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 )
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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)
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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 
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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 |
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