Adaptation and Enhancement of Generalized Polynomial Chaos for Industrial Applications

Time-dependent generalized polynomial chaos

Article history: Received 11 May 2009 Received in revised form 11 June 2010 Accepted 21 July 2010 Available online 13 August 2010

Generalized polynomial chaos and random oscillators

We present a new approach to obtain solutions for general random oscillators using a broad class of polynomial chaos expansions, which are more efficient than the classical Wiener–Hermite expansions. The approach is general but here we present results for linear oscillators only with random forcing or random coefficients. In this context, we are able to obtain relatively sharp error estimates i...

Performance Evaluation of Generalized Polynomial Chaos

In this paper we review some applications of generalized polynomial chaos expansion for uncertainty quantification. The mathematical framework is presented and the convergence of the method is demonstrated for model problems. In particular, we solve the first-order and second-order ordinary differential equations with random parameters, and examine the efficiency of generalized polynomial chaos...

Classification Algorithms based on Generalized Polynomial Chaos

Multi-Element Generalized Polynomial Chaos for Arbitrary Probability Measures

We develop a multi-element generalized polynomial chaos (ME-gPC) method for arbitrary probability measures and apply it to solve ordinary and partial differential equations with stochastic inputs. Given a stochastic input with an arbitrary probability measure, its random space is decomposed into smaller elements. Subsequently, in each element a new random variable with respect to a conditional ...