73,063 research outputs found
Strict bounding of quantities of interest in computations based on domain decomposition
This paper deals with bounding the error on the estimation of quantities of
interest obtained by finite element and domain decomposition methods. The
proposed bounds are written in order to separate the two errors involved in the
resolution of reference and adjoint problems : on the one hand the
discretization error due to the finite element method and on the other hand the
algebraic error due to the use of the iterative solver. Beside practical
considerations on the parallel computation of the bounds, it is shown that the
interface conformity can be slightly relaxed so that local enrichment or
refinement are possible in the subdomains bearing singularities or quantities
of interest which simplifies the improvement of the estimation. Academic
assessments are given on 2D static linear mechanic problems.Comment: Computer Methods in Applied Mechanics and Engineering, Elsevier,
2015, online previe
Strict lower bounds with separation of sources of error in non-overlapping domain decomposition methods
This article deals with the computation of guaranteed lower bounds of the
error in the framework of finite element (FE) and domain decomposition (DD)
methods. In addition to a fully parallel computation, the proposed lower bounds
separate the algebraic error (due to the use of a DD iterative solver) from the
discretization error (due to the FE), which enables the steering of the
iterative solver by the discretization error. These lower bounds are also used
to improve the goal-oriented error estimation in a substructured context.
Assessments on 2D static linear mechanic problems illustrate the relevance of
the separation of sources of error and the lower bounds' independence from the
substructuring. We also steer the iterative solver by an objective of precision
on a quantity of interest. This strategy consists in a sequence of solvings and
takes advantage of adaptive remeshing and recycling of search directions.Comment: International Journal for Numerical Methods in Engineering, Wiley,
201
Address [financing the CAP, enlargement, the German-French relationship, monetary problems, and political union] by President [of Commission] Rey to the General Assembly of the Association of European Journalists. Bordeaux, 12 September 1969
Credit derivatives: instruments of hedging and factors of instability. The example of ?Credit Default Swaps? on French reference entities
Through a long-period analysis of the inter-temporal relations between the
French markets for credit default swaps (CDS), shares and bonds between 2001
and 2008, this article shows how a financial innovation like CDS could heighten
financial instability. After describing the operating principles of credit
derivatives in general and CDS in particular, we construct two difference VAR
models on the series: the share return rates, the variation in bond spreads and
the variation in CDS spreads for thirteen French companies, with the aim of
bringing to light the relations between these three markets. According to these
models, there is indeed an interdependence between the French share, CDS and
bond markets, with a strong influence of the share market on the other two.
This interdependence increases during periods of tension on the markets
(2001-2002, and since the summer of 2007).Comment: 2
Cosmological effects in the local static frame
What is the influence of cosmology (the expansion law and its acceleration,
the cosmological constant...) on the dynamics and optics of a local system like
the solar system, a galaxy, a cluster, a supercluster...? The answer requires
the solution of Einstein equation with the local source, which tends towards
the cosmological model at large distance. There is, in general, no analytic
expression for the corresponding metric, but we calculate here an expansion in
a small parameter, which allows to answer the question. First, we derive a
static expression for the pure cosmological (Friedmann-Lema\^itre) metric,
whose validity, although local, extends in a very large neighborhood of the
observer. This expression appears as the metric of an osculating de Sitter
model. Then we propose an expansion of the cosmological metric with a local
source, which is valid in a very large neighborhood of the local system. This
allows to calculate exactly the (tiny) influence of cosmology on the dynamics
of the solar system: it results that, contrary to some claims, cosmological
effects fail to account for the unexplained acceleration of the Pioneer probe
by several order of magnitudes. Our expression provide estimations of the
cosmological influence in the calculations of rotation or dispersion velocity
curves in galaxies, clusters, and any type of cosmic structure, necessary for
precise evaluations of dark matter and/or cosmic flows. The same metric can
also be used to estimate the influence of cosmology on gravitational optics in
the vicinity of such systems.Comment: to appear in Astron. & Astrop
Problems and prospects of local finance in Italy
Zadanie pt. „Digitalizacja i udostępnienie w Cyfrowym Repozytorium Uniwersytetu Łódzkiego kolekcji czasopism naukowych wydawanych przez Uniwersytet Łódzki” nr 885/P-DUN/2014 dofinansowane zostało ze środków MNiSW w ramach działalności upowszechniającej naukę
A Spectral Study of the Linearized Boltzmann Equation for Diffusively Excited Granular Media
In this work, we are interested in the spectrum of the diffusively excited
granular gases equation, in a space inhomogeneous setting, linearized around an
homogeneous equilibrium.
We perform a study which generalizes to a non-hilbertian setting and to the
inelastic case the seminal work of Ellis and Pinsky about the spectrum of the
linearized Boltzmann operator. We first give a precise localization of the
spectrum, which consists in an essential part lying on the left of the
imaginary axis and a discrete spectrum, which is also of nonnegative real part
for small values of the inelasticity parameter. We then give the so-called
inelastic "dispersion relations", and compute an expansion of the branches of
eigenvalues of the linear operator, for small Fourier (in space) frequencies
and small inelasticity.
One of the main novelty in this work, apart from the study of the inelastic
case, is that we consider an exponentially weighted Banach
setting instead of the classical Hilbertian
case, endorsed with Gaussian weights. We prove in particular that the results
of Ellis and Pinsky holds also in this space.Comment: 30 pages, 2 figure
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