Numerical Techniques for Solving Multirate Partial Differential Algebraic Equations
In electric circuits, signals often include widely separated frequencies. Thus numerical simulation demands a large amount of computational work, since the fastest rate restricts the integration step size. A multidimensional signal model yields an alternative approach, where each time scale is given its own variable. Consequently, underlying differential algebraic equations (DAEs) change into a PDAE model, the multirate partial differential algebraic equations (MPDAEs). A time domain method to determine multiperiodic MPDAE solutions is presented. According discretisations rest upon the specific information transport in the MPDAE system along characteristic curves. In contrast, general time domain methods produce unphysical couplings. Hence enormous savings in computational time and memory arise in the linear algebra part. This technique is applied to driven oscillators including two periodic time scales as well as to oscillators, where one periodic rate is forced and the other is autonomous.
KeywordsDifferential Algebraic Equation Ordinary Differential Equation System Information Transport Drive Oscillator Integration Step Size
Unable to display preview. Download preview PDF.
- 2.Brachtendorf, H. G.; Laur, R.: Multi-rate PDE methods for high Q oscillators. In: Mastorakis, N. (ed.): Problems in Modern Applied Mathematics. CSCC 2000, MCP 2000, MCME 2000 Multi-conference, Athens, July 2000. World Scientific 2000, pp. 391–398.Google Scholar
- 4. Günther, M.; Rentrop, P.: The differential-algebraic index concept in electric circuit simulation. Z. angew. Math. Mech., Berlin 76 (1996) Suppl. 1, pp. 91–94.Google Scholar
- 7. Kundert, K. S.; Sangiovanni-Vincentelli, A.; Sugawara, T.: Techniques for finding the periodic steady-state response of circuits. In: ai]Ozawa, T. (ed.): Analog methods for computer-aided circuit analysis and diagnosis, New York (1988), pp. 169–203.Google Scholar
- 8. Pulch, R.; Günther, M.: A method of characteristics for solving multirate partial differential equations in radio frequency application. To appear in: Appl. Num. Math.Google Scholar
- 9.Pulch, R.: PDE techniques for finding quasi-periodic solutions of oscillators. Preprint 01/09, IWRMM, University Karlsruhe (2001).Google Scholar
- 10.Pulch, R.: A finite difference method for solving multirate partial differential algebraic equations. Preprint 02/04, IWRMM, University Karlsruhe (2002).Google Scholar
- 12. Narayan, O.; Roychowdhury, R.: Multi-time simulation of voltage-controlled oscillators. Proceedings Design Automation Conference, 1999, pp. 629–634.Google Scholar