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A cell functional minimization scheme for domain decomposition method on non-orthogonal and non-matching meshes

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Abstract

We are interested in a robust and accurate domain decomposition algorithm with interface conditions of Robin type on non-matching multiblock grids using a cell functional minimization scheme, which has a good performance on non-orthogonal meshes. In order to treat the non-matching grids at the interface, we introduce the \(L^2\) projection operator to ensure weak continuity of the primary unknown and of the normal flux across the non-matching interface. Furthermore, we prove the wellposedness of local and global problems and obtain as well an error estimate of first order in a discrete \(H^{1}\)-norm only using the \(L^{2}\) projection operator on the non-matching interface, as done in the matching case. Numerical results are presented in confirmation of the theoretical results.

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Acknowledgments

The authors thank the anonymous reviewers for their carefully readings and many useful suggestions.

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Authors and Affiliations

  1. Institute of Applied Physics and Computational Mathematics, Beijing, 10088, China

    Li Yin, Jiming Wu & Yanzhong Yao

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  1. Li Yin
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  2. Jiming Wu
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  3. Yanzhong Yao
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Correspondence to Jiming Wu.

Additional information

This work is supported by the National Natural Science Foundation of China (No. 11271053, 91118001, 11135007), the Science Foundation of China Academy of Engineering Physics (No. 2011A0202012, 2013B0202034) and a grant from the Laboratory of Computational Physics.

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Yin, L., Wu, J. & Yao, Y. A cell functional minimization scheme for domain decomposition method on non-orthogonal and non-matching meshes. Numer. Math. 128, 773–804 (2014). https://doi.org/10.1007/s00211-014-0623-3

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  • DOI: https://doi.org/10.1007/s00211-014-0623-3

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