Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Improved guaranteed computable bounds on homogenized properties of
  periodic media by Fourier-Galerkin method with exact integration   Moulinec and Suquet introduced FFT-based homogenization in 1994, and twenty
years later, their approach is still effective for evaluating the homogenized
properties arising from the periodic cell problem. This paper builds on the
author's (2013) variational reformulation approximated by trigonometric
polynomials establishing two numerical schemes: Galerkin approximation (Ga) and
a version with numerical integration (GaNi). The latter approach, fully
equivalent to the original Moulinec-Suquet algorithm, was used to evaluate
guaranteed upper-lower bounds on homogenized coefficients incorporating a
closed-form double grid quadrature. Here, these concepts, based on the primal
and the dual formulations, are employed for the Ga scheme. For the same
computational effort, the Ga outperforms the GaNi with more accurate guaranteed
bounds and more predictable numerical behaviors. Quadrature technique leading
to block-sparse linear systems is extended here to materials defined via
high-resolution images in a way which allows for effective treatment using the
FFT. Memory demands are reduced by a reformulation of the double to the
original grid scheme using FFT shifts. Minimization of the bounds during
iterations of conjugate gradients is effective, particularly when incorporating
a solution from a coarser grid. The methodology presented here for the scalar
linear elliptic problem could be extended to more complex frameworks.

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The categories of this paper are: gr-qc
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The categories of this paper are: q-alg
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The categories of this paper are: mtrl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: nlin
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The categories of this paper are: hep-ph
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The categories of this paper are: solv-int
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The categories of this paper are: eess
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The categories of this paper are: chem-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: funct-an
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The categories of this paper are: stat
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The categories of this paper are: chao-dyn
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The categories of this paper are: quant-ph