@article {2020,
	title = {A Reduced Order technique to study bifurcating phenomena: application to the Gross-Pitaevskii equation},
	journal = {SIAM Journal on Scientific Computing},
	year = {2020},
	abstract = {<p>We propose a computationally efficient framework to treat nonlinear partial differential equations having bifurcating solutions as one or more physical control parameters are varied. Our focus is on steady bifurcations. Plotting a bifurcation diagram entails computing multiple solutions of a parametrized, nonlinear problem, which can be extremely expensive in terms of computational time. In order to reduce these demanding computational costs, our approach combines a continuation technique and Newton{\textquoteright}s method with a Reduced Order Modeling (ROM) technique, suitably supplemented with a hyper-reduction method. To demonstrate the effectiveness of our ROM approach, we trace the steady solution branches of a nonlinear Schr{\"o}dinger equation, called Gross-Pitaevskii equation, as one or two physical parameters are varied. In the two parameter study, we show that our approach is 60 times faster in constructing a bifurcation diagram than a standard Full Order Method.</p>},
	doi = {https://doi.org/10.1137/20M1313106},
	url = {https://arxiv.org/abs/1907.07082},
	author = {Federico Pichi and Annalisa Quaini and Gianluigi Rozza}
}
