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

Multilevel Fast Multipole Algorithm for Characteristic Mode Analysis