Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Convergence of HX Preconditioner for Maxwell's Equations with Jump
  Coefficients (ii): The Main Results   This paper is the second one of two serial articles, whose goal is to prove
convergence of HX Preconditioner (proposed by Hiptmair and Xu, 2007) for
Maxwell's equations with jump coefficients. In this paper, based on the
auxiliary results developed in the first paper (Hu, 2017), we establish a new
regular Helmholtz decomposition for edge finite element functions in three
dimensions, which is nearly stable with respect to a weight function. By using
this Helmholtz decomposition, we give an analysis of the convergence of the HX
preconditioner for the case with strongly discontinuous coefficients. We show
that the HX preconditioner possesses fast convergence, which not only is nearly
optimal with respect to the finite element mesh size but also is independent of
the jumps in the coefficients across the interface between two neighboring
subdomains.

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The categories of this paper are: funct-an
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-th
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The categories of this paper are: adap-org
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The categories of this paper are: solv-int
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The categories of this paper are: math-ph
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The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
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The categories of this paper are: alg-geom
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-lat
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The categories of this paper are: eess
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-ex
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The categories of this paper are: ao-sci
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The categories of this paper are: astro-ph