The application of the generalized product-type method based on Bi-CG to accelerate the sparse-matrix/canonical grid method

When the sparse-matrix/canonical grid (SMCG) method is applied to analyse scattering of randomly positioned dielectric spheroids, the impedance matrix is decomposed into a strong interaction matrix and a weak interaction matrix. The strong interaction portion of the matrix-vector multiplication is computed directly as the moment method (MOM). The far-interaction portion of matrix-vector multiplication is computed indirectly using fast Fourier transforms by a Taylor series expansion of impedance matrix elements about the canonical grid point. 
However, the condition number of the impedance matrix obtained from the SMCG method becomes large compared to the one from MOM. As a result, the conjugate gradient (CG) method converges slowly. To attack such a trouble, the generalized product-type method based on Bi-CG (GPBi-CG) is used as an iterative solver in this paper. The numerical results show that the GPBi-CG method can achieve good convergence improvement compared to the other iterative methods.