Research

CURRENT RESEARCH INTERESTS

Multiscale Adaptive Modeling and Algorithms

– Static atomistic/continuum coupling
– Dynamic atomistic/continuum coupling
– Kinetic/continuum coupling
– Coarse grained time integrators
– Multiscale methods for the Helmholtz equation
 

Adaptive Methods for Evolutionary Problems

– Error control driven algorithms, a posteriori estimates
– Geometric/Anisotropic adaptivity
– Convergence of adaptive algorithms
– Space-time adaptivity
 

• Wave Propagation Problems

– Shock-wave propagation problems
– DG methods for linear transport
– Error control for wave equations
– Computational methods for dispersive wave equations
– Computational methods for high frequency wave propagation problems

Problems in Fluid Mechanics.

–  Error control for Navier-Stokes
–  Efficient solvers for Navier-Stokes: non-standard time discretizations (fractional step, projection methods)
–  Adaptive methods for turbulent models
–  Isothermal Navier-Stokes Korteweg system
 
Material Defects
 
Computational methods for material defects for static problems
Computational methods for dynamic crack growth and dislocation motion