Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Numerical Tests of Evolution Systems, Gauge Conditions, and Boundary
  Conditions for 1D Colliding Gravitational Plane Waves   We investigate how the accuracy and stability of numerical relativity
simulations of 1D colliding plane waves depends on choices of equation
formulations, gauge conditions, boundary conditions, and numerical methods, all
in the context of a first-order 3+1 approach to the Einstein equations, with
basic variables some combination of first derivatives of the spatial metric and
components of the extrinsic curvature tensor. Hyperbolic schemes, specifically
variations on schemes proposed by Bona and Masso and Anderson and York, are
compared with variations of the Arnowitt-Deser-Misner formulation.
Modifications of the three basic schemes include raising one index in the
metric derivative and extrinsic curvature variables and adding a multiple of
the energy constraint to the extrinsic curvature evolution equations. Redundant
variables in the Bona-Masso formulation may be reset frequently or allowed to
evolve freely. Gauge conditions which simplify the dynamical structure of the
system are imposed during each time step, but the lapse and shift are reset
periodically to control the evolution of the spacetime slicing and the
longitudinal part of the metric. We show that physically correct boundary
conditions, satisfying the energy and momentum constraint equations,
generically require the presence of some ingoing eigenmodes of the
characteristic matrix. Numerical methods are developed for the hyperbolic
systems based on decomposing flux differences into linear combinations of
eigenvectors of the characteristic matrix. These methods are shown to be
second-order accurate, and in practice second-order convergent, for smooth
solutions, even when the eigenvectors and eigenvalues of the characteristic
matrix are spatially varying.

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The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
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The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
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The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: astro-ph
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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: mtrl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: ao-sci
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-lat
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The categories of this paper are: math