23 3 2006 ISCM-20 Pinhas Z Bar-Yoseph Computational

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23. 3. 2006 ISCM-20 Pinhas Z. Bar-Yoseph Computational Mechanics Lab. Mechanical Engineering, Technion Copyright by PZ Bar-Yoseph ©

Bar-Yoseph, Appl. Num. Math. 33, 435 -445, 2000

Aharoni & Bar-Yoseph, Comp. Mech. 9, 359 -374, 1992 DSM for Dynamic systems

Discontinuous element

Nonlinear Spatio-Temporal Dynamics of a Flexible Rod Plat & Bar-Yoseph, 27 th Israel Conf. Mech. Eng. 683 -685, 1998

Bar-Yoseph, Appl. Num. Math. 33, 435 -445, 2000

Nave, Bar-Yoseph & Halevi, Dynamics. & Control. 9, 279 -296, 1999 The unicycle system, presents an example of inherently unstable system which can be autonomously controlled and stabilized by a skilled rider -required to maintain the unicylce’s upright position -required to maintain lateral stability -the friction torque is assumed to be dependent on the yew rate only

The adaptive technique performed very well for all stiff systems that we have experienced with (convection, radiation and chemical reactions), and is competitive with the best Gear-type routines

Space-Time Discontinuous Approximations

Bar-Yoseph & Elata, IJNME, 29, 1229 -1245, 1990

Bar-Yoseph & Elata & Israeli, IJNME, 36, 679 -694, 1993; Golzman & Bar-Yoseph (Project)

Bar-Yoseph & Elata, IJNME, 29, 1229 -1245, 1990

Fischer & Bar-Yoseph, IJNME, 48, 1571 -1582, 2000

Advanced CAD Visualization Methods Adaptive Level of Details Technique for Meshing

Morphing between Meshes at Different Times

CGM Conforming elements. DGM Elements are discontinuous.

Space-Time Discontinuous Approximations

Discontinuous SPECTRAL ELEMENTS • Gauss-Lobatto nodes are clustered near element boundaries and are chosen because of their interpolation and quadrature properties. • Mass lumping by nodal quadrature. • Exponential rate of convergence. • The increase in the due to the discontinuity at the interelement boundaries is balanced in high order elements.