Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Analysis of a New Harmonically Enriched Multiscale Coarse Space for
  Domain Decomposition Methods   We propose a new, harmonically enriched multiscale coarse space (HEM) for
domain decomposition methods. For a coercive high contrast model problem, we
show how to enrich the coarse space so that the method is robust against any
variations and discontinuities in the problem parameters both inside subdomains
and across and along subdomain boundaries. We prove our results for an
enrichment strategy based on solving simple, lower dimensional eigenvalue
problems on the interfaces between subdomains, and we call the resulting coarse
space the spectral harmonically enriched multiscale coarse space (SHEM). We
then also give a variant that performs equally well in practice, and does not
require the solve of eigenvalue problems, which we call non-spectral
harmonically enriched multiscale coarse space (NSHEM). Our enrichment process
naturally reaches the optimal coarse space represented by the full discrete
harmonic space, which enables us to turn the method into a direct solver
(OHEM). We also extensively test our new coarse spaces numerically, and the
results confirm our analysis

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The categories of this paper are: math-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
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The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
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The categories of this paper are: quant-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-th
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The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ph
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The categories of this paper are: cond-mat
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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: supr-con