Initial-boundary value problems of warped MPDAEs including minimisation criteria

Electric circuits, which produce oscillations at widely separated time scales, cause a huge computational effort in a numerical simulation of the mathematical model based on differential-algebraic equations (DAEs). Alternatively, a multidimensional signal model yields a description via multirate par...

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Bibliographic Details
Published in:Mathematics and computers in simulation 2008-11, Vol.79 (2), p.117-132
Main Author: Pulch, R.
Format: Article
Language:English
Subjects:
Frequency modulation
Initial-boundary value problem
Method of lines
Multirate partial differential-algebraic equation
Variational calculus
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Summary:Electric circuits, which produce oscillations at widely separated time scales, cause a huge computational effort in a numerical simulation of the mathematical model based on differential-algebraic equations (DAEs). Alternatively, a multidimensional signal model yields a description via multirate partial differential-algebraic equations (MPDAEs). Initial-boundary value problems of the MPDAE system reproduce solutions of the underlying DAE system. In case of frequency modulation, an additional function occurs in the MPDAE model, which represents a degree of freedom in the multivariate description of the signals. We present two minimisation strategies, which are able to identify the additional parameters such that the resulting solutions exhibit an elementary structure. Thus numerical schemes can apply relatively coarse grids and an efficient simulation is achieved.
ISSN:0378-4754
1872-7166
DOI:10.1016/j.matcom.2007.10.006