A Concurrent Global–Local Numerical Method for Multiscale PDEs

Published

Journal Article

© 2018, Springer Science+Business Media, LLC, part of Springer Nature. We present a new hybrid numerical method for multiscale partial differential equations, which simultaneously captures the global macroscopic information and resolves the local microscopic events over regions of relatively small size. The method couples concurrently the microscopic coefficients in the region of interest with the homogenized coefficients elsewhere. The cost of the method is comparable to the heterogeneous multiscale method, while being able to recover microscopic information of the solution. The convergence of the method is proved for problems with bounded and measurable coefficients, while the rate of convergence is established for problems with rapidly oscillating periodic or almost-periodic coefficients. Numerical results are reported to show the efficiency and accuracy of the proposed method.

Full Text

Duke Authors

Cited Authors

  • Huang, Y; Lu, J; Ming, P

Published Date

  • August 1, 2018

Published In

Volume / Issue

  • 76 / 2

Start / End Page

  • 1188 - 1215

International Standard Serial Number (ISSN)

  • 0885-7474

Digital Object Identifier (DOI)

  • 10.1007/s10915-018-0662-5

Citation Source

  • Scopus