High-order finite difference methods are efficient, easy to program, scale well in multiple
dimensions and can be modified locally for various reasons (such as shock treatment for …

Prudent and sensible deployment of local storage may unlock the potential of mitigating the
adverse impact, especially addressing the challenge of uncertainty from independent …

In this paper, a new path integration method is proposed for stochastic dynamical systems
excited by Poisson white noise. An efficient one-step transition probability density function …

Engine design heavily relies on numerical simulation of engine environments, which greatly
accelerates the design iteration and increases efficiency. Nonetheless, for a long time, the …

A projection-based formulation is presented for non-linear model reduction of problems with
extreme scale disparity. The approach allows for the selection of an arbitrary, but complete …

In the last few years, several methods have been developed to deal with jump singularities
in parametric or stochastic hyperbolic PDEs. They typically use some alignment of the jump …

Stochastic Galerkin formulations of the two-dimensional shallow water systems
parameterized with random variables may lose hyperbolicity, and hence change the nature …

A stochastic Galerkin formulation for a stochastic system of balanced or conservation laws
may fail to preserve the hyperbolicity of the original system. In this work, we develop a …

Quantifying uncertainties in hyperbolic equations is a source of several challenges. First, the
solution forms shocks leading to oscillatory behavior in the numerical approximation of the …

Kinetic equations play a major rule in modeling large systems of interacting particles.
Recently the legacy of classical kinetic theory found novel applications in socio-economic …