A vector fast multipole algorithm for low frequency problems

Instead of the traditional factorization of the scalar Green's function by using scalar addition theorem in the low-frequency fast multipole algorithm (LF-FMA), we adopt the vector addition theorem (VAT) for the factorization of the dyadic Green's function to realize memory savings for large scale problems. We validate this factorization and use it to develop a low-frequency vector fast multipole algorithm (LF-VFMA) for low-frequency problems.