Research

My research is in numerical analysis and scientific computing for partial differential equations, with applications in fluid dynamics, magnetohydrodynamics (MHD), and kinetic plasma physics.

Structure-preserving numerical methods

My expertise includes:

• high-order finite element and summation-by-parts (SBP) finite difference methods;
• conservation, positivity, invariant-domain preservation, entropy inequalities, and nonlinear stability;
• convex limiting, flux-corrected transport, and residual or entropy viscosity;
• nonlinear stabilization for shocks, steep gradients, and multiscale problems.

Fluid dynamics and magnetohydrodynamics

My expertise includes:

• compressible and incompressible flow, nonlinear conservation laws, and ideal, viscous, and resistive MHD;
• high-order and continuous Galerkin discretizations;
• shock capturing and nonlinear stabilization;
• invariant-domain- and entropy-stable methods;
• reliable simulation of high-speed and under-resolved flows.

Kinetic plasma models and fusion

My expertise includes:

• Vlasov–Poisson and Vlasov–Maxwell systems, kinetic transport, and coupled plasma-field models;
• structure-preserving and positivity-preserving discretizations;
• high-order finite element and SBP methods;
• low-rank approximations for high-dimensional phase spaces;
• matrix-free and GPU-accelerated scientific computing.

Additional interests

My broader interests include multiscale and homogenization methods, adaptive computation, parabolic regularization, and reduced representations for high-dimensional PDEs.

For publications related to these topics, see the Publications page.