Editorship
Current Research Interests
- Numerical
Methods and Scientific Computing: researching high order
numerical methods for PDEs, including weighted ENO finite volume / finite
difference methods, discontinuous Galerkin (DG)
finite element methods, large time step schemes (e.g., implicit
integration factor schemes and their high dimensional implementation, and
other exponential integrators), fast and robust iterative methods (e.g.,
fast sweeping
methods for steady state problems, homotopy
methods, etc), and high accuracy numerical
methods on unstructured meshes for complex domain geometries, etc.
- Applications:
numerical solution of PDEs arising in computational biology (e.g.,
morphogenesis and tissue patterning), and computational physics (e.g.,
interaction of shock waves with vortices, interaction of shock waves with
Rayleigh-Taylor flow, and other computational fluid dynamics problems);
computational analysis of physical and biological problems.
Examples:
New high order Krylov IIF schemes
WENO fast sweeping methods
DG fast sweeping methods
Matlab codes for the implicit integration factor methods
ACMS Colloquium: 2011-2012
Notre Dame Conferences:
Midwest Numerical
Analysis Days 2012 - Website