Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A preconditioned iterative solver for the scattering solutions of the
  Schr\"odinger equation   The Schr\"odinger equation defines the dynamics of quantum particles which
has been an area of unabated interest in physics. We demonstrate how simple
transformations of the Schr\"odinger equation leads to a coupled linear system,
whereby each diagonal block is a high frequency Helmholtz problem. Based on
this model, we derive indefinite Helmholtz model problems with strongly varying
wavenumbers. We employ the iterative approach for their solution. In
particular, we develop a preconditioner that has its spectrum restricted to a
quadrant (of the complex plane) thereby making it easily invertible by
multigrid methods with standard components. This multigrid preconditioner is
used in conjuction with suitable Krylov-subspace methods for solving the
indefinite Helmholtz model problems. The aim of this study is to report the
feasbility of this preconditioner for the model problems. We compare this idea
with the other prevalent preconditioning ideas, and discuss its merits. Results
of numerical experiments are presented, which complement the proposed ideas,
and show that this preconditioner may be used in an automatic setting.

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The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
2
The categories of this paper are: math
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
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The categories of this paper are: econ
37
The categories of this paper are: supr-con
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The categories of this paper are: nucl-ex
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The categories of this paper are: alg-geom