Research interests

Numerical analysis and applied mathematics, particularly:

Spectral and high-order difference methods for PDE

Numerical conformal mapping and applications

Domain decomposition

Numerical software for MATLAB

Application areas, such as optical communications, electromagnetic scattering

Education

Ph.D. in Applied Mathematics, Cornell University (1996)

Thesis title: Domain decomposition methods for conformal mapping and eigenvalue problems

Advisor: Lloyd N. Trefethen

M.S. in Applied Mathematics, Cornell University (1993)

B.S. in Mathematics with honors, Pennsylvania State University (1991)

B.S. in Physics, Pennsylvania State University (1991)

Honors thesis title: Comparison of computational efficiency and sensitivity of several solution algorithms for the linear--quadratic optimal control problem

Postgraduate employment

University of Delaware, 2000-present

Assistant professor, Department of Mathematical Sciences

University of Colorado (Boulder), 1996-2000

Research/instruction postdoctoral fellow, Department of Applied Mathematics. Funded by NSF Mathematical Sciences Postdoctoral Research Fellowship and NSF VIGRE grants.

Honors

University of Delaware International Travel Award, 2003

Winner, 100 Digit Challenge (SIAM), 2002

NSF VIGRE Postdoctoral Fellow, 1999-2000

NSF Mathematical Sciences Postdoctoral Research Fellow, 1996-1999

SIAM Outstanding Paper Prize, 1999

Runner-up, Richard C. DiPrima Dissertation Prize, 1998

Second Prize, Leslie Fox competition, 1997

SIAM Student Paper Prize Honorable Mention, 1995

NSF Graduate Fellow, 1991-94

A. D. White Fellow (Cornell), 1991-94

Braddock Scholar (Penn State), 1987-91

Research experience

University of Delaware, 2000-present

University of Colorado (Boulder), 1996-2000

In collaboration with B. Fornberg. Pseudospectral methods, domain decomposition, and high-order time-stepping methods for propagation, numerical solution of nonlinear wave equations, novel uses of Pade approximation, radial basis function approximation.

Cornell University, 1993-96

Under direction of L. N. Trefethen. Research topics included hydrodynamic stability, linear algebra, partial differential equations, conformal mapping, eigenvalue problems, and domain decomposition.

Penn State (University Park), Applied Research Laboratory, 1990-91

Numerical solution of linear--quadratic optimal control problems,under direction of J. Dzielski. Compared efficiency and stability of numericalmethods for the LQ optimal control problem, including Ricatti, Cholesky,and Chebyshev methods. Work led to a senior honors thesis and a conferencepresentation by Dzielski.

Penn State (University Park), Materials Research Laboratory, 1989-90

Spectroscopic ellipsometry for thin-film materials, under direction of R. W. Collins. Calibrated and operated laboratory equipment, proofread papers.

Professional activities

Member, Society for Industrial and Applied Mathematics

Referee for SISC, SINUM, J. Comput. Phys., Proc. Royal Soc. A, J. Comput. Appl. Math., Computers Math. Appl., J. Sci. Comput., Num. Meth. Fluids, J. Phys. A, Phys. Rev. E

Book reviewer for SIAM Review, Wiley.

Reviewer of grant proposals for NSF.

Attended Mathematical Problems in Industry, 2002 (RPI)

Academic visits

Oxford University Computing Laboratory, June 1999

ETH-Zurich (Swiss Federal Institute of Technology) Supercomputing Institute, Summer 1994

Consultations

United Technologies, 2002-2003

Contact: Fabio Bertolotti. Use of spectral methods in investigating thermoacoustic instability (``singing flame'') in power-generating turbines.

Weidlinger Associates, 1998-2000

Contact: Greg Wojcik. High-order and spectral methods in space and time for the numerical simulation of acoustic wave propagation in tissue.

IBM Almaden Research Laboratory, 1995-present

Contact: Martin Hassner.  Applications of conformal mapping to inductive and magnetoresistive read heads for disk drives.

Invited presentations

Conformal mapping 2.0

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

Radial basis function methods for computational PDE

Tufts University, February 2006

SVD-based importance sampling for finding rare events in noisy optical transmission

Rice University, October 2004

SIAM Nonlinear Waves and Coherent Structures, Univ. of Central Florida, October 2004

Schwarz-Christoffel maps to surfaces in space

University of Maryland, Baltimore County, April 2004

AMS/MAA Joint Meetings, Phoenix, Arizona, January 2004

High-order time stepping methods for electromagnetics

Computational Electromagnetics, Math. Forschungsinstitut Oberwolfach, February 2004

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)

Solution of Laplace's equation by conformal mapping

Oxford University Computing Laboratory, 2003

Schwarz-Christoffel mapping in MATLAB

European Microwave Week, Milano, Italy, September 2002 (Workshop)

Schwarz-Christoffel conformal mapping

University of Delaware, 2002

Significant perturbations of NLS from SVD analysis

Northwestern University, January 2002

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, organizer)

Radial basis functions for the simulation of PDEs

Courant Institute (NYU), November 2000

Brown University, October 2000

High-order space and time methods for propagation problems

University of California--Santa Barbara, 2000

University of Michigan, 2000

University of Delaware, 2000

Georgia Institute of Technology, 1999

Staggered time integrators for wave equations

Oxford University Computing Laboratory, 1999

Spectrally accurate summation of Fourier series for functions with jump discontinuities

University of Colorado, 1998

Block pseudospectral methods for Maxwell's equations in inhomogeneous media

Oak Ridge National Laboratory, 1998

Numerical conformal mapping using cross-ratios and Delaunay triangulation

University of Colorado, 1996

Eigenmodes of isospectral drums

Colorado State University, 1997

Colorado School of Mines, 1997

University of Colorado at Denver, 1997

MIT Applied Mathematics Colloquium, 1997

Cornell University, 1995

Schwarz-Christoffel mapping in MATLAB

University of Tennessee at Knoxville, 1998

Wichita State University, 1996

University of Colorado, 1996

Universitat Karlsruhe, 1994

ETH-Zurich, 1994

Cornell Numerical Analysis Day, 1993

Contributed conference presentations

Directed random walks and importance sampling for noisy optical communications

IMACS Conference on Nonlinear Evolution Equations and Wave Phenomena, April 2003

Use of the SVD for finding rare events in noisy optical communcations

SIAM Annual Meeting, Philadelphia, 2002

An efficient spectral method for nonlinear wave equations

Dundee Numerical Analysis Conference, 1999

Colorado Days at Los Alamos Lab, Los Alamos, 1999

Block pseudospectral methods for Maxwell's equations in inhomogeneous media

SIAM Annual Meeting, 1998

SIAM Conference on Wave Propagation, Colorado School of Mines, 1998

Los Alamos Days at Colorado, University of Colorado, 1998

Uses of the Berenger PML with psuedospectral methods for Maxwell's equations (poster)

IUTAM: Computational Methods for Unbounded Domains, University of Colorado, 1997

Numerical conformal mapping using cross-ratios and Delaunay triangulation

Computational Methods and Function Theory, University of Cyprus, 1997

International Society for Analysis, its Applications and Computation, University of Delaware, 1997

Eigenmodes of isospectral drums

MATLAB Conference, 1995

SIAM Annual Meeting, 1995

International Conference on Spectral and High-Order Methods, Houston, 1995

Conformal mapping and the convergence of Krylov iterations

Colorado Conference on Iterative Methods, Breckenridge, CO, 1994

Pseudospectra of the wave operator with an absorbing boundary

SIAM Annual Meeting, Philadelphia, 1993

Book

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

Refereed publications

1. T. A. Driscoll and K. Maki. How rare are large growth factors? To appear in SIAM Review.
2. A. Heryudono, R.J. Braun, T.A. Driscoll, K.L. Maki, L.P. Cook. Single-equation models for the tear film in a blink cycle: Realistic lid motion. Resubmitted to Mathematical Medicine and Biology.
3. T. A. Driscoll and A. Heryudono. Adaptive residual subsampling methods for radial basis function interpolation and collocation problems. Computers Math. Appl. 53 (2007), 927-939.
4. 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 (2006), pp 301-315.
5. R. Platte and T. A. Driscoll. Eigenvalue stability of radial basis function discretizations for time-dependent problems Computers Math. Appl. 51 (2006), 1251-1268.
6. J. A. Pelesko and T. A. Driscoll. The effect of the small-aspect-ratio approximation on canonical electrostatic MEMS models. J. of Engineering Math. 53 (2005), 239-252.
7. R. Platte and T. A. Driscoll. Polynomials and potential theory for Gaussian radial basis function interpolation. SIAM J. Numer. Anal. 43 (2005), 750-766.
8. T. A. Driscoll. Algorithm 843: Improvements to the MATLAB toolbox for Schwarz-Christoffel mapping. ACM Trans. Math. Soft. 31 (2005), 239-251.
9. R. Platte and T. A. Driscoll. Computing eigenmodes of elliptic operators using radial basis functions. Computers Math. Appl. 48 (2004), 561-576.
10. C. R. Collins, T. A. Driscoll, and K. Stephenson. Curvature flow in conformal mapping. Comput. Meth. Function Theory 3 (2003), 325-347.
11. T. A. Driscoll and H. P. W. Gottlieb. Isospectral shapes with Neumann and alternating boundary conditions. Phys. Rev. E 68, 016702 (2003).
12. T. A. Driscoll, A composite Runge-Kutta method for the spectral solution of semilinear PDE. J. Comp. Phys. 182 (2002), 357-367.
13. T. A. Driscoll and B. Fornberg, Interpolation in the limit of increasingly flat radial basis functions. Computers Math. Appl. 43 (2002), pp. 413-422.
14. 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 (2002), 473-490.
15. 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 (2001), pp. 1573-1580.
16. T. A. Driscoll and B. Fornberg. A Pade-based algorithm for overcoming the Gibbs phenomenon. Numerical Algorithms 26 (2001), pp. 77-92.
17. T. A. Driscoll and B. Fornberg. Note on nonsymmetric finite differences for Maxwell's equations.  J. Comput. Phys. 161, pp. 723-727, 2000.
18. M. Ghrist, T. A. Driscoll, and B. Fornberg. Staggered time integrators for wave equations.  SIAM J.  Num. Analy. 38, pp. 718-741, 2000.
19. B. Fornberg and T. A. Driscoll. A fast spectral algorithm for nonlinear wave equations with linear dispersion. J. Comput. Phys. 155, pp. 456-467, 1999.
20. T. A. Driscoll and B. Fornberg. Block pseudospectral methods for Maxwell's equations: II. Two-dimensional, discontinuous-coefficient case.  SIAM J. Sci.  Comput. 21, pp. 1146-1167, 1999.
21. T. A. Driscoll. A nonoverlapping domain decomposition method for Symm's equation for conformal mapping. SIAM J. Num. Analy. 36, pp. 922-934, 1999.
22. T. A. Driscoll and B. Fornberg. A block pseudospectral method for Maxwell's equations: I. One-dimensional case.J. Comput. Phys. 140, pp. 47-65, 1998.
23. T. A. Driscoll, K.-C. Toh, and L. N. Trefethen. Frompotential theory to matrix iterations in six steps. SIAM Review40, pp. 547-578, 1998.
24. T. A. Driscoll and S. A. Vavasis. Numerical conformal mapping using cross-ratios and Delaunay triangulation. SIAM Sci.  Comput. 19, pp. 1783-1803, 1998.
25. T. A. Driscoll. Eigenmodes of isospectral drums. SIAM Review 39, pp. 1-17, 1997.
26. T. A. Driscoll. A MATLAB Toolbox for Schwarz-Christoffel mapping. ACM Trans. Math. Soft. 22, pp. 168-186, 1996.
27. T. A. Driscoll and L. N. Trefethen. Pseudospectra for the wave equation with an absorbing boundary. J. Comp. Appl. Math. 69, pp. 125-142, 1996.
28. J. S. Baggett, T. A. Driscoll, and L. N. Trefethen. A mostly linear model of transition to turbulence. Physics of FluidsA 7, pp. 833-838, 1995.
29. L. N. Trefethen, A. E. Trefethen, S. C. Reddy, and T. A. Driscoll. Hydrodynamicstability without eigenvalues. Science 261, pp. 578-584, 1993.

Software

Schwarz-Christoffel Toolbox for MATLAB. Public domain software.

1994: Initial release, including graphical interface

1996: Inclusion of CRDT algorithm for elongated regions

2000: Object-oriented interface for polygons and maps

2002: Module for solving Laplace's equation with piecewise constant boundary conditions

Other works

• 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, 2002.
• T. A. Driscoll. Review of Computational Conformal Mapping, by P. K. Kythe. SIAM Review 41, pp. 832-834, 1999.
• M. Hassner, D. V. Leykin, and T. A. Driscoll. An analytic model of MR/GMR head sensitivity function. IBM Research Report RJ 10167, 1999.
• 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).
• T. A. Driscoll. Uses of the Berenger PML in pseudospectral methods for Maxwell's equations. Proceedings of the 1997 IUTAM Symposium on Computational Methods for Unbounded Domains, T. L. Geers, ed.
• 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.
• T. A. Driscoll. Domain Decomposition Methods for Conformal Mapping and Eigenvalue Problems. Ph.D. thesis, Center for Applied Mathematics, Cornell University, 1996.
• T. A. Driscoll and B. Land. Vibrations of isospectral drums. Computer animationvideo produced at the Cornell Theory Center, 1995.
• T. A. Driscoll. Schwarz-Christoffel Toolbox user's guide. Cornell Computer Science Technical Report TR 94-1422, 1994.
• T. A. Driscoll and J. E. Dzielski. Computational efficiency of a functional expansion algorithm for linear quadratic optimal control. Proc. 31st IEEE Conf. on Decision and Control, pp. 143-144, 1992.