Center for Computing Research
Phone: 505 2843480
Fax: 505 2842518
Sandia National Laboratories
P.O. Box 5800, MS 1320
I'm interested in mathematical, numerical and computational treatment of Partial Differential Equations (PDE) that arise from various applications, PDE constrained optimization and recently in uncertainty quantification. My favorite numerical scheme for discretizing PDEs, and the one I'm mostly experienced with, is the Galerkin finite element method. Recently I've been working on mesh-free methods, in particular on Smoothed Particle Hydrodynamics and Generalized Moving Least Squares. Also I'm interest in the design and analysis of numerical methods and the mathematical analysis (existence/uniqueness results) of PDEs. I'm currently working on different applications.
- Ice sheet dynamics: we develop a finite element multi-physics implementation (FELIX) of equations governing ice dynamics, including nonlinear Stokes-like equations for ice-flow and enthalpy equation for ice temperature . We also solve PDE constrained optimization to invert for unknown/uncertain parameters by minimizing the mismatch with observed data and climate forcings. Code is written in Albany applications and relies on several Trilinos packages.
- Meshless discretization: We aim at analysing and developing consistent and compatible meshless discretizations using generalized moving least square methods. We mainly target elliptic and transport equations and data-transfer problems.
- Mesoscale Materials: We develop a multifidelity capability for solving electrokinetic phenomena. In particular we work on Poisson-Boltzmann, Poisson-Nernst-Planck and classical density functional theory models to accurately model the distribution of ion at the meso-scale. We also investigate the coupling of model of different fidelities in different regions. In particular we used generalize Schwarz methods and optimization-based methods for coupling.
- Intrepid2: We develop a finite element library that provides performant and portable high-order finite element discretizations spanning all the De Rham complex. The code is a refactoring and enhancement of the library Intrepid.
PhD in Mathematical Engineering at Politecnico di Milano, Italy, in 2009.
Selected Publications & Presentations