A new paradigm for multi-fidelity continuation using parallel model refinement

Abstract

Numerical path continuation is commonly applied to determine how limit states of dynamical systems evolve with a free parameter. For high-fidelity models of complicated nonlinear systems, the sequential nature inherent to continuation can become an unsurmountable obstacle. In the present work, we propose a new paradigm for obtaining the targeted solution curves in a parallelized way. The point of departure is a low-fidelity model, which is of lower order and/or neglects certain nonlinear/coupling terms. The simplifications must be as drastic as necessary to obtain an approximate solution curve with reasonable effort. A subset of relevant points along this approximate solution curve is then selected, and, departing there, points on the targeted solution branch of the high-fidelity model are then iteratively computed. It is important to note that the iterative correction towards the high-fidelity solution branch can be applied independently for each point, and is thus predestined for parallel computation. The proposed generic concept is exemplified for a selection of nonlinear vibration problems. Different types of system models, nonlinearities and analyses are considered, and the Harmonic Balance method is used in all cases to compute periodic limit states. In particular, it is shown that the proposed concept is applicable to modal and harmonic order refinement. Finally, it is shown that the concept is also interesting when instead of a model refinement a second system parameter (besides the continuation parameter) is varied, and it permits to robustly reach parameter ranges that are extremely difficult to obtain with conventional path continuation. The method is available, along with the presented numerical examples, as a branch PEACE (Parallelized Re-analysis Of Solution Curves) of the open source tool NLvib.