Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Combining plane wave expansion and variational techniques for fast
  phononic computations   In this paper the salient features of the Plane Wave Expansion (PWE) method
and the mixed variational technique are combined for the fast eigenvalue
computations of arbitrarily complex phononic unit cells. This is done by
expanding the material properties in a Fourier expansion, as is the case with
PWE. The required matrix elements in the variational scheme are identified as
the discrete Fourier transform coefficients of material properties, thus
obviating the need for any explicit integration. The process allows us to
provide succinct and closed form expressions for all the matrices involved in
the mixed variational method. The scheme proposed here preserves both the
simplicity of expression which is inherent in the PWE method and the superior
convergence properties of the mixed variational scheme. We present numerical
results and comment upon the convergence and stability of the current method.
We show that the current representation renders the results of the method
stable over the entire range of the expansion terms as allowed by the spatial
discretization. When compared with a zero order numerical integration scheme,
the present method results in greater computational accuracy of all
eigenvalues. A higher order numerical integration scheme comes close to the
accuracy of the present method but only with significantly more computational
expense.

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The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
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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: nucl-ex
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
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The categories of this paper are: hep-th
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The categories of this paper are: nlin
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The categories of this paper are: physics
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ex
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The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
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The categories of this paper are: stat
32
The categories of this paper are: atom-ph