Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Robust Preconditioners for Incompressible MHD Models   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 not only applicable 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.

31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
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The categories of this paper are: supr-con
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The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-lat
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The categories of this paper are: plasm-ph
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The categories of this paper are: math-ph
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The categories of this paper are: eess
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The categories of this paper are: patt-sol
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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga