Steady state calculation of oscillators using continuation methods

H. G. Brachtendorf; S. Lampe; R. Laur; R. Melville; R. Feldmann

doi:10.1109/DATE.2002.998497

Steady state calculation of oscillators using continuation methods

H. G. Brachtendorf, S. Lampe, R. Laur, R. Melville, R. Feldmann

Research output: Contribution to journal › Conference article › peer-review

2 Citations (Scopus)

Abstract

Shooting, finite difference or Harmonic Balance techniques in conjunction with Newton's method are widely employed for the numerical calculation of limit cycles of oscillators. The resulting set of nonlinear equations are normally solved by damped Newton's method. In some cases however divergence occurs when the initial estimate of the solution is not close enough to the exact one. A two-dimensional homotopy method is presented in this paper which overcomes this problem. The resulting linear set of equations employing Newton's method is under-determined and is solved in a least squares sense for which a rigorous mathematical basis can be derived.

Original language	English
Article number	998497
Pages (from-to)	1139
Number of pages	1
Journal	Proceedings -Design, Automation and Test in Europe, DATE
DOIs	https://doi.org/10.1109/DATE.2002.998497
Publication status	Published - 2002
Externally published	Yes
Event	2002 Design, Automation and Test in Europe Conference and Exhibition, DATE 2002 - Paris, France Duration: 4 Mar 2002 → 8 Mar 2002

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10.1109/DATE.2002.998497

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AU - Brachtendorf, H. G.

AU - Lampe, S.

AU - Laur, R.

AU - Melville, R.

AU - Feldmann, R.

PY - 2002

Y1 - 2002

N2 - Shooting, finite difference or Harmonic Balance techniques in conjunction with Newton's method are widely employed for the numerical calculation of limit cycles of oscillators. The resulting set of nonlinear equations are normally solved by damped Newton's method. In some cases however divergence occurs when the initial estimate of the solution is not close enough to the exact one. A two-dimensional homotopy method is presented in this paper which overcomes this problem. The resulting linear set of equations employing Newton's method is under-determined and is solved in a least squares sense for which a rigorous mathematical basis can be derived.

AB - Shooting, finite difference or Harmonic Balance techniques in conjunction with Newton's method are widely employed for the numerical calculation of limit cycles of oscillators. The resulting set of nonlinear equations are normally solved by damped Newton's method. In some cases however divergence occurs when the initial estimate of the solution is not close enough to the exact one. A two-dimensional homotopy method is presented in this paper which overcomes this problem. The resulting linear set of equations employing Newton's method is under-determined and is solved in a least squares sense for which a rigorous mathematical basis can be derived.

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M3 - Conference article

AN - SCOPUS:16244417612

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JO - Proceedings -Design, Automation and Test in Europe, DATE

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M1 - 998497

T2 - 2002 Design, Automation and Test in Europe Conference and Exhibition, DATE 2002

Y2 - 4 March 2002 through 8 March 2002

ER -

Steady state calculation of oscillators using continuation methods

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