Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An O(N) and parallel approach to integral problems by a
  kernel-independent fast multipole method: Application to polarization and
  magnetization of interacting particles   Large classes of materials systems in physics and engineering are governed by
magnetic and electrostatic interactions. Continuum or mesoscale descriptions of
such systems can be cast in terms of integral equations, whose direct
computational evaluation requires O(N^2) operations, where N is the number of
unknowns. Such a scaling, which arises from the many-body nature of the
relevant Green's function, has precluded wide-spread adoption of integral
methods for solution of large-scale scientific and engineering problems. In
this work, a parallel computational approach is presented that relies on using
scalable open source libraries and utilizes a kernel-independent Fast Multipole
Method to evaluate the integrals in O(N) operations, with O(N) memory cost,
thereby substantially improving the scalability and efficiency of computational
integral methods. We demonstrate the accuracy, efficiency, and scalability of
our approach in the contest of two examples. In the first, we solve a boundary
value problem for a ferroelectric/ferromagnetic volume in free space. In the
second, we solve an electrostatic problem involving polarizable dielectric
bodies in an unbounded dielectric medium. The results from these test cases
show that our parallel approach, which is built on a kernel-independent FMM,
can enable highly efficient and accurate simulations and allow for considerable
flexibility in a broad range of applications.

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The categories of this paper are: astro-ph
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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: supr-con
36
The categories of this paper are: cmp-lg
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The categories of this paper are: math-ph
1
The categories of this paper are: cs
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The categories of this paper are: comp-gas
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The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: math
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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: hep-lat