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Carlo Danieli
복잡계 이론물리 연구단
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Computational efficiency of numerical integration methods for the tangent dynamics of many-body Hamiltonian systems in one and two spatial dimensions

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Title
Computational efficiency of numerical integration methods for the tangent dynamics of many-body Hamiltonian systems in one and two spatial dimensions
Author(s)
Carlo Danieli; Bertin Many Manda; Thudiyangal Mithun; Charalampos Skokos
Publication Date
2019-05
Journal
Mathematics in Engineering, v.1, no.3, pp.447 - 488
Publisher
AIMS PRESS
Abstract
We investigate the computational performance of various numerical methods for the integration of the equations of motion and the variational equations for some typical classical many-body models of condensed matter physics: the Fermi-Pasta-Ulam-Tsingou (FPUT) chain and the one- and two- dimensional disordered, discrete nonlinear Schro ̈dinger equations (DDNLS). In our analysis we consider methods based on Taylor series expansion, Runge-Kutta discretization and symplectic transformations. The latter have the ability to exactly preserve the symplectic structure of Hamiltonian systems, which results in keeping bounded the error of the system’s computed total energy. We perform extensive numerical simulations for several initial conditions of the studied models and compare the numerical efficiency of the used integrators by testing their ability to accurately reproduce characteristics of the systems’ dynamics and quantify their chaoticity through the computation of the maximum Lyapunov exponent. We also report the expressions of the implemented symplectic schemes and provide the explicit forms of the used differential operators. Among the tested numerical schemes the symplectic integrators ABA864 and S RKNa exhibit the best performance, respectively for moderate and high accuracy levels in 14 the case of the FPUT chain, while for the DDNLS models s9ABC6 and s11ABC6 (moderate accuracy), along with s17ABC8 and s19ABC8 (high accuracy) proved to be the most efficient schemes. C. 2019 the Author(s), licensee AIMS Press.
URI
https://pr.ibs.re.kr/handle/8788114/6310
ISSN
2640-3501
Appears in Collections:
Center for Theoretical Physics of Complex Systems(복잡계 이론물리 연구단) > Journal Papers (저널논문)
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