{"title":"A single layer representation of the scattered field for multiple scattering problems","authors":"","doi":"10.1016/j.wavemoti.2024.103422","DOIUrl":null,"url":null,"abstract":"<div><div>The scattering of scalar waves by a set of scatterers is considered. It is proven that the scattered field can be represented as an integral supported by any smooth surface enclosing the scatterers. This is a generalization of the series expansion over spherical harmonics and spherical Bessel functions for spherical geometries. More precisely, given a set of scatterers, the field scattered by any subset can be expressed as an integral over any smooth surface enclosing the given subset alone. It is then possible to solve the multiple scattering problem by using this integral representation instead of an expansion over spherical harmonics. This result is used to develop an extension of the Fast Multipole Method in order to deal with subsets that are not enclosed within non-intersecting balls.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":null,"pages":null},"PeriodicalIF":2.1000,"publicationDate":"2024-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Wave Motion","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0165212524001525","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ACOUSTICS","Score":null,"Total":0}
引用次数: 0
Abstract
The scattering of scalar waves by a set of scatterers is considered. It is proven that the scattered field can be represented as an integral supported by any smooth surface enclosing the scatterers. This is a generalization of the series expansion over spherical harmonics and spherical Bessel functions for spherical geometries. More precisely, given a set of scatterers, the field scattered by any subset can be expressed as an integral over any smooth surface enclosing the given subset alone. It is then possible to solve the multiple scattering problem by using this integral representation instead of an expansion over spherical harmonics. This result is used to develop an extension of the Fast Multipole Method in order to deal with subsets that are not enclosed within non-intersecting balls.
期刊介绍：
Wave Motion is devoted to the cross fertilization of ideas, and to stimulating interaction between workers in various research areas in which wave propagation phenomena play a dominant role. The description and analysis of wave propagation phenomena provides a unifying thread connecting diverse areas of engineering and the physical sciences such as acoustics, optics, geophysics, seismology, electromagnetic theory, solid and fluid mechanics.
The journal publishes papers on analytical, numerical and experimental methods. Papers that address fundamentally new topics in wave phenomena or develop wave propagation methods for solving direct and inverse problems are of interest to the journal.
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