English
25+ years of wavelets for PDEs
Post-edited
Auteurs : Kunoth, Angela (Auteur de la Conférence)
CIRM (Editeur )
49J20 - Optimal control problems involving partial differential equations
65N12 - Stability and convergence of numerical methods (BVP of PDE)
65N30 - Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE)
65T60 - Wavelets (numerical methods)
94A08 - Image processing (compression, reconstruction, etc.)
CIRM (Editeur )
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| wavelets in image processing wavelets definition elliptic PDEs beyond finite elements convergence and complexity optimal control Questions of the audience |
Résumé :
Ingrid Daubechies' construction of orthonormal wavelet bases with compact support published in 1988 started a general interest to employ these functions also for the numerical solution of partial differential equations (PDEs). Concentrating on linear elliptic and parabolic PDEs, I will start from theoretical topics such as the well-posedness of the problem in appropriate function spaces and regularity of solutions and will then address quality and optimality of approximations and related concepts from approximation the- ory. We will see that wavelet bases can serve as a basic ingredient, both for the theory as well as for algorithmic realizations. Particularly for situations where solutions exhibit singularities, wavelet concepts enable adaptive appproximations for which convergence and optimal algorithmic complexity can be established. I will describe corresponding implementations based on biorthogonal spline-wavelets.
Moreover, wavelet-related concepts have triggered new developments for efficiently solving complex systems of PDEs, as they arise from optimization problems with PDEs.
Codes MSC : Moreover, wavelet-related concepts have triggered new developments for efficiently solving complex systems of PDEs, as they arise from optimization problems with PDEs.
49J20 - Optimal control problems involving partial differential equations
65N12 - Stability and convergence of numerical methods (BVP of PDE)
65N30 - Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE)
65T60 - Wavelets (numerical methods)
94A08 - Image processing (compression, reconstruction, etc.)
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 27/09/2016 Date de captation : 20/09/2016 Sous collection : Research talks arXiv category : Analysis of PDEs ; Numerical Analysis Domaine : PDE ; Analysis and its Applications ; Numerical Analysis & Scientific Computing Format : MP4 (.mp4) - HD Durée : 00:52:07 Audience : Researchers Download : https://videos.cirm-math.fr/2016-09-20_Kunoth.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Multivariate approximation and interpolation with applications - MAIA / Approximation et interpolation à plusieurs variables et applications - MAIAOrganisateurs de la rencontre : Bouhamadi, Abderrahman ; Cohen, Albert ; Conti, Costanza ; Rabut, Christophe Dates : 19/09/2016 - 23/09/2016 Année de la rencontre : 2016 URL Congrès : http://conferences.cirm-math.fr/1444.html
Données de citation
DOI : 10.24350/CIRM.V.19051403Citer cette vidéo: Kunoth, Angela (2016). 25+ years of wavelets for PDEs. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19051403 URI : http://dx.doi.org/10.24350/CIRM.V.19051403 |
Voir aussi
- [Multi angle] Spherical splines / Auteur de la Conférence Prautzsch, Hartmut.
- [Multi angle] Algebraic multigrid and subdivision / Auteur de la Conférence Charina, Maria.
- [Multi angle] Some recent insights into computing with positive definite kernels / Auteur de la Conférence Fasshauer, Greg.
- [Multi angle] The unitary extension principle on LCA groups / Auteur de la Conférence Christensen, Ole.
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