A fast wavelet collocation method for high-speed VLSI circuit simulation

Adaptive Wavelet-Based Method for Simulation of Electronic Circuits

“…This permits the fast computation of function values, derivatives and integrals, which is essential for the efficient numerical solution of a nonlinear problem as given in (4) (see also [25,26]). Spline wavelets have been already used for circuit simulation [27]. However, here we use a completely new approach based on spline wavelets from [22].…”

“…Today wavelet-based algorithms are already in productive use in a broad range of applications [6][7][8][9][10][11][12][13], such as image and signal compression (JPEG2000 standard, FBI fingerprints database), speech recognition, numerical analysis (solving operator equations, boundary value problems), stochastics, smoothing/denoising data, physics (molecular dynamics, geophysics, turbulence), medicine (heart-rate and ECG analysis, DNA analysis) to name just a few. Recent approaches [14][15][16][17][18] to the problem of multirate envelope simulation indicate that wavelets could also be used to address the qualitative challenge by Kai Bittner University of Applied Science of Upper Austria, 4232 Hagenberg, Austria, e-mail: kai.bittner@fh-hagenberg.at Emira Dautbegovic Infineon Technologies AG, 81726 Munich, Germany, e-mail: Emira.Dautbegovic@infineon.com a development of novel wavelet-based circuit simulation techniques capable of an efficient simulation of mixed analog-digital circuits [19].…”

A wavelet balance approach for steady-state analysis of nonlinear circuits

“…Equations (1) to (6), are similar to those illustrated in [16] and [17]. But for steady-state response, the state variables X(l) should further satisfy the two-point boundary constraint…”

“…; M g, are wavelet basis functions, and M is the total number of basis functions that have been employed. The wavelet basis functions can be constructed by many means [13], but in this paper, we prefer to use the basis functions in [16], [17] because they are proved to have a high convergence rate O(h 4 ), where h is the step length [16], [17]. Substituting (4) into (3), we get…”

“…Assume the steady-state response period of the circuit is T , and the Sobolev space H 2 [0; L] is studied for wavelet expansion. Usually, because the period T doesn't satisfy some specific conditions needed for wavelets, for example, L 4 corresponding to the wavelet basis functions in [16], [17], a scaling operation should be applied to map the…”