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A Wideband Fast Multipole Method for the Helmholtz kernel: Theoretical developments

Stéphanie Chaillat 1 Francis Collino 2
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
Abstract : This work presents a new Fast Multipole Method (FMM) based on plane wave expansions, combining the advantages of the low and high frequency formulations. We revisit the method of Greengard et al. 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 are illustrated with a numerical example.
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Stéphanie Chaillat, Francis Collino. A Wideband Fast Multipole Method for the Helmholtz kernel: Theoretical developments. [Research Report] RR-8692, INRIA Saclay; INRIA. 2015, pp.28. ⟨hal-01121687⟩

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