Solving problems with over one billion unknowns by the MLFMA

Using OpenMP to further accelerate the pure MPI parallel MLFMA, an efficient and flexible parallel multilevel fast multipole algorithm (MPI-OpenMP-MLFMA) is proposed. Compared with previous MPI parallel schemes, the MPI-OpenMP-MLFMA improves the load-balance and scalability greatly. The computational capability of the proposed MPI-OpenMP-MLFMA is demonstrated by computing scattering from two extremely large targets: a sphere with a diameter of 1200 wavelengths, modeled by 1,063,706,700 unknowns, and an airplane model with the largest dimension of 1600 wavelengths, involving 288,151,344 unknowns.