A fast wavelet collocation method for high-speed circuit simulation

The advance of very large scale integration (VLSI) systems has been continuously challenging today´s circuit simulators in both computational speed and stability. This paper presents a novel approach, the fast wavelet collocation method (FWCM), for high-speed circuit simulation. FWCM has the following properties: (1) it works in the time domain, so that circuit nonlinearity can be handled and numerical accuracy can be well controlled, unlike the method of working in the frequency domain where numerical error may become uncontrolled during the inverse Laplace transform; (2) the wavelet property of localization in both the time and frequency domains makes a uniform approximation possible, which is generally not found in time-marching methods; (3) it is very effective in treating singularities which often develop in high-speed ICs; (4) an adaptive scheme exists; and (5) it has an O(h⁴) convergence rate, where h is the step length. Numerical experiments further demonstrated the promising features of FWCM in high-speed IC simulation