DYNAMICAL MODEL REDUCTION METHOD FOR SOLVING PARAMETER-DEPENDENT DYNAMICAL SYSTEMS

We propose a projection-based model order reduction method for the solution of parameter-dependent dynamical systems. The proposed method relies on the construction of time dependent reduced spaces generated from evaluations of the solution of the full-order model at some selected parameter values. The approximation obtained by Galerkin projection is the solution of a reduced dynamical system with a modified flux that takes into account the time dependency of the reduced spaces. An a posteriori error estimate is derived, and a greedy algorithm using this error estimate is proposed for the adaptive selection of parameter values. The resulting method can be interpreted as a dynamical low-rank approximation method with a subspace point of view and a uniform control of the error over the parameter set.