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Adaptive integral method combined with the loose GMRES algorithm for planar structures analysis
Author(s) -
Zhuang W.,
Fan Z. H.,
Hu Y. Q.
Publication year - 2009
Publication title -
international journal of rf and microwave computer‐aided engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.335
H-Index - 39
eISSN - 1099-047X
pISSN - 1096-4290
DOI - 10.1002/mmce.20310
Subject(s) - generalized minimal residual method , basis function , mathematics , conjugate gradient method , toeplitz matrix , fast fourier transform , discretization , method of moments (probability theory) , matrix (chemical analysis) , integral equation , algorithm , planar , mathematical analysis , topology (electrical circuits) , iterative method , computer science , combinatorics , computer graphics (images) , statistics , materials science , estimator , pure mathematics , composite material
In this article, the adaptive integral method (AIM) is used to analyze large‐scale planar structures. Discretization of the corresponding integral equations by method of moment (MoM) with Rao‐Wilton‐Glisson (RWG) basis functions can model arbitrarily shaped planar structures, but usually leads to a fully populated matrix. AIM could map these basis functions onto a rectangular grid, where the Toeplitz property of the Green's function would be utilized, which enables the calculation of the matrix‐vector multiplication by use of the fast Fourier transform (FFT) technique. It reduces the memory requirement from O ( N 2 ) to O ( N ) and the operation complexity from O ( N 2 ) to O ( N log N ), where N is the number of unknowns. The resultant equations are then solved by the loose generalized minimal residual method (LGMRES) to accelerate iteration, which converges much faster than the conventional conjugate gradient method (CG). Furthermore, several preconditioning techniques are employed to enhance the computational efficiency of the LGMRES. Some typical microstrip circuits and microstrip antenna array are analyzed and numerical results show that the preconditioned LGMRES can converge much faster than conventional LGMRES. © 2008 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2009.