  This paper presents a new fast power series solution method to solve the
Hierarchal Method of Moment(MoM) matrix for a large complex,perfectly electric
conducting (PEC) 3D structures. The proposed power series solution converges in
just two iterations which is faster than the conventional fast solver-based
iterative solution. The method is purely algebraic in nature and, as such
applicable to existing conventional methods. The method uses regular fast
solver Hierarchal Matrix (H-Matrix) and can also be applied to Multilevel Fast
Multipole Method Algorithm(MLFMA). In the proposed method, we use the scaling
of the symmetric near-field matrix to develop a diagonally dominant overall
matrix to enable a power series solution. Left and right block scaling
coefficients are required for scaling near-field blocks to diagonal blocks
using Schur's complement method. However,only the right-hand scaling
coefficients are computed for symmetric near-field matrix leading to saving of
computation time and memory. Due to symmetric property, the left side-block
scaling coefficients are just the transpose of the right-scaling blocks. Next,
the near-field blocks are replaced by scaled near-field diagonal blocks. Now
the scaled near-field blocks in combination with far-field and scaling
coefficients are subjected to power series solution terminating after only two
terms. As all the operations are performed on the near-field blocks, the
complexity of scaling coefficient computation is retained as O(N). The power
series solution only involves the matrix-vector product of the far-field,
scaling coefficients blocks, and inverse of scaled near-field blocks. Hence,
the solution cost remains O(NlogN). Several numerical results are presented to
validate the efficiency and robustness of the proposed numerical method.
