# Richard Lehoucq

Discrete Math & Optimization

## Discrete Math & Optimization

(505) 845-8929

Sandia National Laboratories, New Mexico

P.O. Box 5800

Albuquerque, NM 87185-1320

## My research interests are:

- Uncertainty quantification for Monte-Carlo sampling of particle models to solve inverse problems, and more generally, design-based optimization problems.
- Markov chains and statistical analysis on directed graphs; and
- Analysis of the peridynamic 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
- 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.

## Education

- Ph.D. in Computational Science and Engineering, RIce University, 1995.
- M.S. in Mathematics, Virginia Polytechnic Institute and State University, 1986.
- B.A. in Mathematics, California University of Pennsylvania, 1984.

## Further information

- Trilinos software
- LOCA: a library of continuation algorithms