English
The sparse cardinal sine decomposition and applications
Multi angle
Auteurs : Alouges, François (Auteur de la Conférence)
CIRM (Editeur )
65R10 - Integral transforms
65T40 - Trigonometric approximation and interpolation
65T50 - Discrete and fast Fourier transforms (numerical methods)
CIRM (Editeur )
Loading the player...
|
Résumé :
When solving wave scattering problems with the Boundary Element Method (BEM), one usually faces the problem of storing a dense matrix of huge size which size is proportional to the (square of) the number N of unknowns on the boundary of the scattering object. Several methods, among which the Fast Multipole Method (FMM) or the H-matrices are celebrated, were developed to circumvent this obstruction. In both cases an approximation of the matrix is obtained with a O(N log(N)) storage and the matrix-vector product has the same complexity. This permits to solve the problem, replacing the direct solver with an iterative method.
The aim of the talk is to present an alternative method which is based on an accurate version of the Fourier based convolution. Based on the non-uniform FFT, the method, called the sparse cardinal sine decomposition (SCSD) ends up to have the same complexity than the FMM for much less complexity in the implementation. We show in practice how the method works, and give applications in as different domains as Laplace, Helmholtz, Maxwell or Stokes equations.
This is a joint work with Matthieu Aussal.
Codes MSC : The aim of the talk is to present an alternative method which is based on an accurate version of the Fourier based convolution. Based on the non-uniform FFT, the method, called the sparse cardinal sine decomposition (SCSD) ends up to have the same complexity than the FMM for much less complexity in the implementation. We show in practice how the method works, and give applications in as different domains as Laplace, Helmholtz, Maxwell or Stokes equations.
This is a joint work with Matthieu Aussal.
65R10 - Integral transforms
65T40 - Trigonometric approximation and interpolation
65T50 - Discrete and fast Fourier transforms (numerical methods)
|
Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 26/08/16 Date de captation : 24/08/16 Sous collection : Research talks arXiv category : Numerical Analysis ; Physics Domaine : Numerical Analysis & Scientific Computing ; Mathematics in Science & Technology Format : MP4 (.mp4) - HD Durée : 01:11:49 Audience : Researchers Download : https://videos.cirm-math.fr/2016-08-24_Alouges.mp4 
|
Informations sur la Rencontre
Nom de la rencontre : CEMRACS: Numerical challenges in parallel scientific computing / CEMRACS : Défis numériques en calcul scientifique parallèleOrganisateurs de la rencontre : Grigori, Laura ; Japhet, Caroline ; Moireau, Philippe ; Parnaudeau, Philippe Dates : 18/07/16 - 26/08/16 Année de la rencontre : 2016 URL Congrès : http://conferences.cirm-math.fr/1430.html
Données de citation
DOI : 10.24350/CIRM.V.19034403Citer cette vidéo: Alouges, François (2016). The sparse cardinal sine decomposition and applications. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19034403 URI : http://dx.doi.org/10.24350/CIRM.V.19034403 |
Voir aussi
- [Multi angle] High performance climate modelling : mimetic finite differences, and beyond? / Auteur de la Conférence Dubos, Thomas.
- [Multi angle] Direct and inverse biomechanical modeling of the heart / Auteur de la Conférence Chapelle, Dominique.
- [Multi angle] Modeling and data assimilation in cardiac electrophysiology / Auteur de la Conférence Collin, Annabelle.
- [Multi angle] A discussion about the impact of scalability constraint on the design of futur dynamical kernels of NWP models / Auteur de la Conférence Voitus, Fabrice.
- [Multi angle] Data-driven wildfire behavior modelling: focus on front level-set data assimilation / Auteur de la Conférence Rochoux, Mélanie.
- [Multi angle] Parametrized model order reduction for component-to-system synthesis / Auteur de la Conférence Patera, Anthony.
- [Multi angle] Efficient iterative solvers: FETI methods with multiple search directions / Auteur de la Conférence Roux, François-Xavier.
- [Multi angle] Optimized Schwarz waveform relaxation methods: theory and applications / Auteur de la Conférence Omnes, Pascal.
- [Multi angle] A posteriori error estimates and solver adaptivity in numerical simulations / Auteur de la Conférence Vohralík, Martin.
- [Multi angle] Multiple applications of high performance computing and numerical simulations in Total group / Auteur de la Conférence Ricoux, Philippe.
- [Multi angle] High performance computing with Feel++: applications and numerical methods / Auteur de la Conférence Prud'homme, Christophe.
- [Multi angle] Linear solvers for reservoir simulation / Auteur de la Conférence Hénon, Pascal.
- [Multi angle] Introduction to data assimilation: Kalman filters and ensembles / Auteur de la Conférence Mallet, Vivien.
- [Multi angle] Data assimilation training course @ CEMRACS: introduction and variational algorithms / Auteur de la Conférence Ricci, Sophie.
- [Multi angle] Tutorial with Freefem++ / Auteur de la Conférence Hecht, Frédéric.
- [Multi angle] Reduced basis methods: approximation of PDE's, interpolation and a posteriori estimate / Auteur de la Conférence Maday, Yvon.
- [Multi angle] A gentle introduction to parallel programming using OpenMP / Auteur de la Conférence Broquedis, François.
- [Multi angle] OpenCL introduction / Auteur de la Conférence Desprez, Frédéric.
- [Multi angle] Overview of architectures and programming language for parallel computing / Auteur de la Conférence Méhaut, Jean-françois.
- [Multi angle] Time parallel time integration / Auteur de la Conférence Gander, Martin.
- [Multi angle] Algorithms for future emerging technologies / Auteur de la Conférence Dongarra, Jack.
- [Multi angle] Domain decomposition, hybrid methods, coarse space corrections / Auteur de la Conférence Nataf, Frédéric.
- [Multi angle] The Portable Extensible Toolkit for Scientific Computing / Auteur de la Conférence Knepley, Matthew.
- [Multi angle] Krylov subspace solvers and preconditioners / Auteur de la Conférence Vuik, Kees.
Bibliographie
