Global sensitivity analysis (SA) aims at quantifying the respective effects of input random
variables (or combinations thereof) onto the variance of the response of a physical or …

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 …

State-of-the-art computer codes for simulating real physical systems are often characterized
by vast number of input parameters. Performing uncertainty quantification (UQ) tasks with …

The@ first graduate-level textbook to focus on fundamental aspects of numerical methods
for stochastic computations, this book describes the class of numerical methods based on …

Mathematical and numerical modelling of the cardiovascular system is a research topic that
has attracted remarkable interest from the mathematical community because of its intrinsic …

Recently there has been a growing interest in designing efficient methods for the solution of
ordinary/partial differential equations with random inputs. To this end, stochastic Galerkin …

In this paper we propose and analyze a stochastic collocation method to solve elliptic partial
differential equations with random coefficients and forcing terms (input data of the model) …

This work proposes and analyzes a Smolyak-type sparse grid stochastic collocation method
for the approximation of statistical quantities related to the solution of partial differential …

We propose an efficient Monte Carlo simulation method to address the multivariate
uncertainties in acoustic–vibration interaction systems. The deep neural network acts as a …

This paper presents a review of the current state-of-the-art of numerical methods for
stochastic computations. The focus is on efficient high-order methods suitable for practical …