000022039 001__ 22039
000022039 005__ 20170622145953.0
000022039 04107 $$aeng
000022039 046__ $$k2015-05-25
000022039 100__ $$aAlmonacid, Pablo Mata
000022039 24500 $$aA VARIATIONAL FORMULATION OF DISCONTINUOUS-GALERKIN TIME INTEGRATORS

000022039 24630 $$n5.$$pComputational Methods in Structural Dynamics and Earhquake Engineering
000022039 260__ $$bNational Technical University of Athens, 2015
000022039 506__ $$arestricted
000022039 520__ $$2eng$$aVariational integrators provide a way to design structure-preserving time integrators for problems presenting a Lagrangian structure. The basic idea consists in obtaining algorithms from a discrete analogue of Hamilton’s variational principle. Then, the discrete trajectories are stationary points of a discrete analogue of the action functional. The resulting methods enjoy a number of remarkable properties: i) they exactly conserves the momenta associated to the symmetries of a discrete version of the Lagrangian, ii) they define a discrete symplectic flow on the phase space and iii) they show an error in the total energy that remains bounded for exponentially long periods of time. A particularly interesting family of such methods is given by the so called Galerkin variational integrators. Their construction is based on approximating the trajectory of the system by means of piecewise continuous polynomials and providing suitable quadrature rules to approximate the action functional. Then, increasing the order of the interpolating polynomials and the accuracy of the quadrature rules allow to obtain higher order time integrators. In this work we extend the Galerkin methods to the discontinuous case yielding to a family of discontinuous-Galerkin (dG)-methods. To this end, we resort to using two key ingredients: 1) the trajectory of the system is approximated by means of piecewise polynomials which may presents a finite number of discontinuities across time interval boundaries and 2) we approximate the velocity of the system by means of an appropriate dG-time-derivative of the trajectory following some ideas presented in [1, 2] for static problems in elasticity. The resulting algorithms corresponds to a family of discontinuous-symplectic Runge-Kutta methods.

000022039 540__ $$aText je chráněný podle autorského zákona č. 121/2000 Sb.
000022039 653__ $$avariational integrators, discontinuous-Galerkin, time integrator.

000022039 7112_ $$aCOMPDYN 2015 - 5th International Thematic Conference$$cCrete (GR)$$d2015-05-25 / 2015-05-27$$gCOMPDYN2015
000022039 720__ $$aAlmonacid, Pablo Mata$$iZiaei-Rad, Vahid$$iShen, Yongxing
000022039 8560_ $$ffischerc@itam.cas.cz
000022039 8564_ $$s136716$$uhttp://invenio.itam.cas.cz/record/22039/files/C1050.pdf$$yOriginal version of the author's contribution as presented on CD, section: 
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000022039 962__ $$r22030
000022039 980__ $$aPAPER