  Tucker decomposition is proposed to reduce the memory requirement of the
far-fields in the fast multipole method (FMM)-accelerated surface integral
equation simulators. It is particularly used to compress the far-fields of FMM
groups, which are stored in three-dimensional (3-D) arrays (or tensors). The
compressed tensors are then used to perform fast tensor-vector multiplications
during the aggregation and disaggregation stages of the FMM. For many practical
scenarios, the proposed Tucker decomposition yields a significant reduction in
the far-fields' memory requirement while dramatically accelerating the
aggregation and disaggregation stages. For the electromagnetic scattering
analysis of a 30{\lambda}-diameter sphere, it reduces the memory requirement of
the far-fields more than 87% while it expedites the aggregation and
disaggregation stages by a factor of 15.8 and 15.2, respectively, where
{\lambda} is the wavelength in free space.
