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.

Group Lead

Aaron Fisher: finite element methods, HPC software development, applications with industrial partnerships

Research Staff

Julian Andrej: nonlinear solvers, preconditioning techniques, computational fluid dynamics, Navier-Stokes solvers

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