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CANCELLED
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Numerical path continuation is commonly applied to determine how limit states of complex nonlinear dynamical systems evolve with a free parameter. For high-fidelity models, the sequential nature inherent to continuation can become an unsurmountable obstacle. Recently, we proposed a seminal method for robustly obtaining the desired high-fidelity solution curves in a parallelized way.
Our approach begins with a low-fidelity model, which is either of lower order or omits certain nonlinear or coupling terms. The simplifications must be substantial enough to produce an approximate solution curve with little or even negligible computational effort. A subset of relevant solution points along this approximate curve is than selected, and from these points, we iteratively compute the points on the targeted solution branch of the high-fidelity model. It is crucial to understand that the steps toward the high-fidelity solution branch can be executed independently for each selected solution point, making it perfectly suited for parallel computation.
We demonstrate the proposed generic concept through a range of both academic and industry-sized nonlinear vibration problems. Various system models, nonlinearities, and analyses are explored, with the Harmonic Balance method applied in all cases to compute periodic limit states. Finally, it is shown how the concept can be applied in combination with the single nonlinear mode theory, where the low-fidelity model is obtained from nonlinear modal analysis of an isolated mode. 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.
