Year: 2010
Communications in Computational Physics, Vol. 8 (2010), Iss. 5 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.071209.240310a
Communications in Computational Physics, Vol. 8 (2010), Iss. 5 : pp. 1183–1207
Published online: 2010-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 25
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Combining analytic preconditioner and Fast Multipole Method for the 3-D Helmholtz equation
Darbas, M.
Darrigrand, E.
Lafranche, Y.
Journal of Computational Physics, Vol. 236 (2013), Iss. P.289
https://doi.org/10.1016/j.jcp.2012.10.059 [Citations: 43]