Senior Member of
- Large-Scale Nonlinear Programming (with Focus on PDE-Constrained Optimization)
Development, analysis, and implementation of robust optimization algorithms geared
toward an efficient solution of problems with very large design spaces (e.g. with billions
of design variables). Application to nonlinear programming problems in which the constraints
involve the solution of PDEs, such as optimal design, control and inverse problems.
(1) Sequential quadratic programming (SQP) algorithms with inexact linear system solves,
(2) Domain decomposition preconditioners for KKT systems,
(3) Development of matrix-free software (Trilinos/Aristos) for the scalable solution of extreme-scale nonlinear programming problems.
Ross Bartlett (Sandia), Matthias Heinkenschloss (Rice University)
- Novel Uses of Optimization in Applied Mathematics (or `Optimization-Based Everything')
- Optimization-based analysis and reformulation of established modeling and simulation
paradigms. Development of more accurate, more robust and significantly faster
algorithms that have the potential to revolutionize the state of the art in select areas of computational mathematics.
(1) Coupling of component physics using ideas from optimization and control,
(2) Optimization-based conservative remap algorithms,
(3) Development and analysis of compatible discretizations for PDE-constrained optimization.
Pavel Bochev (Sandia), Guglielmo Scovazzi (Sandia), Mikhail Shashkov (LANL)
Top of page
Numerical solution of PDEs using advanced compatible and high-order discretization techniques.
Mathematical analysis of finite element methods, including mixed methods, and reformulations
based on natural (mimetic) differential operators.
Development of a software toolset (Trilinos/Intrepid) for PDE-based simulation, whose programming interface supports
simultaneous use of finite element, finite volume, and mimetic finite
difference discretizations on arbitrary grids.
Pavel Bochev (Sandia), Robert Kirby (Texas Tech)
Top of page