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 derivati...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.展开更多
The conventional vector addition theorem is written in a compact notation.Then a new and succinct derivation of the vector addition theorem is presented thatis as close to the derivation of the scalar addition theorem...The conventional vector addition theorem is written in a compact notation.Then a new and succinct derivation of the vector addition theorem is presented thatis as close to the derivation of the scalar addition theorem. Newly derived expressionsin this new derivation are used to diagonalize the vector addition theorem. Thediagonal form of the vector addition theorem is important in the design of fast algorithmsfor computational wave physics such as computational electromagnetics andcomputational acoustics.展开更多
文摘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.
基金Part of this work was done when the author was a Cheng Tsang Man Visiting Professor at Nanyang Technological University,Singapore.This work is dedicated to the memory of Professor Y.T.Lo.Partial support by AFOSR MURI grant FA9550-04-1-0326WC is gratefully acknowledged.Feedback from an anonymous reviewer for improving the manuscript is gratefully acknowledged.
文摘The conventional vector addition theorem is written in a compact notation.Then a new and succinct derivation of the vector addition theorem is presented thatis as close to the derivation of the scalar addition theorem. Newly derived expressionsin this new derivation are used to diagonalize the vector addition theorem. Thediagonal form of the vector addition theorem is important in the design of fast algorithmsfor computational wave physics such as computational electromagnetics andcomputational acoustics.
