This chapter reviews techniques of model reduction of fluid dynamics systems. Fluid systems
are known to be difficult to reduce efficiently due to several reasons. First of all, they exhibit …

The accurate approximation of high-dimensional functions is an essential task in uncertainty
quantification and many other fields. We propose a new function approximation scheme …

The hydraulic fracturing is a nonlinear, fluid-solid coupling and transient problem, in most
cases it is always time-consuming to simulate this process numerically. In recent years …

We present a brief survey on the modern tensor numerical methods for multidimensional
stationary and time-dependent partial differential equations (PDEs). The guiding principle of …

Tensor methods are among the most prominent tools for the numerical solution of high-
dimensional problems where functions of multiple variables have to be approximated. These …

The computational cost of parametric studies currently represents the major limitation to the
application of simulation-based engineering techniques in a daily industrial environment …

The major challenge industrial applications of uncertainty quantification (UQ) are facing, is
the curse of dimensionality as a result of a large number of uncertainties. In this work, an …

This work proposes a stochastic domain decomposition method for solving steady-state
partial differential equations (PDEs) with random inputs. Specifically, based on the efficiency …

In this article, we develop and validate an a priori Reduced-Order Model (ROM) of neutron
transport separated in energy by Proper Generalized Decomposition (PGD) as applied to …

This article presents a proper generalized decomposition (PGD) based Padé approximant
for efficient analysis of the stochastic frequency response. Due to the high nonlinearity of the …