The recursive aggregate interaction matrix algorithm for multiple scatterers

The recursive aggregate interaction matrix algorithm (RAIMA) for calculating a wave scattering solution is developed. This algorithm combines the strength of both the recursive aggregate T matrix algorithm (RATMA) and the recursive interaction matrix algorithm (RIMA) that have been previously developed. The resultant algorithm is robust for scattering problems involving highly singular Green´s functions by avoiding the violation of the addition theorem. It also has reduced computational complexity for inverting the volume integral equation of scattering. The computational complexity of RAIMA is O(N^7/3) in three dimensions and O(N²) in two dimensions