My mathematical interests are in the numerical analysis of differential and integral equations, employing variational, perturbative and geometric strategies, with a focus on scattering problems in acoustics, electromagnetics, and linear elasticity. I also maintain an active program in problems arising in interdisciplinary and industrial applications. Some of the projects I've worked on, and continue to be interested in, are:
  • Scattering from thinly-coated objects
  • High-accuracy Dirichlet-to-Neumann maps
  • Preconditioning strategies for first-kind integral equations
  • Boundary integral equations on manifolds
  • Laplace-beltrami eigenvalues on compact manifolds and for the mixed problem
  • Conforming high-order finite elements on pyramids
    One of the most rewarding features of an academic life is the opportunity to work on research-related problems with students, and I usually have several projects suitable for graduate research. It's little harder to locate good undergraduate projects, and those I supervise tend to be more interdisciplinary in nature.

    Computational Electromagnetics and Acoustics.

    need: PDE, analysis, numerical analysis. Physics helpful.

    Structure-preserving discretizations.

    need: PDE, analysis, numerical analysis.

    Mathematical Biology.

    need: numerical analysis, PDE. Biology helpful.