1. Pinhas Z. Bar-Yoseph Computational Mechanics Lab. Mechanical Engineering, Technion 23.3.2006 ISCM-20 Copyright by PZ Bar-Yoseph ©

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

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

12. Discontinuous element

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

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

17. 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

19. 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

28. Space-Time Discontinuous Approximations

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

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

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

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

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

38. Adaptive Level of Details Technique for Meshing Advanced CAD Visualization Methods

39. Morphing between Meshes at Different Times

40. DGM Elements are discontinuous. CGM Conforming elements.

42. Space-Time Discontinuous Approximations

43. 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. Discontinuous SPECTRAL ELEMENTS

47. Flux Splitting Bar-Yoseph,Comput. Mech., 5, 145-160, 1989

48. Nonlinear Wave Eq. Miles Rubin (2005)

49. Flux splitting for non homogeneous

50. where: The effective wave speed: In a matrix form: Traper & Bar-Yoseph (Project)

51. The Jacobian matrix: The eigenvalues: The corresponding eigenvectors:

54. Displacement Traper & Bar-Yoseph (Project)

55. Velocity

56. Strain

57. -Time for breakdown [Lax (1964)]:

58. Velocity at t = 3 sec x bilinear biquadratic

59. Strain at t = 3 sec x bilinear biquadratic

63. Bar-Yoseph et al., JCP, 119, 62-74, 1995

64. Bar-Yoseph & Moses, IJNMHFF, 7, 215-235, 1997

70. Cockburn& Shu, JCP, 84, 90, 1989; Basi & Rebay, JCP, 131,267-279, 1997