Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stable Multiscale Petrov-Galerkin Finite Element Method for High
  Frequency Acoustic Scattering   We present and analyze a pollution-free Petrov-Galerkin multiscale finite
element method for the Helmholtz problem with large wave number $\kappa$ as a
variant of [Peterseim, ArXiv:1411.1944, 2014]. We use standard continuous $Q_1$
finite elements at a coarse discretization scale $H$ as trial functions,
whereas the test functions are computed as the solutions of local problems at a
finer scale $h$. The diameter of the support of the test functions behaves like
$mH$ for some oversampling parameter $m$. Provided $m$ is of the order of
$\log(\kappa)$ and $h$ is sufficiently small, the resulting method is stable
and quasi-optimal in the regime where $H$ is proportional to $\kappa^{-1}$. In
homogeneous (or more general periodic) media, the fine scale test functions
depend only on local mesh-configurations. Therefore, the seemingly high cost
for the computation of the test functions can be drastically reduced on
structured meshes. We present numerical experiments in two and three space
dimensions.

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The categories of this paper are: mtrl-th
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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-ex
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The categories of this paper are: cs
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The categories of this paper are: hep-ph
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The categories of this paper are: adap-org
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The categories of this paper are: hep-th
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-th
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The categories of this paper are: funct-an
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The categories of this paper are: comp-gas
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The categories of this paper are: chem-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph
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The categories of this paper are: dg-ga