An effective sparse approximate inverse preconditioner for the MLFMA solution of the volume-surface integral equation

In the framework of the multilevel fast multipole algorithm (MLFMA), effective construction of the sparse approximate inverse preconditioner (SAIP) for the volume-surface integral equation (VSIE) is discussed. A high quality SAIP for the entire VSIE matrix is constructed by using the sub-matrix of the near-field interactions between the surface basis and testing functions arising from the surface integral equation alone. In addition, a simple sparse pattern selection scheme based on the geometrical information of nearby basis functions and octree regrouping strategy is proposed to enhance the efficiency of the SAIP. In contrast to the existing sparse pattern selection schemes, the proposed scheme utilizes the near-field matrix in the MLFMA more effectively with only one tuning parameter. Numerical results indicate that with the proposed scheme, both the memory usage and setup time for constructing an effective SAIP are significantly reduced without compromising the efficiency and robustness.