the 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; and
Markov chains and statistical analysis on directed graphs; and
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, spectral graph theory, structural dynamics and radiation transport.
I am an associate editor at
ETNA (Electronic transactions on numerical analysis).
Ph.D. in Computational Science and Engineering, RIce University, 1995.
M.S. in Mathmatics, Virginia Polytechnic Institute and State University, 1986.
B.A. in Mathmatics, California University of Pennsylvania, 1984.