Multiscale and model reduction methods
High-order, high-performance computing algorithms
to simulate wave propagation and absorption in 3-D. Forward and inverse
acoustic and electromagnetic scattering in 3-D.
Efficient algorithms for the Stokes and Navier-Stokes equations on rotating surfaces.
Quadrature finite element methods for elliptic,
parabolic and hyperbolic problems.
Free surface evolutionary systems in
nonlinear water waves and tumor growth.
Constructive approximations on spherical surfaces.
Fully discrete spectral boundary integral and boundary element methods.
Parallel evolutionary computations and
analysis.
Radial basis functions based numerical schemes for PDEs.
MATH 440/540 Parallel Scientific
Computing. BELS/MATH 433
Mathematical Biology.
MATH 550 Numerical Methods for Partial
Differential Equations.
MACS 332
Linear Algebra. CSCI/MATH 407 Introduction to Scientific
Computing.
A fully discrete Galerkin method for high frequency exterior acoustic scattering in three dimensions .
An efficient algorithm for simulating scattering by a large number of two dimensional particles.
A pseudospectral quadrature method for Navier-Stokes equations on rotating spheres
A radial basis Galerkin method for spherical surface Stokes equations.
Convergence analysis with parameter estimates for a reduced basis
acoustics scattering T-matrix method
A reduced basis method for multiple electromagnetic
scatttering in three dimensions
An all-frequency weakly-singular surface integral equation
for electromagnetism in dielectric media: Reformulation and well-posedness analysis
Interpolation and cubature approximation and analysis
for a class of wideband integrals on the sphere