ME Seminar Series: Reduced Order Modeling of Bifurcation Problems
Tuesday, May 22, 2012 - 11:30am to 1:00pm
Bifurcation diagrams are of paramount scientific interest. The increasing necessity to account for nonlinearity in industrial devices is making unavoidable the need to analyze bifurcation problems also in industrial environments. Unfortunately, for realistic physical systems modeled by partial differential equations, current computational tools may require non-affordable CPU time and memory to construct bifurcation diagrams involving complex time dependent attractors. This is because the numerical solver must be run for a large number of values of the bifurcation parameter, in a sufficiently large time-span (which is quite large near bifurcation points), to discard transient dynamics. Thus, increasing the computational efficiency of this process is strongly needed to take advantage of the body of knowledge that has been developed along the last decades in connection with nonlinear dynamics and bifurcations. The main object of the talk will be to provide some recent developments, including some basic ideas to constructing efficient/robust reduced order models for bifurcation problems. The ideas will be illustrated with the complex Ginzburg-Landau equation.