I am a computational mathematician at Sandia National Laboratories. My research interests include numerical analysis, applied mathematics and computational science, with particular focus on

• Compatible and alternative discretizations of PDEs, including mimetic, DG, and stabilized methods.
• Finite element methods of least-squares type
• Finite element methods for PDE constrained optimization
• Multiscale methods: atomistic-to-continuum coupling, domain bridging

Research projects

My current research is in the following three areas:

Compatible discretizations

Compatible, or mimetic discretizations transform partial differential equations to discrete algebraic problems that mimic fundamental properties of the continuum equations. I work on a common framework for mimetic discretizations using algebraic topology to guide the analysis.

Atomistic-to-continuum coupling

Atomistic-to-Continuum (AtC) coupling is a critical component in computational materials science and other applications of interest to the DOE Office of Science. Our goal is to understand and quantify mathematically the limits in AtC coupling and the resulting impact on multiscale simulations.

Multiscale methods

Part of this research deals with application of Variational Multiscale Analysis (VMS)to develop new finite element methods for PDEs. Another research direction is domain bridging where we look at novel Lagrange-multiplier formulations for mesh tying

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