Research Colloquium: Master's Thesis Presentation by Tara Stein

As part of the research colloquium for final theses, doctoral and habiliation candidates, we cordially invite you to join us on Monday, July 13, 2026, at 2:00 p.m. in Room 3513, Mönchebergstr. 7. Ms. Tara Stein, B.Sc., will present the results of her master’s thesis titled

“Numerical Analysis of Null-Space Methods and their Relation to Master-Slave Elimination Schemes in Elastodynamics”

Although the title is in English, the presentation will be given in German . We look forward to seeing you there!

Abstract

A well-established reduction approach for saddle-point problems arising in constrained elastostatics is the master-slave elimination method, which reduces the total number of primary unknowns. In this thesis, this method is extended to constrained elastodynamics, in combination with the modified generalized-α scheme proposed by Arnold and Brüls. In this formulation, the reduction is performed after time discretization. In addition, a second reduction strategy based on the coordinate partitioning method is developed, in which the dimension is reduced prior to time integration. Although both approaches decrease the problem dimension and rely on the same time-integration scheme, they exhibit fundamentally different properties. These differences are investigated theoretically and through numerical examples with respect to accuracy and computational effort. The results show that master-slave elimination also offers advantages in the dynamic case. Furthermore, a proof of second-order convergence for the modified generalized-α scheme is provided, and the relationship between master-slave elimination and a null-space method is analyzed.