full
search.png

Search

close.png

Cancel

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

Yang G. Liu & Weng Cho Chew

DOI: 10.4208/cicp.071209.240310a

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

Published online: 2010-08

Preview Full PDF 3234 30847

Cited by

google scholar semantic scholar
Export citation
  • 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.

  • Keywords

  • AMS Subject Headings

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@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 = {

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 AU - Yang G. Liu & Weng Cho Chew 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 and Weng Cho Chew. (2010). 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
Copy to clipboard
BibteX RIS TXT
The citation has been copied to your clipboard