Model reduction to spectral submanifolds in piecewise smooth dynamical systems
Leonardo Bettini, Mattia Cenedese, George Haller
Abstract
We develop a model reduction technique for piecewise smooth dynamical systems using spectral submanifolds. Specifically, we construct low-dimensional, sparse, nonlinear and piecewise smooth models on unions of slow and attracting spectral submanifolds (SSMs) for each smooth subregion of the phase space and then properly match them. We applied this methodology to both equation-driven and data-driven problems, with and without external forcing.
Topics & Concepts
Reduction (mathematics)PiecewiseMathematicsDynamical systems theoryPure mathematicsMathematical analysisPhysicsGeometryQuantum mechanicsModel Reduction and Neural NetworksComputational Fluid Dynamics and AerodynamicsFluid Dynamics and Vibration Analysis