Publications

(2020). Parameter Estimation for Evaporation-Driven Tear Film Thinning. Bulletin of Mathematical Biology.

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(2019). ComplexRegions.jl: A Julia package for regions in the complex plane. Journal of Open Source Software.

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(2019). Mathematical Models of the Tear Film. Chapter in Ocular Fluid Dynamics: Anatomy, Physiology, Imaging Techniques, and Mathematical Modeling, from Springer-Birkhäuser.

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(2019). A Model for Tear Film Dynamics during a Realistic Blink. Journal for Modeling in Ophthalmology.

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(2019). An Adaptive Partition of Unity Method for Multivariate Chebyshev Polynomial Approximations. SIAM Journal on Scientific Computation.

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(2018). Models for Tear Break Up Dynamics and Imaging. 7th European Conference on Computational Fluid Dynamics.

(2018). Simulation of parabolic flow on an eye-shaped domain with moving boundary. Journal of Engineering Mathematics.

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(2018). An adaptive partition of unity method for Chebyshev polynomial interpolation. SIAM Journal on Scientific Computing.

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(2017). On Tear Film Breakup (TBU): Dynamics and Imaging. Mathematical Medicine and Biology.

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(2017). Fundamentals of Numerical Computation.

(2017). Exploring ODEs.

(2017). Blink Characterization Using Curve Fitting and Clustering Algorithms. Journal for Modeling in Ophthalmology.

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(2016). Simulation of Thin Film Equations on an Eye-Shaped Domain with Moving Boundary. APS March Meeting Abstracts.

(2016). New Directions in Numerical Computation. Notices of the American Mathematical Society.

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(2016). Mathematical Modeling of Glob-Driven Tear Film Breakup. Investigative Ophthalmology & Visual Science.

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(2015). Tear Film Dynamics Around a Rigid Model Blob. APS Meeting Abstracts.

(2015). Solute Dynamics and Imaging in the Tear Film on an Eye-Shaped Domain. APS Meeting Abstracts.

(2015). Rectangular spectral collocation. IMA Journal of Numerical Analysis.

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(2015). Modeling Tear Film Evaporation and Breakup with Duplex Films. APS Meeting Abstracts.

(2015). Computed Tear Film and Osmolarity Dynamics on an Eye-Shaped Domain. Mathematical Medicine and Biology.

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(2015). A Model Problem for Blob-Driven Tear Film Breakup (TBU). APS Meeting Abstracts.

(2014). Optimal domain splitting for interpolation by Chebyshev polynomials. SIAM Journal on Numerical Analysis.

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(2014). Heat Transfer and Tear Film Dynamics over Multiple Blink Cycles. Physics of Fluids.

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(2014). DATA DRIVEN MATHEMATICAL MODELING OF THE SINGLE VENTRICLE ANATOMY AND PHYSIOLOGY. Critical Care Medicine.

(2014). Chebfun Guide.

(2013). Coupling Osmolarity Dynamics within Human Tear Film on an Eye-Shaped Domain. APS Meeting Abstracts.

(2013). Automatic Linearity Detection.

(2013). A Model for the Tear Film and Ocular Surface Temperature for Partial Blinks. Interfacial Phenomena and Heat Transfer.

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(2012). Thin Film Dynamics on a Prolate Spheroid with Application to the Cornea. Journal of Engineering Mathematics.

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(2012). Forming Delocalized Intermediate States with Realistic Quantum Dots. Journal of Applied Physics.

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(2012). Chebfun for PDEs.

(2012). Automatic Fréchet Differentiation for the Numerical Solution of Boundary-Value Problems. ACM Transactions on Mathematical Software (TOMS).

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(2012). A Model Problem for Tear Film Distribution on a Moving Rectangular Domain. APS Meeting Abstracts.

(2012). A Fast Treecode for Multiquadric Interpolation with Varying Shape Parameters. SIAM Journal on Scientific Computing.

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(2011). Adaptive Methods for Analysis of Composite Plates with Radial Basis Functions. Mechanics of Advanced Materials and Structures.

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(2010). Radial Basis Function Interpolation on Irregular Domain through Conformal Transplantation. Journal of Scientific Computing.

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(2010). A Transformative Model for Undergraduate Quantitative Biology Education. CBE—Life Sciences Education.

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(2009). Learning MAtlAB.

(2009). Chebfun Version 2.

(2008). The Chebop System for Automatic Solution of Differential Equations. BIT Numerical Mathematics.

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(2008). Recent Progress on Modeling the Human Tear Film. APS Division of Fluid Dynamics Meeting Abstracts.

(2008). Radial and Circular Slit Maps of Unbounded Multiply Connected Circle Domains. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

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(2008). An Overset Grid Method for the Study of Reflex Tearing. Mathematical Medicine and Biology.

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(2007). Single-Equation Models for the Tear Film in a Blink Cycle: Realistic Lid Motion. Mathematical Medicine and Biology.

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(2007). Searching for Rare Growth Factors Using Multicanonical Monte Carlo Methods. SIAM Review.

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(2007). Pade-Based Interpretation and Correction of the Gibbs Phenomenon. Advances in the Gibbs Phenomenon, Ed. by A. Jerri.

(2007). Adaptive Residual Subsampling Methods for Radial Basis Function Interpolation and Collocation Problems. Computers & Mathematics with Applications.

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(2007). A Overset Grid Method for Fourth Order Evolution Equations of Human Tear Film. APS Division of Fluid Dynamics Meeting Abstracts.

(2006). Eigenvalue Stability of Radial Basis Function Discretizations for Time-Dependent Problems. Computers & Mathematics with Applications.

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(2006). Computation of Multiply Connected Schwarz-Christoffel Maps for Exterior Domains. Computational Methods and Function Theory.

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(2005). The Effect of the Small-Aspect-Ratio Approximation on Canonical Electrostatic MEMS Models. Journal of Engineering Mathematics.

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(2005). Polynomials and Potential Theory for Gaussian Radial Basis Function Interpolation. SIAM Journal on Numerical Analysis.

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(2005). Algorithm 843: Improvements to the Schwarz-Christoffel Toolbox for MATLAB. ACM Transactions on Mathematical Software (TOMS).

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(2004). Curvature Flow in Conformal Mapping. Computational Methods and Function Theory.

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(2004). Computing Eigenmodes of Elliptic Operators Using Radial Basis Functions. Computers & Mathematics with Applications.

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(2004). Approximations in Canonical Electrostatic MEMS Models.

(2003). Numerical Examination of a Model of Thermo-Acoustic Instabilites in Lean, Pre-Mixed Combustors.. APS Division of Fluid Dynamics Meeting Abstracts.

(2003). Isospectral Shapes with Neumann and Alternating Boundary Conditions. Physical Review E.

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(2003). An Improved Schwarz-Chrisoffel Toolbox for MATLAB.

(2003). A Crash Course in Matlab.

(2002). Schwarz–Christoffel Mapping.

(2002). Observations on the Behavior of Radial Basis Function Approximations near Boundaries. Computers & Mathematics with Applications.

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(2002). Interpolation in the Limit of Increasingly Flat Radial Basis Functions. Computers & Mathematics with Applications.

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(2002). A Composite Runge–Kutta Method for the Spectral Solution of Semilinear PDEs. Journal of Computational physics.

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(2001). A Padé-Based Algorithm for Overcoming the Gibbs Phenomenon. Numerical Algorithms.

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(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.

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(2000). Staggered Time Integrators for Wave Equations. SIAM Journal on Numerical Analysis.

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(2000). Note on Nonsymmetric Finite Differences for Maxwell's Equations. Journal of Computational Physics.

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(1999). Computational Conformal Mapping (Book Review). SIAM Review.

(1999). Block Pseudospectral Methods for Maxwell's Equations II: Two-Dimensional, Discontinuous-Coefficient Case. SIAM Journal on Scientific Computing.

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(1999). A Nonoverlapping Domain Decomposition Method for Symm's Equation for Conformal Mapping. SIAM Journal on Numerical Analysis.

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(1999). A Fast Spectral Algorithm for Nonlinear Wave Equations with Linear Dispersion. Journal of Computational Physics.

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(1998). Uses of the Berenger PML in Pseudospectral Methods for Maxwell's Equations. IUTAM Symposium on Computational Methods for Unbounded Domains.

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(1998). Schwarz-Christoffel Mapping in the Computer Era. Proceedings of the International Congress of Mathematicians.

(1998). Numerical Conformal Mapping Using Cross-Ratios and Delaunay Triangulation. SIAM Journal on Scientific Computing.

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(1998). From Potential Theory to Matrix Iterations in Six Steps. SIAM Review.

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(1998). A Block Pseudospectral Method for Maxwell's Equations: I. One-Dimensional Case. Journal of Computational Physics.

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(1997). Pseudospectral Methods for Large-Scale Bioacoustic Models. 1997 IEEE Ultrasonics Symposium Proceedings. An International Symposium (Cat. No. 97CH36118).

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(1997). Eigenmodes of Isospectral Drums. SIAM Review.

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(1996). Pseudospectra for the Wave Equation with an Absorbing Boundary. Journal of Computational and Applied Mathematics.

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(1996). Matrix Iterations: The Six Gaps between Potential Theory and Convergence.

(1996). Algorithm 756: A MATLAB Toolbox for Schwarz-Christoffel Mapping. ACM Transactions on Mathematical Software (TOMS).

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(1995). A Mostly Linear Model of Transition to Turbulence. Physics of Fluids.

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(1994). Schwarz-Christoffel Toolbox User's Guide.

(1994). Schwarz-Christoffel Toolbox for MATLAB.

(1994). Conformal Mapping and Convergence of Krylov Iterations.

(1993). Pseudospectra of the Wave Operator with an Absorbing Boundary.

(1993). Hydrodynamic Stability without Eigenvalues. Science.

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(1993). Error Bound on the Solution of a Linear Differential Equation in Chebyshev Series. International Journal of Systems Science.

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(1992). Computational Efficiency of a Functional Expansion Algorithm for Linear Quadratic Optimal Control. Proceedings of the 31st IEEE Conference on Decision and Control.

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(1992). A New Direction in Hydrodynamic Stability: Beyond Eigenvalues.