Application of the preconditioned GMRES to the Crank‐Nicolson finite‐difference time‐domain algorithm for 3D full‐wave analysis of planar circuits

Abstract

AbstractThe increase of the time step size significantly deteriorates the property of the coefficient matrix generated from the Crank‐Nicolson finite‐difference time‐domain (CN‐FDTD) method. As a result, the convergence of classical iterative methods, such as generalized minimal residual method (GMRES) would be substantially slowed down. To address this issue, this article mainly concerns efficient computation of this large sparse linear equations using preconditioned generalized minimal residual (PGMRES) method. Some typical preconditioning techniques, such as the Jacobi preconditioner, the sparse approximate inverse (SAI) preconditioner, and the symmetric successive over‐relaxation (SSOR) preconditioner, are introduced to accelerate the convergence of the GMRES iterative method. Numerical simulation shows that the SSOR preconditioned GMRES method can reach convergence five times faster than GMRES for some typical structures. © 2008 Wiley Periodicals, Inc. Microwave Opt Technol Lett 50: 1458–1463, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.23396