A Directional Equispaced interpolation-based ...
Document type :
Article dans une revue scientifique
DOI :
Title :
A Directional Equispaced interpolation-based Fast Multipole Method for oscillatory kernels
Author(s) :
Chollet, Igor [Auteur]
Institut des Sciences du Calcul et des Données [ISCD]
Algorithms and parallel tools for integrated numerical simulations [ALPINES]
Claeys, Xavier [Auteur]
Laboratoire Jacques-Louis Lions [LJLL (UMR_7598)]
Algorithms and parallel tools for integrated numerical simulations [ALPINES]
Fortin, Pierre [Auteur]
Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 [CRIStAL]
Performance et Qualité des Algorithmes Numériques [PEQUAN]
Laboratoire d'Informatique de Paris 6 [LIP6]
Grigori, Laura [Auteur]
Laboratoire Jacques-Louis Lions [LJLL (UMR_7598)]
Algorithms and parallel tools for integrated numerical simulations [ALPINES]
Institut des Sciences du Calcul et des Données [ISCD]
Algorithms and parallel tools for integrated numerical simulations [ALPINES]
Claeys, Xavier [Auteur]
Laboratoire Jacques-Louis Lions [LJLL (UMR_7598)]
Algorithms and parallel tools for integrated numerical simulations [ALPINES]
Fortin, Pierre [Auteur]
![refId](/themes/Mirage2//images/idref.png)
Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 [CRIStAL]
Performance et Qualité des Algorithmes Numériques [PEQUAN]
Laboratoire d'Informatique de Paris 6 [LIP6]
Grigori, Laura [Auteur]
Laboratoire Jacques-Louis Lions [LJLL (UMR_7598)]
Algorithms and parallel tools for integrated numerical simulations [ALPINES]
Journal title :
SIAM Journal on Scientific Computing
Pages :
C20-C48
Publisher :
Society for Industrial and Applied Mathematics
Publication date :
2023-02-28
ISSN :
1064-8275
English keyword(s) :
Fast multipole method FMM
Symmetries
Fast Fourier Transform FFT
High performance computing on one CPU core
Highly oscillatory kernels
Non-uniform particle distributions
Symmetries
Fast Fourier Transform FFT
High performance computing on one CPU core
Highly oscillatory kernels
Non-uniform particle distributions
HAL domain(s) :
Mathématiques [math]/Analyse numérique [math.NA]
English abstract : [en]
Fast Multipole Methods (FMMs) based on the oscillatory Helmholtz kernel can reduce the cost of solving N-body problems arising from Boundary Integral Equations (BIEs) in acoustic or electromagnetics. However, their cost ...
Show more >Fast Multipole Methods (FMMs) based on the oscillatory Helmholtz kernel can reduce the cost of solving N-body problems arising from Boundary Integral Equations (BIEs) in acoustic or electromagnetics. However, their cost strongly increases in the high-frequency regime. This paper introduces a new directional FMM for oscillatory kernels (defmm - directional equispaced interpolation-based fmm), whose precomputation and application are FFT-accelerated due to polynomial interpolations on equispaced grids. We demonstrate the consistency of our FFT approach, and show how symmetries can be exploited in the Fourier domain. We also describe the algorithmic design of defmm, well-suited for the BIE non-uniform particle distributions, and present performance optimizations on one CPU core. Finally, we exhibit important performance gains on all test cases for defmm over a state-of-the-art FMM library for oscillatory kernels.Show less >
Show more >Fast Multipole Methods (FMMs) based on the oscillatory Helmholtz kernel can reduce the cost of solving N-body problems arising from Boundary Integral Equations (BIEs) in acoustic or electromagnetics. However, their cost strongly increases in the high-frequency regime. This paper introduces a new directional FMM for oscillatory kernels (defmm - directional equispaced interpolation-based fmm), whose precomputation and application are FFT-accelerated due to polynomial interpolations on equispaced grids. We demonstrate the consistency of our FFT approach, and show how symmetries can be exploited in the Fourier domain. We also describe the algorithmic design of defmm, well-suited for the BIE non-uniform particle distributions, and present performance optimizations on one CPU core. Finally, we exhibit important performance gains on all test cases for defmm over a state-of-the-art FMM library for oscillatory kernels.Show less >
Language :
Anglais
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