A dynamically bi-orthogonal method for time-dependent stochastic partial differential equations II: Adaptivity and generalizations

Mulin Cheng Thomas Y Hou Zhiwen Zhang

Numerical Analysis and Scientific Computing mathscidoc:1912.431037

Journal of Computational Physics, 242, 753-776, 2013.6
This is part II of our paper in which we propose and develop a dynamically bi-orthogonal method (DyBO) to study a class of time-dependent stochastic partial differential equations (SPDEs) whose solutions enjoy a low-dimensional structure. In part I of our paper [9], we derived the DyBO formulation and proposed numerical algorithms based on this formulation. Some important theoretical results regarding consistency and bi-orthogonality preservation were also established in the first part along with a range of numerical examples to illustrate the effectiveness of the DyBO method. In this paper, we focus on the computational complexity analysis and develop an effective adaptivity strategy to add or remove modes dynamically. Our complexity analysis shows that the ratio of computational complexities between the DyBO method and a generalized polynomial chaos method (gPC) is roughly of order O ((m/N p) 3) for a
No keywords uploaded!
[ Download ] [ 2019-12-24 21:14:11 uploaded by Zhiwen_Zhang ] [ 788 downloads ] [ 0 comments ]
@inproceedings{mulin2013a,
  title={A dynamically bi-orthogonal method for time-dependent stochastic partial differential equations II: Adaptivity and generalizations},
  author={Mulin Cheng, Thomas Y Hou, and Zhiwen Zhang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224211411768751601},
  booktitle={Journal of Computational Physics},
  volume={242},
  pages={753-776},
  year={2013},
}
Mulin Cheng, Thomas Y Hou, and Zhiwen Zhang. A dynamically bi-orthogonal method for time-dependent stochastic partial differential equations II: Adaptivity and generalizations. 2013. Vol. 242. In Journal of Computational Physics. pp.753-776. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224211411768751601.
Please log in for comment!
 
 
Contact us: office-iccm@tsinghua.edu.cn | Copyright Reserved