A fast wavelet collocation method for high-speed VLSI circuit simulation
ICCAD '95 Proceedings of the 1995 IEEE/ACM international conference on Computer-aided design
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We have designed a cubic spline wavelet decomposition for the Sobolev space H^2_0I where I is a bounded interval. Based on a special ``point-wise orthogonality'''' of the wavelet basis functions, a fast Discrete Wavelet Transform (DWT) is constructed. This DWT transform will map discrete samples of a function to its wavelet expansion coefficients in Q(N log N) operations. Using this transform, we propose a collocation method for the initial value boundary problem of nonlinear PDE''s. Then, we test the efficiency of the DWT transform and apply the collocation method to solve linear and nonlinear PDE''s.