期刊
MATHEMATICAL AND COMPUTER MODELLING OF DYNAMICAL SYSTEMS
卷 17, 期 4, 页码 395-422出版社
TAYLOR & FRANCIS INC
DOI: 10.1080/13873954.2011.547670
关键词
parabolic partial differential equations; certified reduced basis; a posteriori error estimation; POD/Greedy; hp reduced basis; convection-diffusion; Boussinesq natural convection
资金
- Norwegian University of Science and Technology
- AFOSR [FA9550-07-1-0425]
- OSD/AFOSR [FA9550-09-1-0613]
In this article, we introduce an hp certified reduced basis (RB) method for parabolic partial differential equations. We invoke a Proper Orthogonal Decomposition (POD) (in time)/Greedy (in parameter) sampling procedure first in the initial partition of the parameter domain (h-refinement) and subsequently in the construction of RB approximation spaces restricted to each parameter subdomain (p-refinement). We show that proper balance between additional POD modes and additional parameter values in the initial subdivision process guarantees convergence of the approach. We present numerical results for two model problems: linear convection-diffusion and quadratically non-linear Boussinesq natural convection. The new procedure is significantly faster (more costly) in the RB Online (Offline) stage.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据