@Article{CiCP-8-1183,
author = {Yang G. Liu and Weng Cho Chew},
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 = {<p style="text-align: justify;">In the low-frequency fast multipole algorithm (LF-FMA) [19, 20], scalar addition
theorem has been used to factorize the scalar Green&#39;s function. Instead of this
traditional factorization of the scalar Green&#39;s function by using scalar addition theorem,
we adopt the vector addition theorem for the factorization of the dyadic Green&#39;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.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.071209.240310a},
url = {http://global-sci.org/intro/article_detail/cicp/7612.html}
}