### 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 language | English |
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Title of host publication | Progress in Industrial Mathematics at ECMI 2010 |

Editors | M. Günther, A. Bartel, M. Brunk, S. Schoeps, M. Striebel |

Place of Publication | Berlin |

Publisher | Springer |

Pages | 29-35 |

ISBN (Print) | 978-3-642-25099-6 |

DOIs | |

Publication status | Published - 2012 |

Event | 16th European Conference on Mathematics for Industry (ECMI 2010), July 26-30, 2010, Wuppertal, Germany - Wuppertal, Germany Duration: 26 Jul 2010 → 30 Jul 2010 |

### Publication series

Name | Mathematics in Industry |
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Volume | 17 |

ISSN (Print) | 1612-3956 |

### Conference

Conference | 16th European Conference on Mathematics for Industry (ECMI 2010), July 26-30, 2010, Wuppertal, Germany |
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Abbreviated title | ECMI 2010 |

Country | Germany |

City | Wuppertal |

Period | 26/07/10 → 30/07/10 |

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## Cite this

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