01537nas a2200121   4500008004100000245011600041210006900157520098400226100002001210700002101230700002101251856014301272       2020                        eng d00aA reduced order modeling technique to study bifurcating phenomena: Application to the gross-pitaevskii equation0 areduced order modeling technique to study bifurcating phenomena 3 a<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's method with a reduced order modeling (ROM) technique, suitably supplemented with a hyperreduction method. To demonstrate the effectiveness of our ROM approach, we trace the steady solution branches of a nonlinear Schrödinger equation, called the 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>1 aPichi, Federico1 aQuaini, Annalisa1 aRozza, Gianluigi  uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85096768803&doi=10.1137%2f20M1313106&partnerID=40&md5=47d6012d10854c2f9a04b9737f870592