Computation of time-periodic solutions of fluid interface problems
Jon Wilkening, University of California Berkley
I will describe a spectrally accurate numerical method for finding
time-periodic solutions of nonlinear PDE. We minimize a
the initial condition and the period) that is positive unless the
is periodic, in which case it is zero. We use adjoint methods
developed for shape optimization) to compute the gradient of this
functional with respect to the initial condition. We then
functional using a quasi-Newton gradient descent algorithm, BFGS.
our method to compute families of time-periodic solutions of the vortex
sheet with surface tension and the gravity-driven water wave. If
time permits, I will also talk about the Benjamin-Ono equation and the
compressible Euler equations.