To be or not to be intrusive? The solution of parametric and stochastic equations --- Proper Generalized Decomposition
Abstract
A numerical method is proposed to compute a low-rank Galerkin approximation to the solution of a parametric or stochastic equation in a non-intrusive fashion. The considered nonlinear problems are associated with the minimization of a parameterized differentiable convex functional. We first introduce a bilinear parameterization of fixed-rank tensors and employ an alternating minimization scheme for computing the low-rank approximation. In keeping with the idea of non-intrusiveness, at each step of the algorithm the minimizations are carried out with a quasi-Newton method to avoid the computation of the Hessian. The algorithm is made non-intrusive through the use of numerical integration. It only requires the evaluation of residuals at specific parameter values. The algorithm is then applied to two numerical examples.
Keywords
Cite
@article{arxiv.1405.0875,
title = {To be or not to be intrusive? The solution of parametric and stochastic equations --- Proper Generalized Decomposition},
author = {Loïc Giraldi and Dishi Liu and Hermann G. Matthies and Anthony Nouy},
journal= {arXiv preprint arXiv:1405.0875},
year = {2017}
}