My current research focuses on analysis of the peridynanmic nonlocal continuum theory, including mechanical and mathematical analyses. This includes a probabilistic interpretation for the nonlocal diffusion equation, a special case of the peridynamic energy equation.

My research interests also include the numerical solution of large-scale eigenvalue problems and differential equations. I am a co-author of ARPACK and Anasazi, open source software for computing eigenvalues of large-scale matrices. I have collaborated with scientists to use ARPACK in applications in Quantum physics, CFD, structural dynamics and radiation transport.

I am an associate editor at ETNA (Electronic transactions on numerical analysis) and SINUM (SIAM Journal on Numerical Analysis), and a member of the editorial board of the International Journal of Computational Science and Engineering.