Parallelization and Acceleration Scheme of Multilevel Fast Multipole Method

The iterative methods such as BiCGStab for solving electromagnetic field integer equations have a complexity of O(N
²
), which can be reduced to O(N logN) by multilevel fast multipole method (MLFMM). For large scale problems, MLFMM should be parallelized, and the iterative convergence can be accelerated by preconditioners such as incomplete inverse triangular factorization preconditioner. The interpolation based on spherical harmonic transform at each level of MLFMMpsilas octree can be further accelerated by FFT. Based on this acceleration scheme tested on distributed cluster, the results show this algorithm is feasible.