806 research outputs found
A New Implementation of the Magnetohydrodynamics-Relaxation Method for Nonlinear Force-Free Field Extrapolation in the Solar Corona
Magnetic field in the solar corona is usually extrapolated from photospheric
vector magnetogram using a nonlinear force-free field (NLFFF) model. NLFFF
extrapolation needs a considerable effort to be devoted for its numerical
realization. In this paper we present a new implementation of the
magnetohydrodynamics (MHD)-relaxation method for NLFFF extrapolation. The
magneto-frictional approach which is introduced for speeding the relaxation of
the MHD system is novelly realized by the spacetime conservation-element and
solution-element (CESE) scheme. A magnetic field splitting method is used to
further improve the computational accuracy. The bottom boundary condition is
prescribed by changing the transverse field incrementally to match the
magnetogram, and all other artificial boundaries of the computational box are
simply fixed. We examine the code by two types of NLFFF benchmark tests, the
Low & Lou (1990) semi-analytic force-free solutions and a more realistic
solar-like case constructed by van Ballegooijen et al. (2007). The results show
that our implementation are successful and versatile for extrapolations of
either the relatively simple cases or the rather complex cases which need
significant rebuilding of the magnetic topology, e.g., a flux rope. We also
compute a suite of metrics to quantitatively analyze the results and
demonstrate that the performance of our code in extrapolation accuracy
basically reaches the same level of the present best-performing code, e.g.,
that developed by Wiegelmann (2004).Comment: Accept by ApJ, 45 pages, 13 figure
Distributed Branching Bisimulation Minimization by Inductive Signatures
We present a new distributed algorithm for state space minimization modulo
branching bisimulation. Like its predecessor it uses signatures for refinement,
but the refinement process and the signatures have been optimized to exploit
the fact that the input graph contains no tau-loops.
The optimization in the refinement process is meant to reduce both the number
of iterations needed and the memory requirements. In the former case we cannot
prove that there is an improvement, but our experiments show that in many cases
the number of iterations is smaller. In the latter case, we can prove that the
worst case memory use of the new algorithm is linear in the size of the state
space, whereas the old algorithm has a quadratic upper bound.
The paper includes a proof of correctness of the new algorithm and the
results of a number of experiments that compare the performance of the old and
the new algorithms
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