Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Domain Decomposition Methods based on quasi-optimal transmission
  operators for the solution of Helmholtz transmission problems   We present non-overlapping Domain Decomposition Methods (DDM) based on
quasi-optimal transmission operators for the solution of Helmholtz transmission
problems with piece-wise constant material properties. The quasi-optimal
transmission boundary conditions incorporate readily available approximations
of Dirichlet-to-Neumann operators. These approximations consist of either
complexified hypersingular boundary integral operators for the Helmholtz
equation or square root Fourier multipliers with complex wavenumbers. We show
that under certain regularity assumptions on the closed interface of material
discontinuity, the DDM with quasi-optimal transmission conditions are
well-posed. We present a DDM framework based on Robin-to-Robin (RtR) operators
that can be computed robustly via boundary integral formulations. More
importantly, the use of quasi-optimal transmission operators results in DDM
that converge in small numbers of iterations even in the challenging
high-contrast, high-frequency regime of Helmholtz transmission problems.
Furthermore, the DDM presented in this text require only minor modifications to
handle the case of transmission problems in partially coated domains, while
still maintaining excellent convergence properties. We also investigate the
dependence of the DDM iterative performance on the number of subdomains.

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The categories of this paper are: nucl-th
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The categories of this paper are: q-alg
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The categories of this paper are: funct-an
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The categories of this paper are: gr-qc
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The categories of this paper are: adap-org
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The categories of this paper are: quant-ph
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The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
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The categories of this paper are: nlin
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The categories of this paper are: acc-phys
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-lat
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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: patt-sol