Research interests

• Applications of dynamical system theory
• Numerical methods for partial differential equations
• Scientific computing

Preprint:

1. Dynamics of patchy vegetation patterns in the two-dimensional generalized Klausmeier model
   • With Michael Ward (pdf in Michael’s page)

Publications:

1. A Fast Sweeping Method for Eikonal Equations on Implicit Surfaces (doi)
   • With Shingyu Leung, Journal of Scientific Computing 67 (2016) 837–859.
2. Eulerian Methods for Visualizing Continuous Dynamical Systems using Lyapunov Exponents (arxiv, doi)
   • With Guoqiao You and Shingyu Leung, SIAM Journal on Scientific Computing 39 (2017) A415-A417.
3. Weakly Nonlinear Analysis of Peanut-Shaped Deformations for Localized Spots of Singularly Perturbed Reaction-Diffusion Systems (arxiv, doi)
   • with Michael Ward, SIAM Journal on Applied Dynamical Systems 19 (2020) 2030-2058.
4. Simulation and Optimization of Mean First Passage Time Problems in 2-D Using Numerical Embedded Methods and Perturbation Theory (arxiv, doi)
   • with Sarafa Iyaniwura, Colin Macdonald and Michael Ward, SIAM Journal of Multiscale Modeling and Simulation 19 (2021) 1367–1393.
5. Optimization of the Mean First Passage Time in Near-Disk and Elliptical Domains in 2-D with Small Absorbing Traps (arxiv, doi)
   • with Sarafa Iyaniwura, Colin Macdonald and Michael Ward, SIAM Review 63 (2021), 525-555.
6. Spot Patterns in the 2-D Schnakeberg Model with Localized Heterogeneities (arxiv, doi)
   • with Michael Ward, Studies in Applied Mathematics 146 (2021) 779–833.