12,658 research outputs found
Nonlinear Preconditioning: How to use a Nonlinear Schwarz Method to Precondition Newton's Method
For linear problems, domain decomposition methods can be used directly as
iterative solvers, but also as preconditioners for Krylov methods. In practice,
Krylov acceleration is almost always used, since the Krylov method finds a much
better residual polynomial than the stationary iteration, and thus converges
much faster. We show in this paper that also for non-linear problems, domain
decomposition methods can either be used directly as iterative solvers, or one
can use them as preconditioners for Newton's method. For the concrete case of
the parallel Schwarz method, we show that we obtain a preconditioner we call
RASPEN (Restricted Additive Schwarz Preconditioned Exact Newton) which is
similar to ASPIN (Additive Schwarz Preconditioned Inexact Newton), but with all
components directly defined by the iterative method. This has the advantage
that RASPEN already converges when used as an iterative solver, in contrast to
ASPIN, and we thus get a substantially better preconditioner for Newton's
method. The iterative construction also allows us to naturally define a coarse
correction using the multigrid full approximation scheme, which leads to a
convergent two level non-linear iterative domain decomposition method and a two
level RASPEN non-linear preconditioner. We illustrate our findings with
numerical results on the Forchheimer equation and a non-linear diffusion
problem
SUSY structures, representations and Peter-Weyl theorem for
The real compact supergroup is analized from different perspectives
and its representation theory is studied. We prove it is the only (up to
isomorphism) supergroup, which is a real form of
with reduced Lie group , and a link with SUSY structures on is established. We describe a large family of complex semisimple
representations of and we show that any -representation
whose weights are all nonzero is a direct sum of members of our family. We also
compute the matrix elements of the members of this family and we give a proof
of the Peter-Weyl theorem for
Automated Classification of 2000 Bright IRAS Sources
An Artificial Neural Network (ANN) has been employed using a supervised
back-propagation scheme to classify 2000 bright sources from the Calgary
database of IRAS (Infrared Astronomy Satellite) spectra in the wavelength
region of 8-23 microns. The data base has been classified into 17
pre-determined classes based on spectral morphology. We have been able to
classify more than 80 percent of the 2000 sources correctly at the first
instance. The speed and robustness of the scheme will allow us to classify the
whole of LRS database, containing more than 50,000 sources in the future.Comment: 26 pages, To appear in ApJS after July 200
Integro-differential diffusion equation for continuous time random walk
In this paper we present an integro-differential diffusion equation for
continuous time random walk that is valid for a generic waiting time
probability density function. Using this equation we also study diffusion
behaviors for a couple of specific waiting time probability density functions
such as exponential, and a combination of power law and generalized
Mittag-Leffler function. We show that for the case of the exponential waiting
time probability density function a normal diffusion is generated and the
probability density function is Gaussian distribution. In the case of the
combination of a power-law and generalized Mittag-Leffler waiting probability
density function we obtain the subdiffusive behavior for all the time regions
from small to large times, and probability density function is non-Gaussian
distribution.Comment: 12 page
Realization of Artificial Ice Systems for Magnetic Vortices in a Superconducting MoGe Thin-film with Patterned Nanostructures
We report an anomalous matching effect in MoGe thin films containing pairs of
circular holes arranged in such a way that four of those pairs meet at each
vertex point of a square lattice. A remarkably pronounced fractional matching
was observed in the magnetic field dependences of both the resistance and the
critical current. At the half matching field the critical current can be even
higher than that at zero field. This has never been observed before for
vortices in superconductors with pinning arrays. Numerical simulations within
the nonlinear Ginzburg-Landau theory reveal a square vortex ice configuration
in the ground state at the half matching field and demonstrate similar
characteristic features in the field dependence of the critical current,
confirming the experimental realization of an artificial ice system for
vortices for the first time.Comment: To appear in Phys. Rev. Let
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