微分求积法求解高速大规模集成电路互连线的瞬态响应

Application of Differential Quadrature Method to the Transient Simulation of Interconnects in High Speed VLSI

本文将微分求积法(DQ方法)应用于高速大规模集成电路互连线的瞬态模拟。DQ方法是一种直接的数值方法 ,与差分和有限元法相比 ,它的计算量可以大大降低 ,且具有较高的精度。DQ方法的主要思想是将某坐标方向上的微分算子用该方向上一系列适当的离散点的函数值加权逼近 ,将偏微分方程化为常微分方程或代数方程求解。DQ方法用于高速大规模集成电路互连线系统的瞬态模拟非常有效 。

The numerical technique of differential quadrature (DQ)method is employed for transient simulation of the interconnect systems in high speed VLSI.The DQ method is first introduced by Bellman and his associates for the solution of linear and non linear partial differential equations.It is based on the representation of the derivative operator in a discrete coordinates .The DQ method can lead to accurate results with relatively small computational effort.It can be applied to extensive cases in the problems of transient simulation of lossy transmission lines.Numerical results show that moderately accurate solutions can be derived rapidly.