Français
The sparse cardinal sine decomposition and applications
Multi angle
Authors : Alouges, François (Author of the conference)
CIRM (Publisher )
65R10 - Integral transforms
65T40 - Trigonometric approximation and interpolation
65T50 - Discrete and fast Fourier transforms (numerical methods)
CIRM (Publisher )
|
Abstract :
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.
MSC Codes : 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)
|
Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 26/08/16 Conference Date : 24/08/16 Subseries : Research talks arXiv category : Numerical Analysis ; Physics Mathematical Area(s) : Numerical Analysis & Scientific Computing ; Mathematics in Science & Technology Format : MP4 (.mp4) - HD Video Time : 01:11:49 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2016-08-24_Alouges.mp4 
|
Information on the Event
Event Title : CEMRACS: Numerical challenges in parallel scientific computing / CEMRACS : Défis numériques en calcul scientifique parallèleEvent Organizers : Grigori, Laura ; Japhet, Caroline ; Moireau, Philippe ; Parnaudeau, Philippe Dates : 18/07/16 - 26/08/16 Event Year : 2016 Event URL : http://conferences.cirm-math.fr/1430.html
Citation Data
DOI : 10.24350/CIRM.V.19034403Cite this video as: 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 |
See Also
- [Multi angle] High performance climate modelling : mimetic finite differences, and beyond? / Author of the conference Dubos, Thomas.
- [Multi angle] Direct and inverse biomechanical modeling of the heart / Author of the conference Chapelle, Dominique.
- [Multi angle] Modeling and data assimilation in cardiac electrophysiology / Author of the conference Collin, Annabelle.
- [Multi angle] A discussion about the impact of scalability constraint on the design of futur dynamical kernels of NWP models / Author of the conference Voitus, Fabrice.
- [Multi angle] Data-driven wildfire behavior modelling: focus on front level-set data assimilation / Author of the conference Rochoux, Mélanie.
- [Multi angle] Parametrized model order reduction for component-to-system synthesis / Author of the conference Patera, Anthony.
- [Multi angle] Efficient iterative solvers: FETI methods with multiple search directions / Author of the conference Roux, François-Xavier.
- [Multi angle] Optimized Schwarz waveform relaxation methods: theory and applications / Author of the conference Omnes, Pascal.
- [Multi angle] A posteriori error estimates and solver adaptivity in numerical simulations / Author of the conference Vohralík, Martin.
- [Multi angle] Multiple applications of high performance computing and numerical simulations in Total group / Author of the conference Ricoux, Philippe.
- [Multi angle] High performance computing with Feel++: applications and numerical methods / Author of the conference Prud'homme, Christophe.
- [Multi angle] Linear solvers for reservoir simulation / Author of the conference Hénon, Pascal.
- [Multi angle] Introduction to data assimilation: Kalman filters and ensembles / Author of the conference Mallet, Vivien.
- [Multi angle] Data assimilation training course @ CEMRACS: introduction and variational algorithms / Author of the conference Ricci, Sophie.
- [Multi angle] Tutorial with Freefem++ / Author of the conference Hecht, Frédéric.
- [Multi angle] Reduced basis methods: approximation of PDE's, interpolation and a posteriori estimate / Author of the conference Maday, Yvon.
- [Multi angle] A gentle introduction to parallel programming using OpenMP / Author of the conference Broquedis, François.
- [Multi angle] OpenCL introduction / Author of the conference Desprez, Frédéric.
- [Multi angle] Overview of architectures and programming language for parallel computing / Author of the conference Méhaut, Jean-françois.
- [Multi angle] Time parallel time integration / Author of the conference Gander, Martin.
- [Multi angle] Algorithms for future emerging technologies / Author of the conference Dongarra, Jack.
- [Multi angle] Domain decomposition, hybrid methods, coarse space corrections / Author of the conference Nataf, Frédéric.
- [Multi angle] The Portable Extensible Toolkit for Scientific Computing / Author of the conference Knepley, Matthew.
- [Multi angle] Krylov subspace solvers and preconditioners / Author of the conference Vuik, Kees.
Bibliography
