Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exponential convergence for multipole and local expansions and their
  translations for sources in layered media: 2-D acoustic wave   In this paper, we will first give a derivation of the multipole expansion
(ME) and local expansion (LE) for the far field from sources in general 2-D
layered media and the multipole-to-local translation (M2L) operator by using
the generating function for Bessel functions. Then, we present a rigorous proof
of the exponential convergence of the ME, LE, and M2L for 2-D Helmholtz
equations in layered media. It is shown that the convergence of ME, LE, and M2L
for the reaction field component of the Green's function depends on a polarized
distance between the target and a polarized image of the source.

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The categories of this paper are: q-bio
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The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
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The categories of this paper are: dg-ga
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an