Efficient basis updating for parametric nonlinear model order reduction

Nonlinear model reduction is used to speed up the numerical solution of finite element models for vibration analysis of structures undergoing large deflections. This speed up is highly desired in design and optimization applications where parametric models are considered and the outcoming high‐dimensional differential equation must be solved multiple times. A first step is to approximate the solution vector i.e. the displacements of the nodes by a linear combination of some basis vectors. One common choice for these basis vectors is a combination of vibration modes and static modal derivatives. However, these vectors depend on parameter values of the parameterized system. This contribution shows how these basis vectors can be updated in an efficient manner. The vibration modes are updated by an inverse free preconditioned Krylov subspace method while the static derivatives are updated by a preconditioned conjugate gradient solver. A case study with a parametric beam gives a first insight into the performance of the proposed method.