Parametric Analytical Preconditioning and its Applications to the Reduced Collocation Methods
Numerical Analysis
2014-03-31 v1
Abstract
In this paper, we extend the recently developed reduced collocation method \cite{ChenGottlieb} to the nonlinear case, and propose two analytical preconditioning strategies. One is parameter independent and easy to implement, the other one has the traditional affinity with respect to the parameters which allows for efficient implementation through an offline-online decomposition. Overall, the preconditioning improves the quality of the error estimation uniformly on the parameter domain, and speeds up the convergence of the reduced solution to the truth approximation.
Keywords
Cite
@article{arxiv.1403.7273,
title = {Parametric Analytical Preconditioning and its Applications to the Reduced Collocation Methods},
author = {Yanlai Chen and Sigal Gottlieb and Yvon Maday},
journal= {arXiv preprint arXiv:1403.7273},
year = {2014}
}