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Wavelet‐based Methods for Multirate PDAEs
Author(s) -
Winkler Renate
Publication year - 2010
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201010210
Subject(s) - wavelet , piecewise , computer science , signal (programming language) , algorithm , interval (graph theory) , ansatz , mathematics , mathematical analysis , combinatorics , artificial intelligence , mathematical physics , programming language
We present an adaptive envelope method for the transient simulation of problems with widely separated time scales. Typical applications are circuits where a periodic carrier signal is modulated by a slower signal. The presented method is specifically designed to work even in the case of steep gradients due to digital‐like signal structures. Using different independent variables for the slow and the fast time scales the original system is transformed to a hyperbolic multi‐rate differential‐algebraic system, from which the solution of the original system can be reconstructed. After discretising the slow time scale a periodic boundary value problems in the fast time scale has to be solved for each slow time step. These are solved by wavelet collocation using piecewise linear ansatz‐functions. To adapt the grid the solution is represented in terms of a hierarchical set of biorthogonal wavelets to detect the areas with rapidly changing solutions and to coarse or refine the grid. The performance of the method is illustrated by a circuit example. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)