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Space Reduction for Linear Systems with Local Symmetry

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Abstract

A space reduction method for structural operator equations is proposed in this paper. It turns out that many interface problems derived by applying the idea of domain decomposition can be categorized into this framework. A seemingly simple algebraic technique is proposed to reduce the complexity of operator equations. The connection between this technique and the integral equation method is revealed. Under mild conditions, we prove that the reduced operator equation by space reduction is well-posed, and its solution is the same as that of the original one. As two applications, we apply the proposed method to solve a planar triangular lattice problem and an exterior problem of modified Helmholtz equation with FEM discretization. The numerical evidence validates the effectiveness.

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Acknowledgements

We would like to thank the referees for suggestions which significantly improved the exposition. This work was supported by the Natural Science Foundation of Xinjiang Autonomous Region with No. 2019D01C026, and the National Natural Science Foundation of China (NSFC) under Grant No. 11771248.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, China

    Jia Yin & Chunxiong Zheng

  2. College of Mathematics and Systems Science, Xinjiang University, Urumqi, 830046, China

    Chunxiong Zheng

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  1. Jia Yin
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  2. Chunxiong Zheng
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Correspondence to Jia Yin.

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Yin, J., Zheng, C. Space Reduction for Linear Systems with Local Symmetry. J Sci Comput 89, 59 (2021). https://doi.org/10.1007/s10915-021-01663-0

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  • DOI: https://doi.org/10.1007/s10915-021-01663-0

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