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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. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The anisotropic media and active properties of the perfectly matched layer (PML) absorbers significantly deteriorate the finite element method (FEM) system condition and as a result, convergence of the iterative solver is substantially slowed down. To address this issue, the symmetric successive over-relaxation (SSOR) preconditioning scheme is applied to the generalized minimal residual (GMRES) for solving a large sparse and non-symmetric system of linear equations resulting from the analysis of ferrite waveguide device by use of edge-based FEM. Consequently, this preconditioned GMRES (PGMRES) approach can reach convergence ten times faster than GMRES for the typical structures. Copyright © 2004 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

A novel numerical de-embedding scheme called the short-open calibration (SOC) technique, in conjunction with the vector finite element method (FEM), has been developed to characterize two-port network of arbitrarily shaped, three-dimensional discontinuities in microwave circuits. This SOC technique is effectively implemented into the FEM for boundary truncation of the unbounded circuit structures. In such a manner, fast convergence of iterative solver for large-sparse linear matrix equations from FEM is achieved. The SOC technique is used to remove parasitic effects brought by the approximation of the impressed voltage source and also the problem of resulting consistency between the two- and three-dimensional simulations. Scattering parameters of discontinuous sections are constructed from the definition of port voltages and currents. Numerical solutions are well compared with those published in the available literatures. It is demonstrated that the features of the SOC technique are advantageous when combined with FEM for electromagnetic problems. Copyright © 2002 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]