Weak formulation of dynamical low-rank approximation for parabolic problems
Cancelled
Event details
| Date | 19.03.2020 |
| Hour | 16:15 › 17:15 |
| Speaker | Mr. André Uschmajew |
| Location | |
| Category | Conferences - Seminars |
Computational Mathematics Seminar
Abstract :
Dynamical low-rank approximation of matrices can be used for time integration of matrix valued ODEs on low-rank rank manifolds based on a time dependent variational principle. Several applications arise from two-dimensional PDEs. While after discretization the existence of solutions to the resulting nonlinear ODE is ensured by standard results, setting up a well posed problem in function space is not as obvious. We present a weak formulation of the time dependent variational principle that is applicable to dynamical low-rank approximation of parabolic problems. The existence of solutions can be shown based on a variational time-stepping scheme on the low-rank manifold that is related to practical methods for low-rank integration. (Joint work with Markus Bachmayr and Emil Kieri.)
Abstract :
Dynamical low-rank approximation of matrices can be used for time integration of matrix valued ODEs on low-rank rank manifolds based on a time dependent variational principle. Several applications arise from two-dimensional PDEs. While after discretization the existence of solutions to the resulting nonlinear ODE is ensured by standard results, setting up a well posed problem in function space is not as obvious. We present a weak formulation of the time dependent variational principle that is applicable to dynamical low-rank approximation of parabolic problems. The existence of solutions can be shown based on a variational time-stepping scheme on the low-rank manifold that is related to practical methods for low-rank integration. (Joint work with Markus Bachmayr and Emil Kieri.)
Practical information
- General public
- Free
Organizer
- Prof. Daniel Kressner
Contact
- Prof. Daniel Kressner