Extend two-step preconditioning technique for the Crank-Nicolson finite-difference time-domain method to analyze the 3D microwave circuits

Abstract

The increase of the time-step size significantly deteriorates the property of the coefficient matrix generated from the Crank-Nicolson finite-difference time-domain method. As a result, the convergence of classical iterative methods, such as generalized minimal residual method (GMRES) would be substantially slowed down. The main purpose of this article is to show that the two-step preconditioner can greatly accelerate the convergence of the iterative method, such as GMRES. Numerical simulations show that this two-step preconditioned GMRES iterative method has a faster convergence speed than those methods when the preconditioner is used alone.

Applications of a Three-Dimensional FDTD Method With Weakly Conditional Stability to the Analysis of Microstrip Filters With Fine Scale Structures

“…To eliminate the CFL constraint on the time step size in conventional FDTD, some unconditionally stable implicit methods, such as ADI-FDTD method [2][3][4], Crank-Nicloson FDTD (CN-FDTD) method [5], are advanced. These implicit methods have been proved to be very computationally efficient when the time step exceeding the CFL condition, but they also have restrictions.…”