Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Hierarchical Preconditioning of the PMCHWT Integral Equation on
  Simply and Multiply Connected Geometries   We present a hierarchical basis preconditioning strategy for the
Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) integral equation considering
both simply and multiply connected geometries.To this end, we first consider
the direct application of hierarchical basis preconditioners, developed for the
Electric Field Integral Equation (EFIE), to the PMCHWT. It is notably found
that, whereas for the EFIE a diagonal preconditioner can be used for obtaining
the hierarchical basis scaling factors, this strategy is catastrophic in the
case of the PMCHWT since it leads to a severly ill-conditioned PMCHWT system in
the case of multiply connected geometries. We then proceed to a theoretical
analysis of the effect of hierarchical bases on the PMCHWT operator for which
we obtain the correct scaling factors and a provably effective preconditioner
for both low frequencies and mesh refinements. Numerical results will
corroborate the theory and show the effectiveness of our approach.

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The categories of this paper are: cmp-lg
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The categories of this paper are: nlin
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The categories of this paper are: stat
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The categories of this paper are: comp-gas
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The categories of this paper are: acc-phys
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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: patt-sol
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The categories of this paper are: chao-dyn
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The categories of this paper are: cond-mat
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-th
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The categories of this paper are: funct-an