A mixed-particle scheme for low-frequency fast multipole algorithm for multi-region problems

At low frequencies, loop-tree decomposition is necessary for surface integral equation method. A new loop-loop interaction scheme is implemented to obviate the need for static subtraction. For multi-region problems, in each region, a mixed-particle (mixed basis) scheme is implemented so that only one tree is necessary. To further reduce the cost, a new arrangement of radiation/receiving patterns is proposed so that most of the matrix-vector-product (MVP) procedure is re-used.