Run time estimation of the spectral radius of Jacobians

Day, J.D.

doi:10.1016/0377-0427(84)90006-2

Cited by 7 publications

(2 citation statements)

References 14 publications

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“…With the methods in Day [1] and Sottas [19] for the estimation of Ilf~ll in the explicit part without evaluation of the Jacobian a reduction of the overhead for stiffness detection is possible, but the reduction is essential only for higher dimensions.…”

Section: Partitioned Methods Are Treated For Example In Hofer [8] Grmentioning

confidence: 99%

Partitioned adaptive Runge-Kutta methods for the solution of nonstiff and stiff systems

1988

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Summary.For the numerical solution of initial value problems of ordinary differential equations partitioned adaptive Runge-Kutta methods are studied. These methods consist of an adaptive Runge-Kutta method for the treatment of a stiff system and a corresponding explicit Runge-Kutta method for a nonstiff system. First we modify the theory of Butcher series for partitioned adaptive Runge-Kutta methods. We show that for any explicit Runge-Kutta method there exists a translation invariant partitioned adaptive Runge-Kutta method of the same order. Secondly we derive a special translation invariant partitioned adaptive Runge-Kutta method of order 3. An automatic stiffness detection and a stepsize control basing on Richardson-extrapolation are performed. Extensive tests and comparisons with the partitioned R K F 4 R Walgorithm from Rentrop [-16] and the partitioned algorithm LSODA from Hindmarsh [9] and Petzold [15] show that the partitioned adaptive RungeKutta algorithm works reliable and gives good numerical results. Furthermore these tests show that the automatic stiffness detection in this algorithm is effective.

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Section: Partitioned Methods Are Treated For Example In Hofer [8] Grmentioning

confidence: 99%

Partitioned adaptive Runge-Kutta methods for the solution of nonstiff and stiff systems

1988

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“…Eigenvalue problems are common in the engineering context [1,2]. As such, they have been used in a plethora of applications such as in analysing the state matrix of an electronic power system [3], in studying the aeroelastic instability for wind turbines [4], for determining the spectral radius of Jacobian matrices [5], and in the operational modal analysis of a structures [6]. The most common eigenvalue problem, known as the the direct or forward problem involves determining the arXiv:1812.04214v1 [cs.LG] 11 Dec 2018 impact of a known set of modifications to a group of matrices, either by computing the eigenvalues, eigenvectors, singular values, or singular vectors of the group of matrices.…”

Section: Introductionmentioning

confidence: 99%

New Approaches to Inverse Structural Modification Theory Using Random Projections

Cheema

Alamdari

Vio

2019

Topics in Modal Analysis &Amp; Testing, Volume 8

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In many contexts the modal properties of a structure change, either due to the impact of a changing environment, fatigue, or due to the presence of structural damage. For example during flight, an aircraft's modal properties are known to change with both altitude and velocity. It is thus important to quantify these changes given only a truncated set of modal data, which is usually the case experimentally. This procedure is formally known as the generalised inverse eigenvalue problem. In this paper we experimentally show that first-order gradient-based methods that optimise objective functions defined over a modal are prohibitive due to the required small step sizes. This in turn leads to the justification of using a non-gradient, black box optimiser in the form of particle swarm optimisation. We further show how it is possible to solve such inverse eigenvalue problems in a lower dimensional space by the use of random projections, which in many cases reduces the total dimensionality of the optimisation problem by 80% to 99%. Two example problems are explored involving a ten-dimensional mass-stiffness toy problem, and a one-dimensional finite element massstiffness approximation for a Boeing 737-300 aircraft.

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Initial-Value Problems for ODE

Širca¹,

Horvat²

2018

Computational Methods in Physics

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Run time estimation of the spectral radius of Jacobians

Cited by 7 publications

References 14 publications

Partitioned adaptive Runge-Kutta methods for the solution of nonstiff and stiff systems

Partitioned adaptive Runge-Kutta methods for the solution of nonstiff and stiff systems

New Approaches to Inverse Structural Modification Theory Using Random Projections

Initial-Value Problems for ODE

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