Variational formulations for dissipative systems
50 mins 59 secs,
93.28 MB,
MP3
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| Description: |
Ober-Blöbaum, S
Wednesday 4th September 2019 - 14:00 to 15:00 |
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| Created: | 2019-09-05 12:21 |
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| Collection: | Geometry, compatibility and structure preservation in computational differential equations |
| Publisher: | Isaac Newton Institute |
| Copyright: | Ober-Blöbaum, S |
| Language: | eng (English) |
| Distribution: |
World
(downloadable)
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| Explicit content: | No |
| Aspect Ratio: | 16:9 |
| Screencast: | No |
| Bumper: | UCS Default |
| Trailer: | UCS Default |
| Abstract: | Variational principles are powerful tools for the modelling and simulation of conservative mechanical and electrical systems. As it is well-known, the fulfilment of a variational principle leads to the Euler-Lagrange equations of motion describing the dynamics of such systems. Furthermore, a variational discretisation directly yields unified numerical schemes with powerful structure-preserving properties. Since many years there have been several attempts to provide a variational description also for dissipative mechanical systems, a task that is addressed in the talk in order to construct both Lagrangian and Hamiltonian pictures of their dynamics. One way doing this is to use fractional terms in the Lagrangian or Hamiltonian function which allows for a purely variational derivation of dissipative systems. Another approach followed in this talk is to embed the non-conservative systems in larger conservative systems. These concepts are used to develop variational integrators for which superior qualitative numerical properties such as the correct energy dissipation rate are demonstrated. |
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