Speaker
Description
The talk presents the latest results in the field of viscosity optimization. The first result is the development of an efficient algorithm that leverages new formulas for calculating the trace, as well as the first and second derivatives of the trace, of the associated Lyapunov equation. This approach enhances the precision and computational efficiency of viscosity optimization. The second contribution involves refining the frequency cut-off approximation, which is particularly suited to the types of problems considered in this work. We introduced a novel error bound as an alternative to the standard residual error, offering a new approach that can be efficiently computed with $\mathcal{O}(r n)$ operations for structures with $r$ additional dampers. The effectiveness of these theoretical advancements has been demonstrated through several numerical examples, which validate the practical relevance of our results.
This is a joint work with Ren-Cang Li from
University of Texas at Arlington, Department of Mathematics, Arlington, TX, USA.
