Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Random Sampling and Efficient Algorithms for Multiscale PDEs   We describe a numerical framework that uses random sampling to efficiently
capture low-rank local solution spaces of multiscale PDE problems arising in
domain decomposition. In contrast to existing techniques, our method does not
rely on detailed analytical understanding of specific multiscale PDEs, in
particular, their asymptotic limits. We present the application of the
framework on two examples --- a linear kinetic equation and an elliptic
equation with rough media. On these two examples, this framework achieves the
asymptotic preserving property for the kinetic equations and numerical
homogenization for the elliptic equations.

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The categories of this paper are: hep-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: gr-qc
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The categories of this paper are: physics
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The categories of this paper are: supr-con
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The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
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The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ph
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The categories of this paper are: eess
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The categories of this paper are: math-ph
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The categories of this paper are: solv-int
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The categories of this paper are: stat
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The categories of this paper are: econ