Initial conditions and robust Newton-Raphson for harmonic balance analysis of free-running oscillators

J.E. Virtanen, E.J.W. Maten, ter, M. Honkala, M. Hulkkonen

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Abstract

Poor initial conditions for Harmonic Balance (HB) analysis of free-running oscillators may lead to divergence of the direct Newton-Raphson method or may prevent to find the solution within an optimization approach. We exploit time integration to obtain estimates for the oscillation frequency and for the oscillator solution. It also provides an initialization of the probe voltage. Next we describe new techniques from bordered matrices and eigenvalue methods to improve Newton methods for Finite Difference techniques in the time domain as well as for Harmonic Balance. The method gauges the phase shift automatically. No assumption about the range of values of the Periodic Steady State solution is needed.
Original languageEnglish
Title of host publicationProgress in Industrial Mathematics at ECMI 2010
EditorsM. Günther, A. Bartel, M. Brunk, S. Schoeps, M. Striebel
Place of PublicationBerlin
PublisherSpringer
Pages29-35
ISBN (Print)978-3-642-25099-6
DOIs
Publication statusPublished - 2012
Event16th European Conference on Mathematics for Industry (ECMI 2010), July 26-30, 2010, Wuppertal, Germany - Wuppertal, Germany
Duration: 26 Jul 201030 Jul 2010

Publication series

NameMathematics in Industry
Volume17
ISSN (Print)1612-3956

Conference

Conference16th European Conference on Mathematics for Industry (ECMI 2010), July 26-30, 2010, Wuppertal, Germany
Abbreviated titleECMI 2010
CountryGermany
CityWuppertal
Period26/07/1030/07/10

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    Virtanen, J. E., Maten, ter, E. J. W., Honkala, M., & Hulkkonen, M. (2012). Initial conditions and robust Newton-Raphson for harmonic balance analysis of free-running oscillators. In M. Günther, A. Bartel, M. Brunk, S. Schoeps, & M. Striebel (Eds.), Progress in Industrial Mathematics at ECMI 2010 (pp. 29-35). (Mathematics in Industry; Vol. 17). Springer. https://doi.org/10.1007/978-3-642-25100-9_4