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Documents  65Y15 | enregistrements trouvés : 12

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Research talks

A serious problem common to all interval algorithms is that they suffer from wrapping effects, i.e. unnecessary growth of approximations during a computation. This is essentially connected to functional dependencies inside vectors of data computed from the same inputs. Reducing these effects is an important issue in interval arithmetic, where the most successful approach uses Taylor models.
In TTE Taylor models have not been considered explicitly, as they use would not change the induced computability, already established using ordinary interval computations. However for the viewpoint of efficiency, they lead to significant improvements.
In the talk we report on recent improvements on the iRRAM software for exact real arithmetic (ERA) based on Taylor models. The techniques discussed should also easily be applicable to other software for exact real computations as long as they also are based on interval arithmetic.
As instructive examples we consider the one-dimensional logistic map and a few further discrete dynamical systems of higher dimensions
Joint work with Franz Brauße, Trier, and Margarita Korovina, Novosibirsk.
A serious problem common to all interval algorithms is that they suffer from wrapping effects, i.e. unnecessary growth of approximations during a computation. This is essentially connected to functional dependencies inside vectors of data computed from the same inputs. Reducing these effects is an important issue in interval arithmetic, where the most successful approach uses Taylor models.
In TTE Taylor models have not been considered ...

68Q25 ; 03D60 ; 65Y15

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Research talks

I will review (some of) the HPC solution strategies developed in Feel++. We present our advances in developing a language specific to partial differential equations embedded in C++. We have been developing the Feel++ framework (Finite Element method Embedded Language in C++) to the point where it allows to use a very wide range of Galerkin methods and advanced numerical methods such as domain decomposition methods including mortar and three fields methods, fictitious domain methods or certified reduced basis. We shall present an overview of the various ingredients as well as some illustrations. The ingredients include a very expressive embedded language, seamless interpolation, mesh adaption, seamless parallelisation. As to the illustrations, they exercise the versatility of the framework either by allowing the development and/or numerical verification of (new) mathematical methods or the development of large multi-physics applications - e.g. fluid-structure interaction using either an Arbitrary Lagrangian Eulerian formulation or a levelset based one; high field magnets modeling which involves electro-thermal, magnetostatics, mechanical and thermo-hydraulics model; ... - The range of users span from mechanical engineers in industry, physicists in complex fluids, computer scientists in biomedical applications to applied mathematicians thanks to the shared common mathematical embedded language hiding linear algebra and computer science complexities. I will review (some of) the HPC solution strategies developed in Feel++. We present our advances in developing a language specific to partial differential equations embedded in C++. We have been developing the Feel++ framework (Finite Element method Embedded Language in C++) to the point where it allows to use a very wide range of Galerkin methods and advanced numerical methods such as domain decomposition methods including mortar and three ...

65N30 ; 65N55 ; 65Y05 ; 65Y15

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Research schools

68U20 ; 68W10 ; 65Y15 ; 65Y05

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V

- xxii; 552 p.
ISBN 978-0-898719-97-0

Computational science & engineering

Localisation : Ouvrage RdC (ASCH)

analyse numérique # algorithme # algèbre linéaire # erreur de Roundoff # méthode numérique # équation nonlinéaire # methode directe # méthode itérative # valeur singulière # système nonlinéaire # optimisation # transformée de Fourier # dérivation numérique # intégration numérique # MATLAB

65-01 ; 00A06 ; 65Dxx ; 65Fxx ; 65G50 ; 65Hxx ; 65Kxx ; 65Lxx ; 65Y15

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V

- 508 p.
ISBN 978-0-471-69833-3

Localisation : Ouvrage RdC (Appl)

analyse numérique # traitement de données # MATLAB # approximation numérique # EDP # optimisation # équation non-linéaire

65-01 ; 65Dxx ; 65Fxx ; 65Hxx ; 65Lxx ; 65K05 ; 65Mxx ; 15-04 ; 34-04 ; 35-04 ; 41-04 ; 12-04 ; 68W30 ; 65Y15

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V

- xii; 372 p.
ISBN 978-3-662-43510-6

Problem books in mathematics

Localisation : Ouvrage RdC (LYCH)

MATLAB # traitement automatique des données # calcul numérique # analyse numérique # algèbre linéaire # théorie de la matrice S # valeur propre # vecteur propre # méthode itérative # interpolation polynômiale # courbe de Bézier # polynôme de Bernstein # méthode des moindres carrés

65Dxx ; 65Fxx ; 65Hxx ; 65Lxx ; 68Wxx ; 65-01 ; 00A07 ; 65Y15 ; 65D05 ; 65D17 ; 65D32 ; 65L05 ; 65L12 ; 65M06 ; 65N06

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V

- 308 p.
ISBN 978-1-4020-2099-5

Mathematics and its applications , 0568

Localisation : Ouvrage RdC (IXARU)

ajustement de courbe

65L06 ; 65L05 ; 65D05 ; 34A34 ; 65-02 ; 65Y15 ; 65D32

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V

- xv; 256 p.
ISBN 978-2-8178-0180-3

Pratique R

Localisation : Ouvrage RdC (ROBE)

méthode de Monte-Carlo # langage de programmation R # simulation statistique # analyse bayésienne

65C05 ; 11K45 ; 65C10 ; 65C20 ; 65C40 ; 65C35 ; 62J10 ; 65K05 ; 65C60 ; 65-02 ; 62D05 ; 60J65 ; 62-01 ; 62-04 ; 90C15 ; 90C27 ; 65Y15

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V

- xix; 635 p.
ISBN 978-0-521-87726-8

Localisation : Ouvrage RdC (TRAN)

analyse numérique # équation différentielle elliptique # équation différentielle parabolique

65Mxx ; 65-02 ; 35Lxx ; 65Y15 ; 76B15 ; 76N15 ; 76W05 ; 74C05 ; 76Mxx ; 82D60 ; 86A20

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V

- 217 p.
ISBN 978-1-5848-8492-7

Numerical insights , 0004

Localisation : Ouvrage RdC (WIEN)

analyse numérique # méthode multi-grilles # analyse de Fourier # EDP # équation de Poisson # équation de convection diffusion # équation biharmonique # équation de Green # équation de Stokes # problème à échelle linéaire # élasticité

65N55 ; 42-04 ; 65-02 ; 65N12 ; 35J25 ; 35J40 ; 35Q30 ; 65Y15

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V

- xvii; 385 p.
ISBN 978-3-642-33286-9

Texts in computational science and engineering , 0010

Localisation : Ouvrage RdC (LARS)

analyse numérique # équations aux dérivées partielles # conception par ordinateur # CAD CAE # MATLAB # méthode des éléments finis # approximation polynomiale

65N30 ; 65N15 ; 65M60 ; 65M15 ; 65-02 ; 74S05 ; 76M10 ; 35J25 ; 35Q35 ; 35Q60 ; 65Y15 ; 65F50 ; 65F10

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V

- 1208 p.
ISBN 978-0-387-95011-2

Localisation : Ouvrage RdC (TROT)

mathematica # analyse numérique # approximation numérique # programmation mathématique # transformation de Fourier # algèbre linéaire # EDP # intégration # équation transcendentale

65-00 ; 65-01 ; 65Dxx ; 65Fxx ; 65Hxx ; 65Lxx ; 65K05 ; 65Mxx ; 65Nxx ; 65T50 ; 65Y15

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