Volume 8, Issue 5
A Low Frequency Vector Fast Multipole Algorithm with Vector Addition Theorem

Yang G. Liu & Weng Cho Chew

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

Published online: 2010-08

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  • 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.

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@Article{CiCP-8-1183, author = {}, title = {A Low Frequency Vector Fast Multipole Algorithm with Vector Addition Theorem}, journal = {Communications in Computational Physics}, year = {2010}, volume = {8}, number = {5}, pages = {1183--1207}, 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.071209.240310a}, url = {http://global-sci.org/intro/article_detail/cicp/7612.html} }
TY - JOUR T1 - A Low Frequency Vector Fast Multipole Algorithm with Vector Addition Theorem JO - Communications in Computational Physics VL - 5 SP - 1183 EP - 1207 PY - 2010 DA - 2010/08 SN - 8 DO - http://doi.org/10.4208/cicp.071209.240310a UR - https://global-sci.org/intro/article_detail/cicp/7612.html KW - AB -

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.

Yang G. Liu & Weng Cho Chew. (2020). A Low Frequency Vector Fast Multipole Algorithm with Vector Addition Theorem. Communications in Computational Physics. 8 (5). 1183-1207. doi:10.4208/cicp.071209.240310a
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