Efficient computation of optimal damper positions

Develop an efficient algorithm for determining the optimal damping positions in a mechanical system, together with the associated viscosity optimization when required.

Background

The paper identifies the determination of optimal damping positions as a particularly challenging component of damping optimization. Although heuristic approaches and exhaustive brute-force searches are available, the number of possible damping configurations grows combinatorially with the system dimension, making exhaustive optimization computationally impractical for larger systems. The paper’s SPARDO framework addresses damper placement and viscosity selection for small to moderate dimensions, but it does not provide a generally efficient algorithm for the optimal-position problem itself.

References

Computing the optimal damping positions, on the other hand, is a very challenging problem, studied in . No efficient algorithm for it is known so far, although some heuristics can be found in, e.g., .

— A Scalable Framework for Simultaneously Optimizing Damper Positions and Viscosities  (2609.01398 - Vukojević et al., 1 Sep 2026) in Section 1, Introduction

A systematic description of these families, and of their possible connected components, remains open.

— Maximal Multiplicity Method for Optimal Damping Problem  (2609.25736 - Arnold et al., 22 Sep 2026) in Section 'Discussion and open problems'

For $n=3$, the situation is more complicated. We found explicit passive optimal damping matrices, as well as parameter ranges in which passivity is impossible, but a complete classification is still lacking.

— Maximal Multiplicity Method for Optimal Damping Problem  (2609.25736 - Arnold et al., 22 Sep 2026) in Section 'Discussion and open problems'