Commutator-free Lie group methods

Celledoni, Elena; Marthinsen, Arne; Owren, Brynjulf

doi:10.1016/s0167-739x(02)00161-9

Cited by 85 publications

(152 citation statements)

References 12 publications

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“…Unfortunately the RKMK schemes were shown to exhibit instabilities due to the use of commutators. The commutator free schemes [6] overcome this problem but the overall stiff order achieved is limited to two.…”

Section: Affine Lie Group Schemesmentioning

confidence: 99%

“…The RKMK methods requires the computation of the dexp −1 operator which involves iterated commutators. To overcome the need for commutators which often result in stepsize restrictions Celledoni, Martinsen and Owren [6], constructed the commutator-free methods.…”

Section: A3 Affine Lie Group Schemesmentioning

confidence: 99%

“…This is a stiff order three ETD version [16] of a commutator-free scheme in [6]. This scheme given in [6, Eq.…”

Section: A3 Affine Lie Group Schemesmentioning

confidence: 99%

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EXPINT---A MATLAB package for exponential integrators

Berland

Skaflestad

Wright

2007

ACM Trans. Math. Softw.

114

132

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Recently, a great deal of attention has been focused on the construction of exponential integrators for semi-linear problems. In this paper we describe a matlab package which aims to facilitate the quick deployment and testing of exponential integrators, of Runge-Kutta, multistep and general linear type. A large number of integrators are included in this package along with several well known examples. The so-called ϕ-functions and their evaluation is crucial for stability and speed of exponential integrators, and the approach taken here is through a modification of the scaling and squaring technique; the most common approach used for computing the matrix exponential.

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Section: Affine Lie Group Schemesmentioning

confidence: 99%

Section: A3 Affine Lie Group Schemesmentioning

confidence: 99%

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EXPINT---A MATLAB package for exponential integrators

Berland

Skaflestad

Wright

2007

ACM Trans. Math. Softw.

114

132

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“…The same conditions are satisfied by ETD2RK3 from [3]. The method ETD2CF3 is a variant of the commutator-free Lie group method CF3 due to Celledoni, Marthinsen and Owren [2]. It is given by …”

mentioning

confidence: 97%

Explicit Exponential Runge--Kutta Methods for Semilinear Parabolic Problems

Hochbruck¹,

Ostermann²

2005

SIAM J. Numer. Anal.

361

398

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Abstract. The aim of this paper is to analyze explicit exponential Runge-Kutta methods for the time integration of semilinear parabolic problems. The analysis is performed in an abstract Banach space framework of sectorial operators and locally Lipschitz continuous nonlinearities. We commence by giving a new and short derivation of the classical (nonstiff) order conditions for exponential RungeKutta methods, but the main interest of our paper lies in the stiff case. By expanding the errors of the numerical method in terms of the solution, we derive new order conditions that form the basis of our error bounds for parabolic problems. We show convergence for methods up to order four and we analyze methods that were recently presented in the literature. These methods have classical order four, but they do not satisfy some of the new conditions. Therefore, an order reduction is expected. We present numerical experiments which show that this order reduction in fact arises in practical examples. Based on our new conditions, we finally construct methods that do not suffer from order reduction.

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“…Similar to the cooling case, plaquette, Symanzik, and Iwasaki actions are employed. The flow equation is solved by the fourth order Runge-Kutta in the commutator-free method [8]. The Runge-Kutta step size dt is chosen to be 0.02.…”

Section: Smoothingmentioning

confidence: 99%

Comparative study of topological charge

Namekawa¹

2015

Proceedings of the 32nd International Symposium on Lattice Field Theory — PoS(LATTICE2014)

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Comparative study of topological charge is performed. Topological charges are measured by a cloverleaf operator on smoothed gauge configurations. Various types of smoothing techniques are employed. Agreement of topological charges in fermionic and gluonic definitions is examined. High consistency is observed between topological charges obtained by improved smoothing methods and those by the index theorem with the overlap-Dirac operator.

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Commutator-free Lie group methods

Cited by 85 publications

References 12 publications

EXPINT---A MATLAB package for exponential integrators

EXPINT---A MATLAB package for exponential integrators

Explicit Exponential Runge--Kutta Methods for Semilinear Parabolic Problems

Comparative study of topological charge

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