TY - JOUR
T1 - Robust preconditioners for incompressible MHD models
AU - Ma, Yicong
AU - Hu, Kaibo
AU - Hu, Xiaozhe
AU - Xu, Jinchao
N1 - Publisher Copyright:
© 2016.
PY - 2016/7/1
Y1 - 2016/7/1
N2 - In this paper, we develop two classes of robust preconditioners for the structure-preserving discretization of the incompressible magnetohydrodynamics (MHD) system. By studying the well-posedness of the discrete system, we design block preconditioners for them and carry out rigorous analysis on their performance. We prove that such preconditioners are robust with respect to most physical and discretization parameters. In our proof, we improve the existing estimates of the block triangular preconditioners for saddle point problems by removing the scaling parameters, which are usually difficult to choose in practice. This new technique is applicable not only to the MHD system, but also to other problems. Moreover, we prove that Krylov iterative methods with our preconditioners preserve the divergence-free condition exactly, which complements the structure-preserving discretization. Another feature is that we can directly generalize this technique to other discretizations of the MHD system. We also present preliminary numerical results to support the theoretical results and demonstrate the robustness of the proposed preconditioners.
AB - In this paper, we develop two classes of robust preconditioners for the structure-preserving discretization of the incompressible magnetohydrodynamics (MHD) system. By studying the well-posedness of the discrete system, we design block preconditioners for them and carry out rigorous analysis on their performance. We prove that such preconditioners are robust with respect to most physical and discretization parameters. In our proof, we improve the existing estimates of the block triangular preconditioners for saddle point problems by removing the scaling parameters, which are usually difficult to choose in practice. This new technique is applicable not only to the MHD system, but also to other problems. Moreover, we prove that Krylov iterative methods with our preconditioners preserve the divergence-free condition exactly, which complements the structure-preserving discretization. Another feature is that we can directly generalize this technique to other discretizations of the MHD system. We also present preliminary numerical results to support the theoretical results and demonstrate the robustness of the proposed preconditioners.
KW - Field-of-values analysis
KW - Incompressible MHD
KW - Robust preconditioners
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U2 - 10.1016/j.jcp.2016.04.019
DO - 10.1016/j.jcp.2016.04.019
M3 - Article
AN - SCOPUS:84964466882
SN - 0021-9991
VL - 316
SP - 721
EP - 746
JO - Journal of Computational Physics
JF - Journal of Computational Physics
ER -