  Tensor decomposition methodologies are proposed to reduce the memory
requirement of translation operator tensors arising in the fast multipole
method-fast Fourier transform (FMM-FFT)-accelerated surface integral equation
(SIE) simulators. These methodologies leverage Tucker, hierarchical Tucker
(H-Tucker), and tensor train (TT) decompositions to compress the FFT'ed
translation operator tensors stored in three-dimensional (3D) and
four-dimensional (4D) array formats. Extensive numerical tests are performed to
demonstrate the memory saving achieved by and computational overhead introduced
by these methodologies for different simulation parameters. Numerical results
show that the H-Tucker-based methodology for 4D array format yields the maximum
memory saving while Tucker-based methodology for 3D array format introduces the
minimum computational overhead. For many practical scenarios, all methodologies
yield a significant reduction in the memory requirement of translation operator
tensors while imposing negligible/acceptable computational overhead.
