  Characteristic mode (CM) analysis poses challenges in computational
electromagnetics (CEM) as it calls for efficient solutions of dense generalized
eigenvalue problems (GEP). Multilevel fast multipole algorithm (MLFMA) can
greatly reduce the computational complexity and memory cost for matrix-vector
product operations, which is powerful in iteratively solving large scattering
problems. In this article, we demonstrate that MLFMA can be easily incorporated
into the implicit restarted Arnoldi (IRA) method for the calculation of CMs,
where MLFMA with the sparse approximate inverse (SAI) preconditioning technique
is employed to accelerate the construction of Arnoldi vectors. This work paves
the way of CM analysis for large-scale and complicated three-dimensional
($3$-D) objects with limited computational resources.
