Application of multilevel inverse-based ILU preconditioning approach to hybrid FE/BI/MLFMA for 3D scattering

A novel multilevel inverse-based ILU (MIB-ILU) preconditioning approach is applied to the hybrid finite-element/boundary-integral/multilevel fast multipole algorithm (FE/BI/MLFMA) for 3D scattering problems. Unlike the traditional ILU preconditioning technique, this MIB-ILU approach borrows the concept of the algebraic multi-grid method (AMG) to construct an algebraic multilevel recursive ILU preconditioning framework. Moreover, a new version of ILU factorization and an inverse-based dropping strategy are employed to improve the robust of the preconditioning approach. The numerical performance of the proposed MIB-ILU approach is studied. It is demonstrated that this approach exhibits high efficiency in memory and CPU time. Then, the proposed MIB-ILU approach is applied to the hybrid FE/BI/MLFMA method. A variety of numerical experiments are carried out, demonstrating that the proposed approach offers a good compromise between robustness and efficiency, and greatly improves the computing capability of the hybrid FE/BI/MLFMA.