000013404 001__ 13404
000013404 005__ 20161114164233.0
000013404 04107 $$aeng
000013404 046__ $$k2011-05-25
000013404 100__ $$aPichler, L.
000013404 24500 $$aNumerical Solution of the Fokker-Planck Equation by Finite Difference and Finite Element Methods - a Comparative Study

000013404 24630 $$n3.$$pComputational Methods in Structural Dynamics and Earhquake Engineering
000013404 260__ $$bNational Technical University of Athens, 2011
000013404 506__ $$arestricted
000013404 520__ $$2eng$$aFinite element and finite difference methods have been widely used, among other methods, to numerically solve the Fokker-Planck equation for investigating the time history of the probability density function of linear and nonlinear 2d and 3d problems, and also the application to 4d problems has been addressed. However, due to the enormous increase of the computational costs, different strategies are required for an efficient application to problems of dimension ≥ 3. Recently, a stabilized multi-scale finite element method has been effectively applied to the Fokker-Planck equation effectively by means of a considerably reduction of the required number of elements. Also, the alternating directions implicit method shows good performance in terms of efficiency and accuracy. In this paper various finite difference and finite element methods are discussed and the results are compared using various numerical examples.

000013404 540__ $$aText je chráněný podle autorského zákona č. 121/2000 Sb.
000013404 653__ $$aFokker-Planck Equation, Finite Difference Method, Finite Element Method, MultiScale Finite Element Method, Linear Oscillator, Duffing Oscillator.

000013404 7112_ $$aCOMPDYN 2011 - 3rd International Thematic Conference$$cIsland of Corfu (GR)$$d2011-05-25 / 2011-05-28$$gCOMPDYN2011
000013404 720__ $$aPichler, L.$$iMasud, A.$$iBergman L., A.
000013404 8560_ $$ffischerc@itam.cas.cz
000013404 8564_ $$s617582$$uhttps://invenio.itam.cas.cz/record/13404/files/059.pdf$$yOriginal version of the author's contribution as presented on CD, section: MS 31 Uncertainty and Reliability in Computational Structural Dynamics.
000013404 962__ $$r13401
000013404 980__ $$aPAPER