一种多层不完全LU分解预处理方法在合元极技术中的应用

Application of Multilevel Inverse-Based ILU Preconditioning Approach to Hybrid FE/BI/MLFMA for 3D Scattering

本文将一种多层不完全LU分解预处理方法应用于合元极技术(即混合有限元、边界元、快速多极子技术).理论和数值实验表明,此种预处理方法能大大减少合元极技术的内存需求,同时兼有极高的计算效率.本文首先给出此种预处理方法的构造方式和实施步骤,接着对此种预处理方法在合元极技术中的数值性能进行了理论和数值实验的分析研究;最后,本文计算了几种电大尺寸复杂目标的散射,以展示应用了此种预处理方法的合元极技术的计算能力.

A novel multilevel inverse-based ILU （MIB-ILU） preconditioning approach is applied to the hybrid finite-element/boundary-integral/multilevel fast mullipole algorithm （FE/BI/MLFMA） for 3D scattering problems. Unlike the traditional ILU precoaditioning technique, this MIB-ILU approach borrows the concept of the algebraic multi-grid method （AMG） to construct an algebraic multilevel recursive ILU precondifioning framework. Moreover, a new version of ILU factorizafion and an inverse-based dropping strategy are employed to improve the robust of the preconditioning approach. The numerical performance of the MIB-ILU approach is studied.It is demonstrated that this approach exhibits high efficiency in memory and CPU time. Then,the posed MIB-ILU approach is applied to the hybrid FE/BI/MLFMA method. A variety of numerical experiments are carded 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.