Documents  65N15 | enregistrements trouvés : 30

- vii; 148 p.
ISBN 978-1-4704-1923-3

Contemporary mathematics , 0660

Localisation : Collection 1er étage

équation aux dérivées partielles # traitement du signal # imagerie

35B10 ; 35B30 ; 35J05 ; 35J25 ; 35R30 ; 35R60 ; 65N15 ; 65T60 ; 86A15 ; 35-06 ; 35Bxx ; 35Jxx ; 35Rxx ; 00B25

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- 179 p.
ISBN 978-0-387-15234-9

Lecture notes in mathematics , 1129

Localisation : Collection 1er étage

35J25 ; 41A50 ; 41A63 ; 65N15 ; 65N30

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- 386 p.
ISBN 978-0-8218-3662-0

Contemporary mathematics , 0383

Localisation : Collection 1er étage

analyse numérique # méthode des éléments finis # EDP # convergence des méthodes numériques # génération de maillage # erreur # méthode multigrille # mécanique des fluides # équation de Navier-Stokes

65M12 ; 65M50 ; 65N12 ; 65N15 ; 65N30 ; 65N50 ; 65N55 ; 76-02 ; 76D05

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- 403 p.
ISBN 978-0-8218-3017-8

Proceedings of the Steklov institute of mathematics , 0117

Localisation : Collection 1er étage

24AXX ; 35-02 ; 41A08 ; 41A63 ; 65N15

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We review how to bound the error between the unknown weak solution of a PDE and its numerical approximation via a fully computable a posteriori estimate. We focus on approximations obtained at an arbitrary step of a linearization (Newton-Raphson, fixed point, ...) and algebraic solver (conjugate gradients, multigrid, domain decomposition, ...). Identifying the discretization, linearization, and algebraic error components, we design local stopping criteria which keep them in balance. This gives rise to a fully adaptive inexact Newton method. Numerical experiments are presented in confirmation of the theory. We review how to bound the error between the unknown weak solution of a PDE and its numerical approximation via a fully computable a posteriori estimate. We focus on approximations obtained at an arbitrary step of a linearization (Newton-Raphson, fixed point, ...) and algebraic solver (conjugate gradients, multigrid, domain decomposition, ...). Identifying the discretization, linearization, and algebraic error components, we design local ...

65N15 ; 65N22 ; 65Y05

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49M15 ; 65N15 ; 65N30 ; 76TXX

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Many problems in computational science require the approximation of a high-dimensional function from limited amounts of data. For instance, a common task in Uncertainty Quantification (UQ) involves building a surrogate model for a parametrized computational model. Complex physical systems involve computational models with many parameters, resulting in multivariate functions of many variables. Although the amount of data may be large, the curse of dimensionality essentially prohibits collecting or processing enough data to reconstruct such a function using classical approximation techniques. Over the last five years, spurred by its successful application in signal and image processing, compressed sensing has begun to emerge as potential tool for surrogate model construction UQ. In this talk, I will give an overview of application of compressed sensing to high-dimensional approximation. I will demonstrate how the appropriate implementation of compressed sensing overcomes the curse of dimensionality (up to a log factor). This is based on weighted l1 regularizers, and structured sparsity in so-called lower sets. If time, I will also discuss several variations and extensions relevant to UQ applications, many of which have links to the standard compressed sensing theory. These include dealing with corrupted data, the effect of model error, functions defined on irregular domains and incorporating additional information such as gradient data. I will also highlight several challenges and open problems. Many problems in computational science require the approximation of a high-dimensional function from limited amounts of data. For instance, a common task in Uncertainty Quantification (UQ) involves building a surrogate model for a parametrized computational model. Complex physical systems involve computational models with many parameters, resulting in multivariate functions of many variables. Although the amount of data may be large, the curse ...

41A05 ; 41A10 ; 65N12 ; 65N15 ; 94A12

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Parametrized PDE (Partial Differential Equation) Apps are PDE solvers which satisfy stringent per-query performance requirements: less-than or approximate 5-second problem specification time; less-than or approximate 5-second problem solution time, field and outputs; less-than or approximate 5% solution error, specified metrics; less-than or approximate 5-second solution visualization time. Parametrized PDE apps are relevant in many-query, real-time, and interactive contexts such as design, parameter estimation, monitoring, and education.
In this talk we describe and demonstrate a PDE App computational methodology. The numerical approach comprises three ingredients: component => system synthesis, formulated as a static-condensation procedure; model order reduction, informed by evanescence arguments at component interfaces (port reduction) and low-dimensional parametric manifolds in component interiors (reduced basis techniques); and parallel computation, implemented in a cloud environment. We provide examples in acoustics and also linear elasticity. Parametrized PDE (Partial Differential Equation) Apps are PDE solvers which satisfy stringent per-query performance requirements: less-than or approximate 5-second problem specification time; less-than or approximate 5-second problem solution time, field and outputs; less-than or approximate 5% solution error, specified metrics; less-than or approximate 5-second solution visualization time. Parametrized PDE apps are relevant in many-query, ...

65N30 ; 65N15 ; 65M60 ; 65M15 ; 93B50

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- xx; 393 p.
ISBN 978-0-19-967942-3

Numerical mathematics and scientific computation

Localisation : Ouvrage RdC (VERF)

estimation d'erreur a posteriori # méthode de discrétisation auto-adaptive # méthode des éléments finis # équations elliptiques linéaires # équations elliptiques non-linéaires # équations paraboliques linéaires # équations paraboliques non-linéaires # méthode des volumes finis # adaptation de maillage # équation de Poisson

65N15 ; 65M15 ; 65-02 ; 65N30 ; 65N50 ; 65M60 ; 65M08 ; 35J25 ; 35J60 ; 35K20 ; 35K55 ; 65M50 ; 65N08

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- xi; 316 p.
ISBN 978-3-11-019153-0

Radon Series on Computational and Applied Mathematics , 0004

Localisation : Ouvrage RdC (REPI)

EDP # équation différentielle # estimation d'erreur à postériori # équation de poisson # problème de diffusion # elaticity # fluide incompressible # problème non linéaire

35-02 ; 00-02 ; 35J05 ; 35K05 ; 65M15 ; 65N15 ; 74BXX ; 76Dxx

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- xvi; 317 p.
ISBN 978-3-03719-206-1

Tracts in mathematics , 0033

Localisation : Ouvrage RdC (REPI)

modèle mathématique # erreur de modélisation # erreur a posteriori majeure # simplification du modèle # réduction des dimensions # homogénéisation # conversion des modèles

35-02 ; 35J20 ; 35J50 ; 35J60 ; 35J88 ; 49M29 ; 65N15 ; 65N85 ; 74K20

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- 153 p.

Bonner mathematische schriften , 0251

Localisation : Publication 1er étage

inégalité de Campanato # méthode des différences finies # méthode des éléments finis # estimation d'erreur # projection de Ritz # équation de Ritz # équation biharmonique

65N30 ; 65N06 ; 65N15

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- xi; 622 p.
ISBN 978-3-0348-0132-4

International series of numerical mathematics , 0160

Localisation : Ouvrage RdC (CONS)

analyse numérique # calcul de variations # EDP # méthode aux différences finies # programmation non-linéaire

35K55 ; 49J20 ; 49K20 ; 49M25 ; 65K10 ; 65M60 ; 65N15 ; 65N30 ; 76D55 ; 90C30 ; 35-06 ; 35R99 ; 90C90

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- 197 p.
ISBN 978-3-540-41083-6

Lecture notes in computational science and engineering , 0017

Localisation : Ouvrage RdC (WOHL)

analyse numérique # méthode de discrétisation # estimation d'erreur # méthode itérative # décomposition de domaine # méthode des éléments finis avec joints # méthode de Schwarz # multigrille

65N55 ; 65N15 ; 65N22 ; 65N30 ; 65N50

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- xviii; 267 p.
ISBN 978-1-84265-913-7

Localisation : Ouvrage RdC (EFFE)

nombre de condition # nombre de condition effectif # analyse de la stabilité # équation de Poisson # limite d'erreur # élimination de Gauss # factorisation QR # méthode des différences finies

65N06 ; 65F05 ; 65F35 ; 65N15 ; 35J05

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- 374 p.
ISBN 978-3-540-15796-0

Springer series in computational mathematics , 0005

Localisation : Ouvrage RdC (GIRA)

approximation d'éléments finis # équation de Navier-Stokes # mécanique des fluides # méthode d'élément fini # solution numérique # viscosité

35A15 ; 35G20 ; 35Q10 ; 46E35 ; 65N15

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- 145 p.
ISBN 978-0-89871-533-0

Frontiers in applied mathematics

Localisation : Ouvrage RdC (HOLL)

analyse numérique # méthode des éléments finis # B-spline # base pondérée # estimation d'erreur # technique multigrille # problème aux valeurs limites

65-02 ; 65N30 ; 65N55 ; 65N15 ; 65D07 ; 35J25

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ISBN 978-3-540-64684-6

Mathématiques & applications , 0030

Localisation : Collection 1er étage

analyse statistique # application # dynamique des fluides # fluide incompressible visqueux # mathématique appliquée # mécanique des fluides # météorologie # nombre de Reynolds # turbulence # écoulement # équation de Navier-Stokes

65C20 ; 65N15 ; 68U20 ; 76-01 ; 76-02 ; 76D05 ; 76F05 ; 76F10 ; 76F99 ; 93E11

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ISBN 978-3-540-66346-1

Mathématiques & applications , 0032

Localisation : Collection 1er étage

analyse des correspondances # analyse des différences locales # analyse relationnelle # analyse statistique des données # aspect géométrique # donnée de comparaison par paire # donnée de tri # donnée ordinal # donnée à choix multiple # mathématiques et sciences humaines # modèle probabiliste # méthode de quantification de variable qualitative # méthode point et flèche # tableau

65C20 ; 65N15 ; 68U20 ; 76-01 ; 76-02 ; 76D05 ; 76F05 ; 76F10 ; 76F99 ; 93E11

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