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A regularized domain decomposition method with Lagrange multiplier

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Abstract

In this paper, we are concerned with the nonoverlapping domain decomposition method with Lagrange multiplier for three-dimensional second-order elliptic problems with no zeroth-order term. It is known that the methods result in a singular subproblem on each internal (floating) subdomain. To handle the singularity, we propose a regularization technique which transforms the corresponding singular problems into approximate positive definite problems. For the regularized method, one can build the interface equation of the multiplier directly. We first derive an optimal error estimate of the regularized approximation, and then develop a cheap preconditioned iterative method for solving the interface equation. For the new method, the cost of computation will not be increased comparing the case without any floating subdomain. The effectiveness of the new method will be confirmed by both theoretical analyzes and numerical experiments.

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Authors and Affiliations

  1. Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing, 100080, China

    Qiya Hu

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  1. Qiya Hu
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Correspondence to Qiya Hu.

Additional information

Communicated by Achui Zhou

The work is supported by Natural Science Foundation of China G10371129.

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Hu, Q. A regularized domain decomposition method with Lagrange multiplier. Adv Comput Math 26, 367–401 (2007). https://doi.org/10.1007/s10444-004-4094-4

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  • DOI: https://doi.org/10.1007/s10444-004-4094-4

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