Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Bramble-Pasciak conjugate gradient method for discrete Stokes problems
  with lognormal random viscosity   We study linear systems of equations arising from a stochastic Galerkin
finite element discretization of saddle point problems with random data and its
iterative solution. We consider the Stokes flow model with random viscosity
described by the exponential of a correlated random process and shortly discuss
the discretization framework and the representation of the emerging matrix
equation. Due to the high dimensionality and the coupling of the associated
symmetric, indefinite, linear system, we resort to iterative solvers and
problem-specific preconditioners. As a standard iterative solver for this
problem class, we consider the block diagonal preconditioned MINRES method and
further introduce the Bramble-Pasciak conjugate gradient method as a promising
alternative. This special conjugate gradient method is formulated in a
non-standard inner product with a block triangular preconditioner. From a
structural point of view, such a block triangular preconditioner enables a
better approximation of the original problem than the block diagonal one. We
derive eigenvalue estimates to assess the convergence behavior of the two
solvers with respect to relevant physical and numerical parameters and verify
our findings by the help of a numerical test case. We model Stokes flow in a
cavity driven by a moving lid and describe the viscosity by the exponential of
a truncated Karhunen-Loeve expansion. Regarding iteration counts, the
Bramble-Pasciak conjugate gradient method with block triangular preconditioner
is superior to the MINRES method with block diagonal preconditioner in the
considered example.

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The categories of this paper are: plasm-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: supr-con
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The categories of this paper are: hep-th
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The categories of this paper are: econ
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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: adap-org
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The categories of this paper are: patt-sol
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The categories of this paper are: mtrl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: gr-qc
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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: bayes-an
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The categories of this paper are: ao-sci