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Application of the preconditioned GMRES to the Crank‐Nicolson finite‐difference time‐domain algorithm for 3D full‐wave analysis of planar circuits
Author(s) -
Yang Y.,
Fan Z. H.,
Ding D. Z.,
Liu S. B.
Publication year - 2008
Publication title -
microwave and optical technology letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.304
H-Index - 76
eISSN - 1098-2760
pISSN - 0895-2477
DOI - 10.1002/mop.23396
Subject(s) - generalized minimal residual method , preconditioner , mathematics , iterative method , crank–nicolson method , convergence (economics) , algorithm , residual , numerical analysis , mathematical analysis , economics , economic growth
The 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