Numerical Techniques for Solving Multirate Partial Differential Algebraic Equations

Abstract

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.