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Wavelet‐based Adaptive Grids for the Simulation of Multirate Partial Differential‐Algebraic Equations
Author(s) -
Bartel Andreas,
Knorr Stephanie
Publication year - 2006
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200610011
Subject(s) - wavelet , transformation (genetics) , signal (programming language) , limit (mathematics) , filter (signal processing) , partial differential equation , algebraic number , computer science , grid , control theory (sociology) , differential (mechanical device) , digital filter , capacitor , mathematics , topology (electrical circuits) , mathematical analysis , physics , engineering , voltage , geometry , electrical engineering , biochemistry , chemistry , control (management) , combinatorics , artificial intelligence , computer vision , gene , programming language , thermodynamics
We present an adaptive method to solve biperiodic problems in chip design with widely separated time scales and steep gradients due to digital‐like signal structures. Motivated from the example of the switched capacitor filter, we explain the multidimensional signal model and the transformation of network equations to the hyperbolic multirate differential‐algebraic system. Then adapted hat‐wavelets are introduced to detect the steep gradients. In this way, an adaptive grid is defined for the efficient application of a finite difference method to solve the limit cycle problem. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)