Low-Frequency Fast Multipole Method Based on Multiple-Precision Arithmetic

We present a low-frequency fast multipole method for the solution of three-dimensional electromagnetic problems involving small objects and their dense discretizations with respect to wavelength. The diagonalization of the Green's function is stabilized using a multiple-precision arithmetic (MPA) for accurate and efficient computations of subwavelength interactions. MPA provides a direct remedy for the low-frequency breakdown of the standard diagonalization based on plane waves, and it enables straightforward implementations for low-frequency problems.