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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, 23-27 March 2009, p. 845 How to Cite? |
Abstract | Abstract— In the low-frequency fast multipole algorithm (LF-FMA), 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 mixed-form fast multipole algorithm for the dyadic Green’s function [3].
By using the new integral operator factorization with vector addition theorem and loop-tree
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 large-scale 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 mixed-form 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 | 2010-07-13T03:51:32Z | - |
dc.date.available | 2010-07-13T03:51:32Z | - |
dc.date.issued | 2009 | en_HK |
dc.identifier.citation | Progress In Electromagnetics Research Symposium, Beijing, China, 23-27 March 2009, p. 845 | - |
dc.identifier.uri | http://hdl.handle.net/10722/61985 | - |
dc.description.abstract | Abstract— In the low-frequency fast multipole algorithm (LF-FMA), 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 mixed-form fast multipole algorithm for the dyadic Green’s function [3]. By using the new integral operator factorization with vector addition theorem and loop-tree 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 large-scale 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 mixed-form 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 |