A Wideband Fast Multipole Method for the Helmholtz Kernel: Theoretical DevelopmentsReport as inadecuate

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1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation Inria Saclay - Ile de France, ENSTA ParisTech UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231 2 CERFACS

Abstract : This work presents a new Fast Multipole Method FMM based on plane wave expansions PWFMM, combining the advantages of the low and high frequency formulations.
We revisit the method of Greengard et al.
1 devoted to the low frequency regime and based on the splitting of the Green-s function into a propagative and an evanescent part.
More precisely, we give an explicit formula of the filtered translation function for the propagative part, we derive a new formula for the evanescent part and we provide a new interpolation algorithm.
At all steps, we check the accuracy of the method by providing error estimates.
These theoretical developments are used to propose a wideband FMM based entirely on plane wave expansions.
The numerical efficiency and accuracy of this broadband PWFMM are illustrated with a numerical example.

Keywords : Fast Multipole Method Quadrature errors Plane wave expansion Helmholtz equation Broadband

Author: Stéphanie Chaillat - Francis Collino -

Source: https://hal.archives-ouvertes.fr/


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