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MONOLITHIC MULTIGRID FOR REDUCED MAGNETOHYDRODYNAMIC EQUATIONS

Xiaodi Zhang1,2, Weiying Zheng1,2   

  1. 1. LSEC, NCMIS, Institute of Computational Mathematics and Scientific Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China;
    2. School of Mathematical Science, University of Chinese Academy of Sciences, Beijing 100049, China
  • Received:2020-03-25 Revised:2020-03-25 Published:2021-04-12
  • Contact: Weiying Zheng,Email:zwy@lsec.cc.ac.cn
  • Supported by:
    Weiying Zheng was supported in part by the National Science Fund for Distinguished Young Scholars 11725106 and China NSF grant 11831016.

Xiaodi Zhang, Weiying Zheng. MONOLITHIC MULTIGRID FOR REDUCED MAGNETOHYDRODYNAMIC EQUATIONS[J]. Journal of Computational Mathematics, 2021, 39(3): 453-470.

In this paper, the monolithic multigrid method is investigated for reduced magnetohydrodynamic equations. We propose a diagonal Braess-Sarazin smoother for the finite element discrete system and prove the uniform convergence of the MMG method with respect to mesh sizes. A multigrid-preconditioned FGMRES method is proposed to solve the magnetohydrodynamic equations. It turns out to be robust for relatively large physical parameters. By extensive numerical experiments, we demonstrate the optimality of the monolithic multigrid method with respect to the number of degrees of freedom.

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