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Parallel finite element computation of incompressible magnetohydrodynamics based on three iterations

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Abstract

Based on local algorithms, some parallel finite element (FE) iterative methods for stationary incompressible magnetohydrodynamics (MHD) are presented. These approaches are on account of two-grid skill include two major phases: find the FE solution by solving the nonlinear system on a globally coarse mesh to seize the low frequency component of the solution, and then locally solve linearized residual subproblems by one of three iterations (Stokes-type, Newton, and Oseen-type) on subdomains with fine grid in parallel to approximate the high frequency component. Optimal error estimates with regard to two mesh sizes and iterative steps of the proposed algorithms are given. Some numerical examples are implemented to verify the algorithm.

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Acknowledgements

The authors would like to thank the editors and referees for their helpful suggestions.

Funding

Project supported by the National Natural Science Foundation of China (Nos. 11971410 and 12071404), the Natural Science Foundation of Hunan Province of China (No. 2019JJ40279), the Excellent Youth Program of Scientific Research Project of Hunan Provincial Department of Education (Nos. 18B064 and 20B564), the China Postdoctoral Science Foundation (Nos. 2018T110073 and 2018M631402), and the International Scientific and Technological Innovation Cooperation Base of Hunan Province for Computational Science (No. 2018WK4006)

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  1. Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Key Laboratory of Intelligent Computing & Information Processing of Ministry of Education, School of Mathematics and Computational Science, Xiangtan University, Xiangtan, Hunan Province, 411105, China

    Qili Tang & Yunqing Huang

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  1. Qili Tang
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  2. Yunqing Huang
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Correspondence to Qili Tang.

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Citation: TANG, Q. L. and HUANG, Y. Q. Parallel finite element computation of incompressible magnetohydrodynamics based on three iterations. Applied Mathematics and Mechanics (English Edition), 43(1), 141–154 (2022) https://doi.org/10.1007/s10483-022-2802-7

Project supported by the National Natural Science Foundation of China (Nos. 11971410 and 12071404), the Natural Science Foundation of Hunan Province of China (No. 2019JJ40279), the Excellent Youth Program of Scientific Research Project of Hunan Provincial Department of Education (Nos. 18B064 and 20B564), the China Postdoctoral Science Foundation (Nos. 2018T110073 and 2018M631402), and the International Scientific and Technological Innovation Cooperation Base of Hunan Province for Computational Science (No. 2018WK4006)

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Tang, Q., Huang, Y. Parallel finite element computation of incompressible magnetohydrodynamics based on three iterations. Appl. Math. Mech.-Engl. Ed. 43, 141–154 (2022). https://doi.org/10.1007/s10483-022-2802-7

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  • DOI: https://doi.org/10.1007/s10483-022-2802-7

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