Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rapidly convergent representations for 2D and 3D Green's functions for a
  linear periodic array of dipole sources   Hybrid spectral-spatial representations are introduced to rapidly calculate
periodic scalar and dyadic Green's functions of the Helmholtz equation for 2D
and 3D configurations with a 1D (linear) periodicity. The presented schemes
work seamlessly for any observation location near the array and for any
practical array periodicities, including electrically small and large
periodicities. The representations are based on the expansion of the periodic
Green's functions in terms of the continuous spectral integrals over the
transverse (to the array) spectral parameters. To achieve high convergence and
numerical efficiency, the introduced integral representations are cast in a
hybrid form in terms of (i) a small number of contributions due to sources
located around the unit cell of interest, (ii) a small number of symmetric
combinations of the Floquet modes, and (iii) an integral evaluated along the
steepest descent path (SDP). The SDP integral is regularized by extracting the
singular behavior near the saddle point of the integrand and integrating the
extracted components in closed form. Efficient quadrature rules are established
to evaluate this integral using a small number of quadrature nodes with
arbitrary small error for a wide range of structure parameters. Strengths of
the introduced approach are demonstrated via extensive numerical examples.

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The categories of this paper are: supr-con
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The categories of this paper are: ao-sci
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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: nucl-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: quant-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: nlin
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The categories of this paper are: astro-ph
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The categories of this paper are: q-bio
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The categories of this paper are: gr-qc
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The categories of this paper are: cmp-lg
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The categories of this paper are: chem-ph