Splitting Methods and Applications
Event details
| Date | 27.11.2013 |
| Hour | 17:15 › 18:00 |
| Speaker | Jonathan Rochat |
| Location |
MA A3 31
|
| Category | Conferences - Seminars |
Hamiltonian Dynamics Seminar
Abstract: Operator splitting (or the fractional steps method) is a very common tool for analyzing nonlinear partial differential equations both numerically and analytically. By applying operator splitting to a complicated system one can often split it into simpler problems that can be analyzed separately. A splitting scheme is then a composition of flows associated with each part of the system with fractional time steps. We introduce these methods and present some conditions on the fractional steps to obtain high order methods using geometric tools. The existence of backward fractional time steps in methods of order higher than three is in fact unavoidable. Some example of other composition methods involving only positive coefficients will also be discussed.
These numerical schemes have been successfully applied for solving a large number of problems. We present some applications for differential equations and Hamiltonian systems, but also some partial differential equations like the Navier-Stokes problem.
Abstract: Operator splitting (or the fractional steps method) is a very common tool for analyzing nonlinear partial differential equations both numerically and analytically. By applying operator splitting to a complicated system one can often split it into simpler problems that can be analyzed separately. A splitting scheme is then a composition of flows associated with each part of the system with fractional time steps. We introduce these methods and present some conditions on the fractional steps to obtain high order methods using geometric tools. The existence of backward fractional time steps in methods of order higher than three is in fact unavoidable. Some example of other composition methods involving only positive coefficients will also be discussed.
These numerical schemes have been successfully applied for solving a large number of problems. We present some applications for differential equations and Hamiltonian systems, but also some partial differential equations like the Navier-Stokes problem.
Practical information
- Expert
- Free
Organizer
- Sonja Hohloch, Martins Bruveris, Tudor Ratiu