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Journal Articles Computers & Mathematics with Applications Year : 2015

A Wideband Fast Multipole Method for the Helmholtz Kernel: Theoretical Developments

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.
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Dates and versions

hal-01154119 , version 1 (21-05-2015)

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Stéphanie Chaillat, Francis Collino. A Wideband Fast Multipole Method for the Helmholtz Kernel: Theoretical Developments. Computers & Mathematics with Applications, 2015, ⟨10.1016/j.camwa.2015.05.019⟩. ⟨hal-01154119⟩
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