Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rational-based model order reduction of Helmholtz frequency response
  problems with adaptive finite element snapshots   We introduce several spatially adaptive model order reduction approaches
tailored to non-coercive elliptic boundary value problems, specifically,
parametric-in-frequency Helmholtz problems. The offline information is computed
by means of adaptive finite elements, so that each snapshot lives on a
different discrete space that resolves the local singularities of the solution
and is adjusted to the considered frequency value. A rational surrogate is then
assembled adopting either a least-squares or an interpolatory approach,
yielding the standard rational interpolation method (SRI), a vector- or
function-valued version of it ($\mathcal{V}$-SRI), and the minimal rational
interpolation method (MRI). In the context of building an approximation for
linear or quadratic functionals of the Helmholtz solution, we perform several
numerical experiments to compare the proposed methodologies. Our simulations
show that, for interior resonant problems (whose singularities are encoded by
poles on the real axis), the spatially adaptive $\mathcal{V}$-SRI and MRI work
comparably well. Instead, when dealing with exterior scattering problems, whose
frequency response is mostly smooth, the $\mathcal{V}$-SRI method seems to be
the best-performing one.

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The categories of this paper are: math-ph
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The categories of this paper are: adap-org
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The categories of this paper are: stat
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The categories of this paper are: q-fin
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The categories of this paper are: patt-sol
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The categories of this paper are: funct-an
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The categories of this paper are: q-alg
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The categories of this paper are: hep-lat
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The categories of this paper are: dg-ga
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The categories of this paper are: econ
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The categories of this paper are: cond-mat
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The categories of this paper are: astro-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: mtrl-th