Numerical simulation of microstrip circuits using unconditional stable CN-FDTD method combined with preconditioned GMRES

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 paper 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 three times faster than GMRES for this structure.