Random sampling and efficient algorithms for multiscale pdes
Journal Article (Journal Article)
We describe a numerical framework that uses random sampling to efficiently capture low-rank local solution spaces of multiscale PDE problems arising in domain decomposition. In contrast to existing techniques, our method does not rely on detailed analytical understanding of specific multiscale PDEs, in particular, their asymptotic limits. We present the application of the framework on two examples-a linear kinetic equation and an elliptic equation with rough media. On these two examples, this framework achieves the asymptotic preserving property for the kinetic equations and numerical homogenization for the elliptic equations.
Full Text
Duke Authors
Cited Authors
- Chen, K; Li, Q; Lu, J; Wright, SJ
Published Date
- January 1, 2020
Published In
Volume / Issue
- 42 / 5
Start / End Page
- A2974 - A3005
Electronic International Standard Serial Number (EISSN)
- 1095-7197
International Standard Serial Number (ISSN)
- 1064-8275
Digital Object Identifier (DOI)
- 10.1137/18M1207430
Citation Source
- Scopus