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 …

The quantification of probabilistic uncertainties in the outputs of physical, biological, and
social systems governed by partial differential equations with random inputs require, in …

Explicit time integration schemes coupled with Galerkin discretizations of time-dependent
partial differential equations require solving a linear system with the mass matrix at each …

We apply the tensor train (TT) decomposition to construct the tensor product polynomial
chaos expansion (PCE) of a random field, to solve the stochastic elliptic diffusion PDE with …

The solution of PDE with stochastic data commonly leads to very high-dimensional algebraic
problems, eg when multiplicative noise is present. The Stochastic Galerkin FEM considered …

For parametrised equations, which arise, for example, in equations dependent on random
parameters, the solution naturally lives in a tensor product space. The application which we …

We consider the numerical solution of a steady-state diffusion problem where the diffusion
coefficient is the exponent of a random field. The standard stochastic Galerkin formulation of …

Stochastic Galerkin finite element approximation of PDEs with random inputs leads to linear
systems of equations with coefficient matrices that have a characteristic Kronecker product …

The goal of this paper is the efficient numerical simulation of optimization problems
governed by either steady-state or unsteady partial differential equations involving random …

In this article we introduce new methods for the analysis of high dimensional data in tensor
formats, where the underling data come from the stochastic elliptic boundary value problem …