Scientific machine learning and forward/inverse data-driven stochastic algorithms
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
Efficient algorithms for atmospheric flows on rotating surfaces
Quadrature finite element methods for elliptic,
parabolic and hyperbolic problems
Free surface nonlinear evolutionary systems
with applications
Hybrid Finite and Boundary Element Methods (FEM-BEM) for unbounded media models
Parallel evolutionary computations and
analysis
Supported (as a single-PI) with research funds from
the National Science Foundation (NSF), Los Alamos National Laboratory (LANL),
National Renewable Energy Lab (NREL), DoD Ordnance Technology Consortium (DOTC),Simons Foundation ...
PI/CO-PI of several grants funded by the ARC,DOTC, LANL, NREL, NSF and other agencies
ARC -- Australian Research Council (Australian equivalent of the NSF, USA)
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
A high performance computing and sensitivity analysis algorithm
for stochastic many-particle wave scattering
Sobolev estimates for constructive uniform-grid FFT
interpolatory approximations of spherical functions
Scattering by stochastic boundaries: hybrid low- and high-order quantification algorithms
High-order FEM-BEM computer models for wave propagation in unbounded and heterogeneous media: Application to time-harmonic acoustic horn problem
An offline/online algorithm for a class of stochastic multiple obstacle configurations in half-plane.
Parallel mixed FEM simulation of a class of single-phase models with non-local operators
An efficient multigrid algorithm for heterogeneous acoustic media sign-indefinite high-order FEM model
Computing spatial correlation of ground motion intensities for shakeMap
Algorithm 975: TMATROM -- A T-matrix Reduced Order Model Software
Sign-definite preconditioned high-order FEM. Part 1: Formulation and simulation for acoustic wave propagation in bounded homogeneous media.
A spectrally accurate algorithm and
analysis for a Ginzburg-Landau model on superconducting surfaces
High-order FEM domain decomposition models for high-frequency wave propagation in heterogeneous media.
An FEM-MLMC algorithm for a moving shutter diffraction in time stochastic model.
A fast high order algorithm for multiple scattering from
large sound-hard configurations in three dimensions
An efficient algorithm for a class of stochastic forward and inverse Maxwell models in R^3.
A coercive heterogeneous media Helmholtz model: Formulation, wavenumber-explicit analysis, and preconditioned high-order FEM
A well-posed surface currents and charges
system for electromagnetism in dielectric media
An overlapping decomposition framework for wave propagation in heterogeneous and unbounded media:
Formulation, analysis, algorithm, and simulation.
Quasi-Monte Carlo finite element analysis for wave propagation in heterogeneous random media.
An efficient multi-level high-order algorithm for simulation of a class of Allen-Cahn stochastic systems.
An Efficient Bayesian Neural Network Surrogate Algorithm for Shape Detection.
Approximation of radiating waves in the near-field: Error estimates and application to a class of inverse problems.
Analysis and application of an overlapped FEM-BEM for wave propagation in unbounded and heterogeneous media.
A surrogate Bayesian framework for a SARS-CoV-2 data driven stochastic model.
A numerically stable T-matrix method for acoustic scattering by nonspherical particles with large aspect ratios and size parameters.
(With S. C. Hawkins
.)
J. Acoust. Soc. Am (JASA), 151 (2022), 1978-1988. (https://doi.org/10.1121/10.0009679)
A high-order algorithm for time-domain scattering in three dimensions. Submitted.
A stochastic domain decomposition and post-processing algorithm for epistemic uncertainity quantification. Submitted.