Wavelet-based adaptive grids for multirate partial differential-algebraic equations

• Published in: Applied numerical mathematics 2009-03, Vol.59 (3), p.495-506
• Main Authors: Bartel, A., Knorr, S., Pulch, R.
• Format: Article
• Language: English
• Subjects: Differential-algebraic equations; Electric circuits; Exact sciences and technology; Fourier analysis; Hyperbolic systems; Mathematical analysis; Mathematics; Method of characteristics; Multirate partial differential-algebraic equations; Numerical analysis; Numerical analysis. Scientific computation; Partial differential equations, boundary value problems; Partial differential equations, initial value problems and time-dependant initial-boundary value problems; Sciences and techniques of general use; Wavelets
• ISSN: 0168-9274; 1873-5460
• DOI: 10.1016/j.apnum.2008.03.003

The mathematical model of electric circuits yields systems of differential-algebraic equations (DAEs). In radio frequency applications, a multivariate model of oscillatory signals transforms the DAEs into a system of multirate partial differential-algebraic equations (MPDAEs). Considering quasiperiodic signals, an approach based on a method of characteristics yields efficient numerical schemes for the MPDAEs in time domain. If additionally digital signal structures occur, an adaptive grid is required to achieve the efficiency of the technique. We present a strategy applying a wavelet transformation to construct a mesh for resolving steep gradients in respective signals. Consequently, we employ finite difference methods to determine an approximative solution of characteristic systems in according grid points. Numerical simulations demonstrate the performance of the adaptive grid generation, where radio frequency signals with digital structures are resolved.