic solution of differential equations in the Chebfun system,” Meeting of the Canadian Applied and Industrial Mathematics Society, University of Western Ontario, June 2009.

“Automatic solution of differential equations in the Chebfun system,” SIAM Southeastern-Atlantic Section Conference, University of South Carolina, April 2009.

“Automatic solution of differential equations in the Chebfun system,” Courant Institute Seminar, February 2009.

2008 “Solving continuous differential equations numerically: chebfun and chebop”

“Least squares methods for conformal mapping and boundary value problems,” SIAM Annual Meeting, San Diego, July 2008.

2007 “Modeling and simulation of human tear film dynamics,” Colloquium, SUNY Buffalo, November 2007.

“Detection and approximation of jumps using complex-variable techniques,” 7th International Conference on Spectral and High-Order Methods (ICOSAHOM), Beijing, China, June 2007 (minisymposium).

“Spectral least-squares for conformal mapping and potential theory,” Computational and Conformal Geometry Workshop, SUNY Stony Brook, April 2007.

“Radial basis function methods for meshless PDE computation,” Seminar, New Jersey Institute of Technology, January 2007.

“Radial basis function methods for meshless PDE computation,” Oxford University Computing Laboratory, January 2007.

2006 “Conformal mapping 2.0,” Seminar, Dartmouth College, October 2006.

“Developing a computational framework for conformal mapping,” SIAM Annual Meeting, Boston, July 2006.

“Optimal node placement for Gaussian radial basis function interpolation,” SIAM Annual Meeting, Boston, July 2006.

“Optimal node placement for Gaussian radial basis function interpolation,” Seminar, Tufts University, February 2006.

2004 “SVD-based importance sampling for finding rare events in noisy optical transmission,” Rice University, October 2004.

“SVD-based importance sampling for an optics-based dynamical system,” SIAM Nonlinear Waves and Coherent Structures, University of Central Florida, October 2004.

“Schwarz–Christoffel maps to surfaces in space,” University of Maryland, Baltimore County, April 2004.

“High-order time stepping methods for electromagnetics,” Computational Electromagnetics, Math. Forschungsinstitut Oberwolfach, February 2004.

2003 “Solution of Laplace’s equation by conformal mapping,” Oxford University Computing Laboratory, 2003.

“The EigTool system for exploring matrix eigenmode problems,” International Congress on Industrial and Applied Mathematics, Sydney, Australia, July 2003 (minisymposium).

“Numerical conformal mapping in 2003: A survey,” International Congress on Industrial and Applied Mathematics, Sydney, Australia, July 2003 (minisymposium, organizer).

“Overdetermined formulations for eigenmode problems,” International Congress on Industrial and Applied Mathematics, Sydney, Australia, July 2003 (minisymposium).

“Directed random walks and importance sampling for noisy optical communications,” IMACS Nonlinear Evolution Equations and Wave Phenomena, April 2003.

2002 “Schwarz–Christoffel mapping in MATLAB,” European Microwave Week, Milan, Italy, September 2002.

“Use of the SVD for finding rare events in noisy optical communcations,” SIAM Annual Meeting, July 2002.

“Schwarz–Christoffel conformal mapping,” University of Delaware, 2002.

“Significant perturbations of NLS from SVD analysis,” Northwestern University, January 2002.

2001 “Significant perturbations of NLS from SVD analysis,” University of Maryland, Baltimore County, August 2001.

“Schwarz–Christoffel conformal mapping,” Computational Methods and Function Theory, University of Aveiro, Portugal, June 2001 (Plenary speaker).

“Fast time stepping methods for semilinear evolution equations,” Northwestern University, June 2001.

“Wavenumber-dependent time stepping methods for semilinear evolution equations,” IMACS Conference on Nonlinear Waves, University of Georgia, April 2001 (Minisymposium).

2000 “Radial basis functions for the simulation of PDEs”

“High-order space and time methods for propagation problems”

1999 “High-order space and time methods for propagation problems,” Georgia Institute of Technology, 1999.

“An efficient spectral method for the solution of nonlinear wave equations”

“Staggered time integrators for wave equations,” Oxford University Computing Laboratory, 1999.

1998 “Block pseudospectral methods for Maxwell’s equations in inhomogeneous media”

“Spectrally accurate summation of Fourier series for functions with jump discontinuities,” University of Colorado, Boulder, 1998.

“Block pseudospectral methods for Maxwell’s equations in inhomogeneous media,” Oak Ridge National Laboratory, 1998.

“Schwarz–Christoffel mapping in MATLAB,” University of Tennessee, Knoxville, 1998.

1997 “Uses of the Berenger PML with psuedospectral methods for Maxwell’s equations” (poster), IUTAM: Computational Methods for Unbounded Domains, Boulder, CO, 1997.

“Numerical conformal mapping using cross-ratios and Delaunay triangulation,”

“Numerical conformal mapping using cross-ratios and Delaunay triangulation,” Lesile Fox Prize Competition, 1997.

“Eigenmodes of isospectral drums”

1996 “Numerical conformal mapping using cross-ratios and Delaunay triangulation,” University of Colorado, Boulder, 1996.

“Schwarz–Christoffel mapping in MATLAB”

1995 “Eigenmodes of isospectral drums”

1994 “Conformal mapping and the convergence of Krylov iterations,” Colorado Conference on Iterative Methods, Breckenridge, CO, 1994.

“Schwarz–Christoffel mapping in MATLAB”

1993 “Pseudospectra of the wave operator with an absorbing boundary,” SIAM Annual Meeting, July 1993.

“Schwarz–Christoffel mapping in MATLAB,” Cornell Numerical Analysis Day, 1993.

Students supervised

Kevin Aiton, Ph.D., 2019

Shawn Abernethy, M.S. with thesis, 2013

Quan Deng, Ph.D., 2013

Alfa Heryudono, Ph.D., 2008

Rodrigo Platte, Ph.D., 2005

Teaching

Philosophy

While I enjoy lecturing, I no longer believe it should be the only or even primary way of teaching most math classes. The marginal benefits of a live lecture over a recorded one are overshadowed by supervised active learning, where the instructor shares expertise with students as they wrestle with the material themselves. I use techniques such as problem-based learning, laboratory exploration, personal response systems, and flipping the classroom to create active learning opportunities. In addition, I believe mathematics needs to embrace teaching computation throughout the curriculum, rather than quarantining it into a few courses or lab sections.

Undergraduate

Calculus A,B,C

Linear algebra (math and engineering majors)

ODEs (math and engineering majors)

PDEs (math and engineering majors)

Computational mathematics (two-semester sequence)

Complex analysis

Graduate

Numerical linear algebra and nonlinear equations

Numerical ODEs/PDEs

Spectral/high-order methods for PDEs

Radial basis functions

Professional activities

Associate Editor of Advances in Computational Mathematics, 2019–present

Director of Undergraduate Studies (Delaware), 2018–present

At-Large Member of the SIAM Council, 2015–2018

Associate Editor of the SIAM Journal on Scientific Computing, 2008–2014

Associate Editor of Journal of Engineering Mathematics, 2010–2015

Director of Graduate Studies (Delaware), 2014–2014

Member, Society for Industrial and Applied Mathematics

Organizing committee of Mathematical Problems in Industry, 2004 (Delaware)

Academic visits

Institute for Mathematics and Its Applications, University of Minnesota, September–December 2010

Oxford University Computing Laboratory, January–June 2008

Oxford University Computing Laboratory, Summer 1999

ETH Supercomputing Institute, Zürich, Summer 1994

Consultations

United Technologies, 2002–2003

Weidlinger Associates, 1998–2000

IBM Almaden Research Center, 1995–2001