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