A paralleled fast multipole algorithm based on nystrom discretization

The fast multipole algorithm (FMA) has been thought of as one of top ten algorithms in science and engineering in the 20th century and its multilevel variant (MLFMA) was first proposed in electromagnetics. The memory usage and CPU time for solving a dense matrix equation iteratively are of O(N
²
) complexity, where N is the number of unknowns, and this cost usually prevents one from solving large-scale problems. The MLFMA can diminish the cost to a level of O(N logN) by accelerating matrix-vector multiplications in iterative solvers, greatly enhancing the capability of solving large problems.