Compression of Far-Fields in the Fast Multipole Method via Tucker Decomposition

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.