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Conference Paper: Saving Memory With Vector Addition Theorem
Title  Saving Memory With Vector Addition Theorem 

Authors  
Issue Date  2009 
Publisher  Progress In Electromagnetics Research Symposium 
Citation  Progress In Electromagnetics Research Symposium, Beijing, China, 2327 March 2009, p. 845 How to Cite? 
Abstract  Abstract— In the lowfrequency fast multipole algorithm (LFFMA), instead of the traditional
factorization of the scalar Green’s function using scalar addition theorem, we adopt the vector
addition theorem for the factorization of the dyadic Green’s function to realize the memory
savings. Recently, the factorization and the diagonalization of the dyadic Green’s function is
possible based entirely on the use of vector wave functions and vector addition theorem [1, 2]. In
this work, we shall validate this factorization and diagonalization. This factorization can be used
to develop a vector mixedform fast multipole algorithm for the dyadic Green’s function [3].
By using the new integral operator factorization with vector addition theorem and looptree
basis, every element of the matrix resulting from applying the method of moments (MoM) to the
electric field integral equation (EFIE) can be expressed by the radiation patterns, translator and
receiving patterns. The storage of the radiation patterns and receiving patterns can be reduced
by 25 percent compared with the one when the factorization of the scalar Green’s function is
used. In addition, since the elements of the new translator can be calculated on the fly from
the elements of the translator given by the factorization of the scalar Green’s function using
scalar addition theorem, we need only to store the latter. Therefore the whole memory usage is
reduced and the memory saving is important for the largescale computation with finite computer
resource.
REFERENCES
1. Chew, W. C., “Vector addition theorem and its diagonalization,” Comm. Comput. Phys.,
Vol. 3, No. 2, 330–341, Feb. 2008.
2. He, B. and W. C. Chew, “Diagonalizations of vector and tensor addition theorems,” Comm.
Comput. Phys., Vol. 4, No. 4, 797–819, 2008.
3. Jiang, L. J. and W. C. Chew, “A mixedform fast multipole algorithm,” IEEE Trans. Antennas
Propag., Vol. 53, No. 12, 4145–4156, Dec. 2005. 
Persistent Identifier  http://hdl.handle.net/10722/61985 
DC Field  Value  Language 

dc.contributor.author  Liu, Y  en_HK 
dc.contributor.author  Chew, WC  en_HK 
dc.date.accessioned  20100713T03:51:32Z   
dc.date.available  20100713T03:51:32Z   
dc.date.issued  2009  en_HK 
dc.identifier.citation  Progress In Electromagnetics Research Symposium, Beijing, China, 2327 March 2009, p. 845   
dc.identifier.uri  http://hdl.handle.net/10722/61985   
dc.description.abstract  Abstract— In the lowfrequency fast multipole algorithm (LFFMA), instead of the traditional factorization of the scalar Green’s function using scalar addition theorem, we adopt the vector addition theorem for the factorization of the dyadic Green’s function to realize the memory savings. Recently, the factorization and the diagonalization of the dyadic Green’s function is possible based entirely on the use of vector wave functions and vector addition theorem [1, 2]. In this work, we shall validate this factorization and diagonalization. This factorization can be used to develop a vector mixedform fast multipole algorithm for the dyadic Green’s function [3]. By using the new integral operator factorization with vector addition theorem and looptree basis, every element of the matrix resulting from applying the method of moments (MoM) to the electric field integral equation (EFIE) can be expressed by the radiation patterns, translator and receiving patterns. The storage of the radiation patterns and receiving patterns can be reduced by 25 percent compared with the one when the factorization of the scalar Green’s function is used. In addition, since the elements of the new translator can be calculated on the fly from the elements of the translator given by the factorization of the scalar Green’s function using scalar addition theorem, we need only to store the latter. Therefore the whole memory usage is reduced and the memory saving is important for the largescale computation with finite computer resource. REFERENCES 1. Chew, W. C., “Vector addition theorem and its diagonalization,” Comm. Comput. Phys., Vol. 3, No. 2, 330–341, Feb. 2008. 2. He, B. and W. C. Chew, “Diagonalizations of vector and tensor addition theorems,” Comm. Comput. Phys., Vol. 4, No. 4, 797–819, 2008. 3. Jiang, L. J. and W. C. Chew, “A mixedform fast multipole algorithm,” IEEE Trans. Antennas Propag., Vol. 53, No. 12, 4145–4156, Dec. 2005.   
dc.language  eng  en_HK 
dc.publisher  Progress In Electromagnetics Research Symposium   
dc.relation.ispartof  Progress In Electromagnetics Research Symposium Abstracts   
dc.title  Saving Memory With Vector Addition Theorem  en_HK 
dc.type  Conference_Paper  en_HK 
dc.identifier.email  Liu, Y: liuyang@eee.hku.hk  en_HK 
dc.identifier.email  Chew, WC: wcchew@hku.hk  en_HK 
dc.identifier.authority  Chew, WC=rp00656  en_HK 
dc.identifier.hkuros  150496  en_HK 