Toby Driscoll is a Unidel Chaired Professor in the Department of Mathematical Sciences at the University of Delaware. His research interests are in scientific computation, mathematical software, and applications of mathematics in the life sciences.

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Interests

- High-order and spectral methods in scientific computing
- Mathematical software in Matlab and Julia
- Applied mathematics, especially in biomedicine

Education

PhD in Applied Mathematics, 1996

Cornell University

MS in Applied Mathematics, 1993

Cornell University

BS in Mathematics, 1991

Pennsylvania State University

BS in Physics, 1991

Pennsylvania State University

Preconditioned nonlinear iterations for overlapping Chebyshev discretizations with independent grids

The additive Schwarz method is usually presented as a preconditioner for a PDE linearization based on overlapping subsets of nodes from a global discretization. It has previously been shown how to apply Schwarz preconditioning to a nonlinear problem. By first replacing the original global PDE with the Schwarz overlapping problem, the global discretization becomes a simple union of subdomain discretizations, and unknowns do not need to be shared. In this way, restrictive-type updates can be avoided, and subdomains need to communicate only via interface interpolations. The resulting preconditioner can be applied linearly or nonlinearly. In the latter case, nonlinear subdomain problems are solved independently in parallel, and the frequency and amount of interprocess communication can be greatly reduced compared to global preconditioning of the sequence of linearized problems.

Read More: https://epubs.siam.org/doi/abs/10.1137/19M1242483?casa_token=NFkef7E_brwAAAAA:Kguze98V4mNMIobvPkTrYLGbEjwTCWChkGppg0IJ8syF7Y9x-A2yDo6FsTElYqFmZ9PVe4hkAg

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Fitting ODE models of tear film breakup.
preprint.

(2023).
(2023).
Dynamics and mechanisms for tear breakup (TBU) on the ocular surface.
Math Biosci Eng.

(2021).
Automatic detection of the cornea location in video captures of fluorescence.
Modeling and Artificial Intelligence in Ophthalmology.

(2021).
Fitting Simplified Models to Machine Learning-Identified Tear Film Breakup.
*Investigative Ophthalmology & Visual Science*.

(2021).