Commun. Comput. Phys., 8 (2010), pp. 1183-1207.


A Low Frequency Vector Fast Multipole Algorithm with Vector Addition Theorem

Yang G. Liu 1, Weng Cho Chew 2*

1 Department of Electrical and Electronic Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong.
2 Department of Electrical and Electronic Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong. On Leave of Absence from the University of Illinois, Urbana-Champaign.

Received 7 December 2009; Accepted (in revised version) 24 March 2010
Available online 23 June 2010
doi:10.4208/cicp.071209.240310a

Abstract

In the low-frequency fast multipole algorithm (LF-FMA) [19, 20], scalar addition theorem has been used to factorize the scalar Green's function. Instead of this traditional factorization of the scalar Green's function by using scalar addition theorem, we adopt the vector addition theorem for the factorization of the dyadic Green's function to realize memory savings. We are to validate this factorization and use it to develop a low-frequency vector fast multipole algorithm (LF-VFMA) for low-frequency problems. In the calculation of non-near neighbor interactions, the storage of translators in the method is larger than that in the LF-FMA with scalar addition theorem. Fortunately it is independent of the number of unknowns. Meanwhile, the storage of radiation and receiving patterns is linearly dependent on the number of unknowns. Therefore it is worthwhile for large scale problems to reduce the storage of this part. In this method, the storage of radiation and receiving patterns can be reduced by 25 percent compared with the LF-FMA.

AMS subject classifications: 65R20, 78A45, 78M16
PACS: 02.70.Pt, 03.50.De, 89.20.Ff
Key words: LF-VFMA, electromagnetics, low frequency, loop-tree basis, memory saving, surface integral equation, vector addition theorem.

*Corresponding author.
Email: liuyang@eee.hku.hk (Y. G. Liu), wcchew@hku.hk (W. C. Chew)
 

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