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Research Focus:

Numerical analysis and scientific computing, wave propagation, compressible flows.

Prof. Hagstrom's research is focused on computational methods for simulating time-domain wave propagation phenomena. Current projects include: 
- The development and analysis of radiation boundary conditions and fast propagation algorithms for scattering problems utilizing novel plane wave representations of the wave field, 
- Adaptive, high-order Hermite discretization methods on structured, composite or embedded grids, 
- High-order/high-resolution discontinuous Galerkin discretizations on unstructured grids utilizing polynomial and nonpolynomial bases, 
- Efficient time-stepping for equations with stiff components and on adapted grids.

Applications include electromagnetic and acoustic scattering, the generation of sound by unsteady and turbulent flows, gas-phase combustion, and the multiscale coupling of kinetic models, such as the Boltzmann equation, with continuum models such as the Navier-Stokes-Fourier system.

This research has been supported by the National Science Foundation, the Air Force Office of Scientific Research, the Army Research Office, and NASA. Recent publications have appeared in the SIAM Journals on Numerical Analysis, Applied Mathematics,and Scientific Computing, the Journal of Computational Physics, Communications in Applied Mathematics and Computational Science, the Journal of Computational Mathematics, and Communications in Partial Differential Equations.