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Finite Series

  • Gérard Gouesbet
  • Gérard Gréhan

Abstract

As previously discussed, evaluations of BSCs \(g_{n}^{m}\) may be carried out by using quadratures. Historically, the quadrature techniques have been the first to be developed in so far as they quite naturally arise in the development of the GLMT. Because they are flexible, i.e. only kernels in the quadratures have to be modified when the incident beam is changed, they are well adapted to some specific problems, such as the study of shaped beam scattering by adjacent spherical particles [138]. However, when the nature of the incident beam is well defined, quadratures constitute the worst methods because they are very time-consuming in terms of CPU. An effort has been therefore performed to develop other techniques to evaluate BSCs. In this chapter, a technique using finite series is presented. The technique is rigorous and indeed mathematically equivalent to quadrature techniques when the incident beam description exactly satisfies Maxwell’s equations. However, it is much faster running. There is nevertheless a price to pay for such an advantage. Indeed, when using the quadrature techniques, only quadrature integrands have to be changed when the incident beam description is modified. Conversely, when using the finite series technique, an extra analytical work and significant program modifications are required when the beam description is modified. Performing by hand these modifications may typically take one month. Fortunately, the procedure is quite general and the whole process may be in principle carried out in an automatic way by using a formal computation procedure which would furthermore generate FORTRAN sources. For details about published work on finite series, the reader may refer to Gouesbet et al [87], [367] and references therein.

Keywords

Incident Beam Gaussian Beam Series Technique Fast Running Intermediary Result 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Gérard Gouesbet
    • Gérard Gréhan

      There are no affiliations available

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