Abstract
Widely seperated time scales appear in many electronic circuits, making analysis with the usual numerical methods very difficult and costly. In this article we present a quasilinear system of partial differential equations (PDE) of first order, where the time scales are treated seperately. The PDE corresponds to the system of differential-algebraic equations (DAE) describing the electronic circuit in the sense that the solution of the PDE restricted to one of its characteristics is the solution of the DAE. This embedding method is described in a general setting. Hence it can be used for various applications in circuit simulation.
Since generalized quasiperiodic functions, which are presented here, conceptualize physical properties, they have a basic significance for the embedding method.
Theoretical investigations are presented as well as new approaches for numerical methods based on the connection between the PDE and the DAE.
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Lang, B., Bunse-Gerstner, A., Lemanczyk, H., Brachtendorf, H.G., Laur, R. (2004). An Embedding Method for High Frequency Circuits. In: Schilders, W.H.A., ter Maten, E.J.W., Houben, S.H.M.J. (eds) Scientific Computing in Electrical Engineering. Mathematics in Industry, vol 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55872-6_14
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DOI: https://doi.org/10.1007/978-3-642-55872-6_14
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