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Multirate Partial Differential Algebraic Equations

In radio frequency (RF) applications, electric circuits produce signals exhibiting fast oscillations, whereas the amplitude and/or frequency change slowly in time. Thus, solving a system of differential algebraic equations (DAEs), which describes the circuit's transient behaviour, becomes inefficient, since the fast rate restricts the step sizes in time. A multivariate model is able to decouple the widely separated time scales of RF signals and provides an alternative approach. Consequently, a system of DAEs changes into a system of multirate partial differential algebraic equations (MPDAEs). The determination of multivariate solutions allows for the exact reconstruction of corresponding time-dependent signals. Hence, an efficient numerical simulation is obtained by exploiting the periodicities in fast time scales. On the one hand, the simulation of enveloppe-modulated signals requires the solution of initial-boundary value problems of the MPDAEs. On the other hand, the simulation of quasiperiodic signals implies multiperiodic boundary conditions only for the MPDAEs. In case of quasiperiodic signals, a method of characteristics solves the multirate model efficiently, since the system of partial differential algebraic equations exhibits a hyperbolic structure.

Publications

Referenzen
6.
Roland Pulch
Initial-boundary value problems of warped MPDAEs including minimisation criteria
Mathematics and Computers in Simulation, 79:117 -- 132
2008
5.
Julia Greb; Roland Pulch
Simulation of quasiperiodic signals via warped MPDAEs using Houben's approach
In Ciuprina, G., Editor, Scientific Computing in Electrical Engineering. Mathematics in Industry , Seite 237 -- 243.
Herausgeber: Springer, Berlin
2007
4.
Stephanie Knorr; Uwe Feldmann
Simulation of pulsed signals in MPDAE-modelled SC-circuits
In Di Bucchianico, A. and Mattheij, Robert and Peletier, M. A., Editor, Progress in Industrial Mathematics at ECMI 2004. Mathematics in Industry , Seite 159 -- 163.
Herausgeber: Springer, Berlin
2006
3.
Roland Pulch
Semidiscretisation methods for warped MPDAEs
In Anile, A. M. and Ali, Guiseppe and Mascali, Giovanni, Editor, Scientific Computing in Electrical Engineering. Mathematics in Industry , Seite 101 -- 106.
Herausgeber: Springer, Berlin
2006
2.
Roland Pulch
Warped MPDAE models with continuous phase conditions
In Di Bucchianico, A. and Mattheij, Robert and Peletier, M. A., Editor, Progress in Industrial Mathematics at ECMI 2004. Mathematics in Industry , Seite 179 -- 183.
Herausgeber: Springer, Berlin
2006
1.
Roland Pulch
Warped MPDAE models including minimisation criteria for the simulation of RF signals
Proceedings in Applied Mathematics and Mechanics , Seite 811 -- 814.
2005
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