During the last years, low‐rank tensor approximation has been established as a new tool in
scientific computing to address large‐scale linear and multilinear algebra problems, which …

This paper revisits a new model reduction methodology based on the use of separated
representations, the so called Proper Generalized Decomposition—PGD. Space and time …

A powerful tool in computational stochastic mechanics is the stochastic finite element
method (SFEM). SFEM is an extension of the classical deterministic FE approach to the …

We propose a method for the approximation of solutions of PDEs with stochastic coefficients
based on the direct, ie, non-adapted, sampling of solutions. This sampling can be done by …

Over the past years, model reduction techniques have become a necessary path for the
reduction of computational requirements in the numerical simulation of complex models. A …

This work proposes and analyzes a stochastic collocation method for solving elliptic partial
differential equations with random coefficients and forcing terms. These input data are …

Mathematical models are widely used in many science disciplines, such as physics, biology
and meteorology. They are aimed at better understanding and explaining real-world …

The main object of this paper is to study the bifurcation, chaotic pattern and traveling wave
solution of the perturbed stochastic nonlinear Schrödinger equation with generalized anti …

This paper demonstrates the use of polynomial chaos expansions for the nonlinear, non-
Gaussian propagation of orbit state uncertainty. Using linear expansions in tensor products …

Many models in polymer processing and composites manufacturing are defined in
degenerated three-dimensional domains, involving plate or shell geometries. The reduction …