The finite-difference time-domain (FDTD) method is a widespread numerical tool for full-
wave analysis of electromagnetic fields in complex media and for detailed geometries …

In computational fluid dynamics simulations of industrial flows, models based on the
Reynolds-averaged Navier–Stokes (RANS) equations are expected to play an important …

Numerical simulations on fluid dynamics problems primarily rely on spatially or/and
temporally discretization of the governing equation using polynomials into a finite …

We present a deep learning framework for quantifying and propagating uncertainty in
systems governed by non-linear differential equations using physics-informed neural …

We develop a non-intrusive reduced basis (RB) method for parametrized steady-state partial
differential equations (PDEs). The method extracts a reduced basis from a collection of high …

Closed-loop turbulence control is a critical enabler of aerodynamic drag reduction, lift
increase, mixing enhancement, and noise reduction. Current and future applications have …

Uncertainty quantification serves a central role for simulation-based analysis of physical,
engineering, and biological applications using mechanistic models. From a broad …

Parameter studies are everywhere in computational science. Complex engineering
simulations must run several times with different inputs to effectively study the relationships …

This book results from a course developed by the author and reflects both his own and
collaborative research regarding the development and implementation of uncertainty …

Along with finite differences and finite elements, spectral methods are one of the three main
methodologies for solving partial differential equations on computers. This book provides a …