Multiscale and model reduction methods
Quantification of uncertainties in parallel scientific computing models
Computational electromagnetics & High-performance computing
High-order, high-performance computing algorithms
for wave propagation and absorption simulations 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.
Current: NSF Grant (July 2012-June 2015; Single-PI) ---
Algorithms, analyses, and model reductions for a class of parameterized systems
PI/CO-PI of several grants funded by the ARC, NSF and other agencies grants for 15 years (since 2000)
ARC -- Australian Research Council (Australian equivalent of the NSF, USA) MATH 440/540 Parallel Scientific
Computing. BELS/MATH 433
Mathematical Biology.
MATH 550 Numerical Methods for Partial
Differential Equations.
MATH 332/342
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 electromagnetic
scatttering by multiple particles in three dimensions
A stochastic pseudospectral and T-matrix algorithm for
acoustic scattering by a class of multiple particle configurations
Interpolation and cubature approximation and analysis
for a class of wideband integrals on the sphere
An efficient algorithm for simulation of
stochastic scattering cross-sections
An all-frequency weakly-singular surface integral equation
for electromagnetism in dielectric media: Reformulation and well-posedness analysis
Spectral properties of Schrodinger operators
on superconducting surfaces
An efficient O(N) algorithm for computing O(N^2)
acoustic wave interactions in large N-obstacle three dimensional configurations
Schrodinger eigenbasis
on a class of superconducting surfaces : Ansatz, analysis, FEM approximations and computations