We propose a new computational approach for embedded boundary simulations of
hyperbolic systems and, in particular, the linear wave equations and the nonlinear shallow …

A spectral element method is developed for solving the two-dimensional Helmholtz's
equation, which is the equation governing time-harmonic acoustic waves. Computational …

We consider fully discrete embedded finite element approximations for a shallow water
hyperbolic problem and its reduced-order model. Our approach is based on a fixed …

Massively parallel finite element methods for large‐scale computation of storm surges and
tidal flows are discussed here. The finite element computations, carried out using …

Massively parallel finite element strategies for large‐scale computations of shallow water
flows and contaminant transport are presented. The finite element discretizations, carried out …

A Neumann subproblem a posteriori finite element procedure for the efficient and accurate
calculation of rigorous, constant‐free upper and lower bounds for non‐linear outputs of the …

We propose a new Nitsche-type approach for the weak enforcement of Dirichlet and
Neumann boundary conditions in the context of time-domain wave propagation problems in …

We propose a new approach to the enforcement of Dirichlet, Neumann, or Robin boundary
conditions in finite element computations of wave propagation problems. The key idea is to …

Parallel finite element method for the analysis of quasi-three dimensional shallow water flow
is presented. The mode splitting technique and the sigma coordinate (generalized …

Sediment transport by waves and currents in the Pearl River estuary Sediment transport by
waves and currents in the Pearl River estuary Abstract The dissertation describes a study of …