On the multi-level splitting of finite element spaces
Numerische Mathematik
Wavelet methods for fast resolution of elliptic problems
SIAM Journal on Numerical Analysis
A general framework of compactly supported splines and wavelets
Journal of Approximation Theory
Uniform high-order spectral methods for one- and two-dimensional Euler equations
Journal of Computational Physics
An introduction to wavelets
Orthonormal wavelets, analysis of operators, and applications to numerical analysis
Wavelets: a tutorial in theory and applications
Computer-Aided Analysis of Electronic Circuits: Algorithms and Computational Techniques
Computer-Aided Analysis of Electronic Circuits: Algorithms and Computational Techniques
ADAPTIVE WAVELET COLLOCATION METHODS FOR INITIAL VALUE BOUNDARY PROBLEMS OF NONLINEAR PDE''S
ADAPTIVE WAVELET COLLOCATION METHODS FOR INITIAL VALUE BOUNDARY PROBLEMS OF NONLINEAR PDE''S
ON THE DIFFERENTIATION MATRIX FOR DAUBECHIES-BASED WAVELETS ON AN INTERVAL
ON THE DIFFERENTIATION MATRIX FOR DAUBECHIES-BASED WAVELETS ON AN INTERVAL
Microelectronic Engineering
Design and verification of high-speed VLSI physical design
Journal of Computer Science and Technology
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This paper presents a fast wavelet collocation method (FWCM) for high- speed circuit simulation. The FWCM has the following properties: (1) It works in the time domain, so that the circuit nonlinearity can be handled, and the accuracy of the result can be well controlled, unlike the method working in the frequency domain where the numerical error may get uncontrolled during the inverse Laplace transform; (2) The wavelet property of localization in both time and frequency domains makes a uniform approximation possible, which is generally not found in the time marching methods; (3) It is very effective in treating the singularities often developed in high-speed ICs due to the property of the wavelets; (4) Calculation of derivatives at all collocation points is optimal and takes O(n\log n), where n is the number of collocation points; (5) An adaptive scheme exists; and (6) It has an O(h^4) convergence rate while the most existing methods only have an O(h^2) convergence rate, where h is the step length. Numerical experiments further demonstrated the promising features of FWCM in high-speed IC simulation.