Community integration algorithms (CIAs): A novel computational approach for large-scale dynamical systems and extensions to networks (Mechthild Thalhammer, Innsbruck)

22.06.2026 16:00

The algorithm applied for the evaluation of the defining function constitutes a crucial factor in the numerical simulation of a large-scale dynamical system. This fundamental tool is essential for the significance of the obtained results and the overall performance. A novel modus operandi based on well-adapted global approximations and precomputations of reappearing quantities is proposed. It is demonstrated that this approach is expedient for a wide range of dynamical systems and permits substantial reductions from polynomial to linear computational complexity. Combining such concepts with state-of-the-art algorithms for the detection of communities in networks leads to community integration algorithms (CIAs) for dynamical systems on graphs. Numerical comparisons for relevant test problems with applications in various disciplines including higher-order Kuramoto–Daido-type systems arising in the description of synchronisation, Cucker–Smale systems exhibiting flocking behaviour, and extended systems on real world graphs for animal networks, confirm the robustness and efficiency of the novel computational approach.

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Bâtiment: Conseil Général 7-9

Room 1-07, Séminaire d'analyse numérique
ATT. unusual time and place!

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