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**Harvard**

Rahrovani, S., Abrahamsson, T. och Modin, K. (2014) *An Efficient Exponential Integrator for Large Nonlinear Stiff Systems Part 1: Theoretical Investigation*.

** BibTeX **

@conference{

Rahrovani2014,

author={Rahrovani, Sadegh and Abrahamsson, Thomas and Modin, Klas},

title={An Efficient Exponential Integrator for Large Nonlinear Stiff Systems Part 1: Theoretical Investigation},

booktitle={Proceedings of the 32nd IMAC, A Conference and Exposition on Structural Dynamics, 2014. Nonlinear Dynamics, Volume 2},

isbn={978-3-319-04521-4},

pages={259-268},

abstract={In the first part of this study an exponential integration scheme for computing solutions of large stiff systems is
introduced. It is claimed that the integrator is particularly effective in large-scale problems with localized nonlinearity when compared with the general purpose methods. A brief literature review of different integration schemes is presented and theoretical aspect of the proposed method is discussed in detail. Computational efficiency concerns that arise in simulation of large-scale systems are treated by using an approximation of the Jacobian matrix. This is achieved by combining the
proposed integration scheme with the developed methods for model reduction, in order to treat the large nonlinear problems.
In the second part, geometric and structural properties of the presented integrator are examined and the preservation of these properties such as area in the phase plane and also energy consistency are investigated. The error analysis is given through small scale examples and the efficiency and accuracy of the proposed exponential integrator is investigated through a large-scale size problem that originates from a moving load problem in railway mechanics. The superiority of the proposed
method in sense of computational efficiency, for large-scale problems particularly system with localized nonlinearity, has been demonstrated, comparing the results with classical Runge–Kutta approach.},

year={2014},

keywords={Exponential integrators; Quadrature rule; Stiff ODE; Runge–Kutta method; Semi-linear problems},

}

** RefWorks **

RT Conference Proceedings

SR Electronic

ID 197026

A1 Rahrovani, Sadegh

A1 Abrahamsson, Thomas

A1 Modin, Klas

T1 An Efficient Exponential Integrator for Large Nonlinear Stiff Systems Part 1: Theoretical Investigation

YR 2014

T2 Proceedings of the 32nd IMAC, A Conference and Exposition on Structural Dynamics, 2014. Nonlinear Dynamics, Volume 2

SN 978-3-319-04521-4

SP 259

OP 268

AB In the first part of this study an exponential integration scheme for computing solutions of large stiff systems is
introduced. It is claimed that the integrator is particularly effective in large-scale problems with localized nonlinearity when compared with the general purpose methods. A brief literature review of different integration schemes is presented and theoretical aspect of the proposed method is discussed in detail. Computational efficiency concerns that arise in simulation of large-scale systems are treated by using an approximation of the Jacobian matrix. This is achieved by combining the
proposed integration scheme with the developed methods for model reduction, in order to treat the large nonlinear problems.
In the second part, geometric and structural properties of the presented integrator are examined and the preservation of these properties such as area in the phase plane and also energy consistency are investigated. The error analysis is given through small scale examples and the efficiency and accuracy of the proposed exponential integrator is investigated through a large-scale size problem that originates from a moving load problem in railway mechanics. The superiority of the proposed
method in sense of computational efficiency, for large-scale problems particularly system with localized nonlinearity, has been demonstrated, comparing the results with classical Runge–Kutta approach.

LA eng

DO 10.1007/978-3-319-04522-1_25

LK http://dx.doi.org/10.1007/978-3-319-04522-1_25

OL 30