Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometric scaling: a simple preconditioner for certain linear systems
  with discontinuous coefficients   Linear systems with large differences between coefficients ("discontinuous
coefficients") arise in many cases in which partial differential
equations(PDEs) model physical phenomena involving heterogeneous media. The
standard approach to solving such problems is to use domain decomposition
techniques, with domain boundaries conforming to the boundaries between the
different media. This approach can be difficult to implement when the geometry
of the domain boundaries is complicated or the grid is unstructured. This work
examines the simple preconditioning technique of scaling the equations by
dividing each equation by the Lp-norm of its coefficients. This preconditioning
is called geometric scaling (GS). It has long been known that diagonal scaling
can be useful in improving convergence, but there is no study on the general
usefulness of this approach for discontinuous coefficients. GS was tested on
several nonsymmetric linear systems with discontinuous coefficients derived
from convection-diffusion elliptic PDEs with small to moderate convection
terms. It is shown that GS improved the convergence properties of restarted
GMRES and Bi-CGSTAB, with and without the ILUT preconditioner. GS was also
shown to improve the distribution of the eigenvalues by reducing their
concentration around the origin very significantly.

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The categories of this paper are: dg-ga
2
The categories of this paper are: math
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
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The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
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The categories of this paper are: eess
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The categories of this paper are: chao-dyn
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The categories of this paper are: astro-ph
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The categories of this paper are: supr-con