The Numerical Analysis and Simulations Group (NASG) conducts mathematical research and develops simulation codes for the discretization and solution of partial differential equations (PDEs) that arise in a wide variety of physics and engineering disciplines including fluid dynamics, solid mechanics, electromagnetics, combustion, geodynamics, plasma physics, and quantum computing. Our interests span the spectrum of theoretical and practical work in numerical methods and software required for PDE-based modeling and simulation. Of particular interest are high-order methods including finite difference, finite volume, and finite element methods for spatial PDE discretization, scalable linear solvers, embedded boundary methods, and adaptive mesh refinement.
The NASG is home to MFEM, a notable open-source finite element discretization library.
Aaron Fisher: finite element methods, HPC software development, applications with industrial partnerships
Julian Andrej: nonlinear solvers, preconditioning techniques, computational fluid dynamics, Navier-Stokes solvers
John Camier: scientific computing, parallel programming models, compilation toolchains, heterogeneous architectures, performance analysis, code optimization
Dylan Copeland: finite element methods, iterative linear solvers, computational electromagnetics, reduced order modeling, parallel computing
Veselin Dobrev: PDE discretization, discontinuous Galerkin methods, preconditioners, multigrid methods, domain decomposition, scalable parallel algorithms, mesh refinement, visualization, high-order finite elements, ALE methods, hydrodynamics, mesh optimization/smoothing
Andrew Gillette: numerical methods for PDEs, computational geometry, high performance computing, machine learning
Tzanio Kolev: high-order finite elements, linear solvers, scientific software, high performance computing
Chak Lee: numerical discretizations for PDEs, linear and nonlinear solvers
Ketan Mittal: high-order methods, finite/spectral element methods, mesh generation and optimization, overlapping Schwarz-based solvers, multirate time-stepping schemes, stability analysis
Socratis Petrides: high-order finite element methods, hp-adaptivity, multilevel solvers, high-frequency wave propagation, computational electromagnetics, matrix-free preconditioning
Mark Stowell: computational electromagnetics, high-order finite element methods, mixed finite element methods, H(Curl) and H(Div) basis functions
Vladimir Tomov: finite element methods for multi-material ALE and radiation hydrodynamics, high-order mesh optimization