Parallel FE-BI-MLFMA for scattering by extremely large targets with cavities

The finite element-boundary integral-multilevel fast multipole algorithm (FE-BI-MLFMA) has shown to be very general and powerful for 3D scattering. To efficiently model cavity targets, a concave FE-BI-MLFMA is presented in this paper, which can significantly reduce the dispersion error from the FEM and improve the efficiency of FE-BI-MLFMA especially for nonuniform cavities. To eliminate the problem of slow convergence caused by concave surface, an efficient preconditioner based on the sparse approximate inverse (SAI) is constructed in this paper. Numerical experiments demonstrate the accuracy and efficiency of this SAI-preconditioned concave FE-BI-MLFMA for nonuniform deep and large cavites. Furthermore, the FE-BI-MLFMA is parallelized and has successfully compute the scattering from a conducting sphere with 1000 -wavelength diameter using more than 400 million unknowns.