UC Berkeley

We use a limited memory BFGS optimization method to seek time-periodic solutions of the Stokes-Oldroyd-B system of equations with a 4-roller forcing field and periodic boundary conditions. The gradient of the objective function for the optimization is found using a method which is based on the calculus of variations, and employs a pseudo-spectral implicit-explicit Runge-Kutta scheme. Once solutions are found, their asymptotic stability is calculated via an eigenvalue method. A variety of stationary and periodic solutions are found, plotted and systematized in a manner that suggests a global structure of periodic solutions.