My general research interests are in applied mathematics, scientific computing, numerical analysis and mathematical biology. My primary research interests are in the numerical solution of a variety of partial differential equations. Specifically, I work in the areas of computational electromagnetics and computational magnetohydrodynamics which involve the numerical discretization of Maxwell's equations and the magnetic induction equation. I am also working on several problems in mathematical biology, specifically involving population dynamics, epidemiology and spatial ecology. In all these fields, I am interested in multiscale aspects that arise due to a variety of mechanisms operating at varying spatial and temporal scales. In addition, I am interested in how uncertainty propagates through these systems and studying techniques for quantifying such uncertainty.
Computational Electromagnetics
Past Grant Funding
- PI, NSF DMS #2012882: Computational and Multi-Scale Methods for Nonlinear Electromagnetic Models in Plasmas and Nanocomposites, in collaboration with Drs Nathan Gibson and Pallavi Dhagat, both at Oregon State.
- PI, NSF DMS #1720116 OP: Collaborative Research: Compatible Discretizations for Maxwell Models in Nonlinear Optics, in collaboration with Drs Yingda Cheng at Michigan State and Fengyan Li at RPI.
- PI, NSF DMS # 0811223:Time Domain Numerical Methods for Electromagnetic Wave Propagation Problems in Complex Dispersive Dielectrics.
Mathematical Biology and Epidemiology
Past Grant Funding
- PI, Transatlantic Research Partnership, Albertine Foundation: Mathematical epidemiology of viruses coinfecting plants: Modeling, Analysis and Optimal Control Strategies, funded by the Transaltlantic Research Partnership (previously Thomas Jefferson Fund) launched by the French-American Cultural Exchange Albertine Foundation (previously FACE Foundation). In collaboration with co-PI, Professor Frederic Hamelin of Agrocampus Ouest in Rennes, France.
- Co-PI, NSF Mathematical Biology: Residence and First Passage Time Functionals in Heterogeneous Ecological Dispersion, with Edward Waymire (PI), Nathan Gibson (Co-PI), Enrique Thomann (Co-PI) and Brian Wood (Co-PI).
- Co-PI, NSF Mathematical Geosciences, Opportunities for Research CMG: Mathematical and Experimental Analysis of Reactive Transport in Discontinuous Porous Media, with Brian Wood (PI), Enrique Thomann (Co-PI), Edward Waymire (Co-PI) and Dorthe Wildenschild (Co-PI).