4,142 research outputs found
Constructing Two Edge-Disjoint Hamiltonian Cycles in Locally Twisted Cubes
The -dimensional hypercube network is one of the most popular
interconnection networks since it has simple structure and is easy to
implement. The -dimensional locally twisted cube, denoted by , an
important variation of the hypercube, has the same number of nodes and the same
number of connections per node as . One advantage of is that the
diameter is only about half of the diameter of . Recently, some
interesting properties of were investigated. In this paper, we
construct two edge-disjoint Hamiltonian cycles in the locally twisted cube
, for any integer . The presence of two edge-disjoint
Hamiltonian cycles provides an advantage when implementing algorithms that
require a ring structure by allowing message traffic to be spread evenly across
the locally twisted cube.Comment: 7 pages, 4 figure
A Nonlinear Multigrid Steady-State Solver for Microflow
We develop a nonlinear multigrid method to solve the steady state of
microflow, which is modeled by the high order moment system derived recently
for the steady-state Boltzmann equation with ES-BGK collision term. The solver
adopts a symmetric Gauss-Seidel iterative scheme nested by a local Newton
iteration on grid cell level as its smoother. Numerical examples show that the
solver is insensitive to the parameters in the implementation thus is quite
robust. It is demonstrated that expected efficiency improvement is achieved by
the proposed method in comparison with the direct time-stepping scheme
Numerical Regularized Moment Method of Arbitrary Order for Boltzmann-BGK Equation
We introduce a numerical method for solving Grad's moment equations or
regularized moment equations for arbitrary order of moments. In our algorithm,
we do not need explicitly the moment equations. As an instead, we directly
start from the Boltzmann equation and perform Grad's moment method \cite{Grad}
and the regularization technique \cite{Struchtrup2003} numerically. We define a
conservative projection operator and propose a fast implementation which makes
it convenient to add up two distributions and provides more efficient flux
calculations compared with the classic method using explicit expressions of
flux functions. For the collision term, the BGK model is adopted so that the
production step can be done trivially based on the Hermite expansion. Extensive
numerical examples for one- and two-dimensional problems are presented.
Convergence in moments can be validated by the numerical results for different
number of moments.Comment: 33 pages, 13 figure
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