1,811 research outputs found
Differential-Algebraic Equations and Beyond: From Smooth to Nonsmooth Constrained Dynamical Systems
The present article presents a summarizing view at differential-algebraic
equations (DAEs) and analyzes how new application fields and corresponding
mathematical models lead to innovations both in theory and in numerical
analysis for this problem class. Recent numerical methods for nonsmooth
dynamical systems subject to unilateral contact and friction illustrate the
topicality of this development.Comment: Preprint of Book Chapte
A new nonlocal thermodynamical equilibrium radiative transfer method for cool stars
Context: The solution of the nonlocal thermodynamical equilibrium (non-LTE)
radiative transfer equation usually relies on stationary iterative methods,
which may falsely converge in some cases. Furthermore, these methods are often
unable to handle large-scale systems, such as molecular spectra emerging from,
for example, cool stellar atmospheres.
Aims: Our objective is to develop a new method, which aims to circumvent
these problems, using nonstationary numerical techniques and taking advantage
of parallel computers.
Methods: The technique we develop may be seen as a generalization of the
coupled escape probability method. It solves the statistical equilibrium
equations in all layers of a discretized model simultaneously. The numerical
scheme adopted is based on the generalized minimum residual method.
Result:. The code has already been applied to the special case of the water
spectrum in a red supergiant stellar atmosphere. This demonstrates the fast
convergence of this method, and opens the way to a wide variety of
astrophysical problems.Comment: 13 pages, 9 figure
Bounded perturbation resilience of extragradient-type methods and their applications
In this paper we study the bounded perturbation resilience of the
extragradient and the subgradient extragradient methods for solving variational
inequality (VI) problem in real Hilbert spaces. This is an important property
of algorithms which guarantees the convergence of the scheme under summable
errors, meaning that an inexact version of the methods can also be considered.
Moreover, once an algorithm is proved to be bounded perturbation resilience,
superiorizion can be used, and this allows flexibility in choosing the bounded
perturbations in order to obtain a superior solution, as well explained in the
paper. We also discuss some inertial extragradient methods. Under mild and
standard assumptions of monotonicity and Lipschitz continuity of the VI's
associated mapping, convergence of the perturbed extragradient and subgradient
extragradient methods is proved. In addition we show that the perturbed
algorithms converges at the rate of . Numerical illustrations are given
to demonstrate the performances of the algorithms.Comment: Accepted for publication in The Journal of Inequalities and
Applications. arXiv admin note: text overlap with arXiv:1711.01936 and text
overlap with arXiv:1507.07302 by other author
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