OS Numerical Optimization: 'Controllability and Observability Gramians for Linear-Time-Invariant systems' and 'Space-Time Reduced Basis Method for Solving Parameterized Heat Equations'
Dienstag, 19. Dezember 2023
15:15 bis 16:45 Uhr
B. Azmi & S. Volkwein
Vortragende Person/Vortragende Personen:
Johannes Mayenberger and Joshua Braun
On 19th Dezember 2023 at 15:15, Johannes Mayenberger and Joshua Braun from the University of Konstanz will give two talks.
The first title will be 'Controllability and Observability Gramians for Linear-Time-Invariant systems' with the abstract:
Empirical gramians are a data driven approach to approximate the controllability and observability gramians for linear-time-invariant systems. In this thesis, a summary of Gramian theory is given. Further, the convergence of empirical gramians is tested. Simple strategies to optimize convergence are developed and tested.
The second title will be 'Space-Time Reduced Basis Method for Solving Parameterized Heat Equations' with the abstract:
In this thesis, we present a reduced basis space-time finite element method for solv- ing the parameterized initial boundary value heat equation. The space-time finite element approach allows for unstructured finite elements without any tensor struc- ture. This makes the mesh more general and due to the variational treatment of space and time many steps from elliptic equations can be taken over by slight modi- fications. In this way, we also give a parabolic version of the reduced basis method to solve the parameterized heat equation for varying parameters extremely fast (”real- time”), very often (”multi-query”) and with limited memory (”cold computing”). In the numerical experiments we want to confirm the derived a priori error estimator between a known solution and its finite element approximation as well as the derived a posteriori error estimator between the finite element solution and the reduced ba- sis approximation. This error estimator will then be of crucial importance in the greedy algorithm for generating a reduced basis.