Brown's research interests include scalable solvers for implicit multiphysics, high order PDE discretization in complex geometry, compatible discretizations for heterogeneous flows, and PDE-constrained optimization. His work emphasizes robust and high performance parallel software, often relating to PETSc.
multilevel solvers, simulation and analysis of PDE systems, parallel algorithms and software, computational fluid dynamics, geodynamics, glaciology, structural mechanics, uncertainty quantification, experimental design
CSCI 3656 - Numerical Computation
Spring 2018 / Spring 2019
Covers development, computer implementation, and analysis of numerical methods for applied mathematical problems. Explores topics such as floating point arithmetic, numerical solution of linear systems of equations, root finding, numerical interpolation, differentiation, and integration.
CSCI 5636 - Numerical Solution of Partial Differential Equations
Fall 2018 / Fall 2019
Focuses on discretization techniques such as finite difference, finite element and finite volume methods, and parallel solution algorithms such as Krylov subspace methods, domain decomposition and multilevel methods.