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Adaptive numerical integration of dynamical contact problem

Staff - Faculty of Informatics

Start date: 15 June 2010

End date: 16 June 2010

The Faculty of Informatics is pleased to announce a seminar given by Peter Deuflhard

DATE: Tuesday, June 15th 2010
PLACE: USI Università della Svizzera italiana, room A24, Red building (Via G. Buffi 13)
TIME: 15.30

ABSTRACT:
The author and his research group in computational medicine have come across dynamical contact problems in the context of a collaboration in orthopaedic surgery (SFB 765). Special first attention has focussed on the motion of the patient-specific knee.

As it turned out, the numerical integration of time dependent contact problems has stayed unsatisfactory for decades. The classical Newmark method, which is quite popular in the engineering world, is a real ''perpetuum mobile'' in that in generates energy! A rather recent improvement due to the Caltech group around Marsden and Ortiz is energy dissipative, but still unsatisfactory, since it produces artificial oscillations (untolerable in the collaboration with surgeons!).
More recently, the author together with Krause has suggested a further modification meanwhile called ''contact-stabilized Newmark method''.
This scheme is energy dissipative, too, but avoids artificial oscillations.

However, all Newmark schemes escape the usual domain of consistency theory for numerical integration.
After a long investigative period, Klapproth, Schiela, and the author eventually found the proper key to a consistency theory.
Surprisingly, the new theoretical characterization requires bounded variation in terms of a physical energy functional that includes kinetic energy, elastic energy, and visco-elastic energy.
On this basis, an adaptive timestep control has been worked out, which is shown to give satisfactory results in a Hertzian contact problem.
In this context new issues come up when constructing a higher order Newmark type scheme via extrapolation.

BIO:

  • 1944: Born in Dorfen (Bavaria), Germany
  • 1963-68: Studies of Pure Physics, TH Munich
  • 1968: Diploma Degree in Physics, TH Munich
  • 1969-73: Scientific Assistant in Mathematics, University of Cologne (with R. Bulirsch)
  • 1972: Dissertation in Mathematics, University of Cologne
  • 1973-78: Senior Scientific Assistant (Tenure) in Mathematics, TU Munich
  • 1977: Habilitation in Mathematics, TU Munich
  • 1978-86: Full Professor, University of Heidelberg, chair Numerical Analysis (following W. Romberg)
  • 1986-present: Full Professor FU Berlin, chair Scientific Computing
  • 1986: Founder of ZIB as a scientific research institute
  • 1987-present: President of ZIB
  • 2002: Co-founder of DFG Research Center Matheon
  • 2002-present: Member of the Executive Board of Matheon

HOST: Prof. Rolf Krause