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Journal of Scientific Computing

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20-02-2018

A Concurrent Global–Local Numerical Method for Multiscale PDEs

Authors: Yufang Huang, Jianfeng Lu, Pingbing Ming

Published in: Journal of Scientific Computing | Issue 2/2018

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Abstract

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.

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Title: A Concurrent Global–Local Numerical Method for Multiscale PDEs
Authors: Yufang Huang
Jianfeng Lu
Pingbing Ming
Publication date: 20-02-2018
Publisher: Springer US
Published in: Journal of Scientific Computing / Issue 2/2018
Print ISSN: 0885-7474
Electronic ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-018-0662-5

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