A Low Frequency Vector Fast Multipole Algorithm with Vector Addition Theorem (Communications in Computational Physics, 2010)
In the low-frequency fast multipole algorithm (LF-FMA) [19, 20], scalar additiontheorem has been used to factorize the scalar Green's function. Instead of thistraditional 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'sfunction to realize memory savings. We are to validate this factorization and useit to develop a low-frequency vector fast multipole algorithm (LF-VFMA) for low-frequencyproblems. In the calculation of non-near neighbor interactions, the storageof translators in the method is larger than that in the LF-FMA with scalar additiontheorem. Fortunately it is independent of the number of unknowns. Meanwhile, thestorage 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 ofthis part. In this method, the storage of radiation and receiving patterns can be reducedby 25 percent compared with the LF-FMA.