Volume 4, Issue 4
Diagonalizations of Vector and Tensor Addition Theorems
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Commun. Comput. Phys., 4 (2008), pp. 797-819.

Published online: 2008-04

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• Abstract

Based on the generalizations of the Funk-Hecke formula and the Rayleigh plan-wave expansion formula, an alternative and succinct derivation of the addition theorem for general tensor field is obtained. This new derivation facilitates the diagonalization of the tensor addition theorem. In order to complete this derivation, we have carried out the evaluation of the generalization of the Gaunt coefficient for tensor fields. Since vector fields (special case of tensor fields) are very useful in practice, we discuss vector multipole fields and vector addition theorem in details. The work is important in multiple scattering and fast algorithms in wave physics.

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@Article{CiCP-4-797, author = {}, title = {Diagonalizations of Vector and Tensor Addition Theorems}, journal = {Communications in Computational Physics}, year = {2008}, volume = {4}, number = {4}, pages = {797--819}, abstract = {

Based on the generalizations of the Funk-Hecke formula and the Rayleigh plan-wave expansion formula, an alternative and succinct derivation of the addition theorem for general tensor field is obtained. This new derivation facilitates the diagonalization of the tensor addition theorem. In order to complete this derivation, we have carried out the evaluation of the generalization of the Gaunt coefficient for tensor fields. Since vector fields (special case of tensor fields) are very useful in practice, we discuss vector multipole fields and vector addition theorem in details. The work is important in multiple scattering and fast algorithms in wave physics.

}, issn = {1991-7120}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cicp/7815.html} }
TY - JOUR T1 - Diagonalizations of Vector and Tensor Addition Theorems JO - Communications in Computational Physics VL - 4 SP - 797 EP - 819 PY - 2008 DA - 2008/04 SN - 4 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cicp/7815.html KW - AB -

Based on the generalizations of the Funk-Hecke formula and the Rayleigh plan-wave expansion formula, an alternative and succinct derivation of the addition theorem for general tensor field is obtained. This new derivation facilitates the diagonalization of the tensor addition theorem. In order to complete this derivation, we have carried out the evaluation of the generalization of the Gaunt coefficient for tensor fields. Since vector fields (special case of tensor fields) are very useful in practice, we discuss vector multipole fields and vector addition theorem in details. The work is important in multiple scattering and fast algorithms in wave physics.

B. He & W. C. Chew. (2020). Diagonalizations of Vector and Tensor Addition Theorems. Communications in Computational Physics. 4 (4). 797-819. doi:
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