A unified framework for mesh refinement in random and physical space

JOURNAL OF COMPUTATIONAL PHYSICS

卷:323

Article

Li, Jing¹  Stinis, Panos¹ 

[1] Pacific Northwest Natl Lab, Richland, WA 99352 USA

关键词: Adaptive mesh refinement;    Multi-element;    gPC;    Uncertainty quantification;    Discontinuities;   

DOI  :  10.1016/j.jcp.2016.07.027

来源: Elsevier

【 摘 要 】

In recent work we have shown how an accurate reduced model can be utilized to perform mesh refinement in random space. That work relied on the explicit knowledge of an accurate reduced model which is used to monitor the transfer of activity from the large to the small scales of the solution. Since this is not always available, we present in the current work a framework which shares the merits and basic idea of the previous approach but does not require an explicit knowledge of a reduced model. Moreover, the current framework can be applied for refinement in both random and physical space. In this manuscript we focus on the application to random space mesh refinement. We study examples of increasing difficulty (from ordinary to partial differential equations) which demonstrate the efficiency and versatility of our approach. We also provide some results from the application of the new framework to physical space mesh refinement. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free