Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The effective conductivity of arrays of squares: large random unit cells
  and extreme contrast ratios   An integral equation based scheme is presented for the fast and accurate
computation of effective conductivities of two-component checkerboard-like
composites with complicated unit cells at very high contrast ratios. The scheme
extends recent work on multi-component checkerboards at medium contrast ratios.
General improvement include the simplification of a long-range preconditioner,
the use of a banded solver, and a more efficient placement of quadrature
points. This, together with a reduction in the number of unknowns, allows for a
substantial increase in achievable accuracy as well as in tractable system
size. Results, accurate to at least nine digits, are obtained for random
checkerboards with over a million squares in the unit cell at contrast ratio
10^6. Furthermore, the scheme is flexible enough to handle complex valued
conductivities and, using a homotopy method, purely negative contrast ratios.
Examples of the accurate computation of resonant spectra are given.

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The categories of this paper are: q-fin
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-ex
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The categories of this paper are: eess
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The categories of this paper are: nucl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: econ
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The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ph
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The categories of this paper are: q-alg
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The categories of this paper are: ao-sci
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The categories of this paper are: q-bio
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The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg