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A Concurrent Global–Local Numerical Method for Multiscale PDEs

Publication ,  Journal Article
Huang, Y; Lu, J; Ming, P
Published in: Journal of Scientific Computing
August 1, 2018

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.

Duke Scholars

Published In

Journal of Scientific Computing

DOI

ISSN

0885-7474

Publication Date

August 1, 2018

Volume

76

Issue

2

Start / End Page

1188 / 1215

Related Subject Headings

  • Applied Mathematics
  • 4903 Numerical and computational mathematics
  • 4901 Applied mathematics
  • 0802 Computation Theory and Mathematics
  • 0103 Numerical and Computational Mathematics
  • 0102 Applied Mathematics
 

Citation

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Huang, Y., Lu, J., & Ming, P. (2018). A Concurrent Global–Local Numerical Method for Multiscale PDEs. Journal of Scientific Computing, 76(2), 1188–1215. https://doi.org/10.1007/s10915-018-0662-5
Huang, Y., J. Lu, and P. Ming. “A Concurrent Global–Local Numerical Method for Multiscale PDEs.” Journal of Scientific Computing 76, no. 2 (August 1, 2018): 1188–1215. https://doi.org/10.1007/s10915-018-0662-5.
Huang Y, Lu J, Ming P. A Concurrent Global–Local Numerical Method for Multiscale PDEs. Journal of Scientific Computing. 2018 Aug 1;76(2):1188–215.
Huang, Y., et al. “A Concurrent Global–Local Numerical Method for Multiscale PDEs.” Journal of Scientific Computing, vol. 76, no. 2, Aug. 2018, pp. 1188–215. Scopus, doi:10.1007/s10915-018-0662-5.
Huang Y, Lu J, Ming P. A Concurrent Global–Local Numerical Method for Multiscale PDEs. Journal of Scientific Computing. 2018 Aug 1;76(2):1188–1215.
Journal cover image

Published In

Journal of Scientific Computing

DOI

ISSN

0885-7474

Publication Date

August 1, 2018

Volume

76

Issue

2

Start / End Page

1188 / 1215

Related Subject Headings

  • Applied Mathematics
  • 4903 Numerical and computational mathematics
  • 4901 Applied mathematics
  • 0802 Computation Theory and Mathematics
  • 0103 Numerical and Computational Mathematics
  • 0102 Applied Mathematics