The Error Control of Mixed-Form Fast Multipole Algorithm Based on the High-Order Multipole Rotation

In this letter, the mixed-form fast multipole algorithm (MF-FMA) with feasible error controllability is implemented through high-order multipole rotation that can make the translation matrices very sparse. The saving of both storage and CPU time makes it attainable to increase the number of harmonics in the middle frequency regime, thus shifting up the transition region of MF-FMA. Consequently, the broadband accuracy of the MF-FMA can be improved significantly.