Error Control of MLFMA within a Multiple-Precision Arithmetic Framework

We present a new error control scheme that provides the truncation numbers as well as the required digits of machine precision for the multilevel fast multipole algorithm (MLFMA). The proposed method is valid for all frequencies, whereas the previous studies on error control are valid only for high-frequency problems. When combined with a multiple-precision arithmetic framework, the proposed method can be used to solve low-frequency problems that would otherwise experience overflow issues. Numerical results in the form of optimal truncation numbers and machine precisions for a variety of box sizes and desired relative error thresholds are presented and compared with the results available in the literature.