Computations and analysis of the initial value problem for hydroelastic waves

Department of Mathematics, New Jersey Institute of Technology

The hydroelastic problem describes the evolution of a thin elastic membrane in potential flow. It arises in many applications, including the dynamics of flapping flags and ice sheets in the ocean. An efficient, nonstiff boundary integral method for the 3D hydroelastic problem is presented. The stiffness is removed by a small-scale decomposition, following prior work on 2D interfacial flow with surface tension. A convergence proof for a version the numerical method will be briefly discussed (joint work with David Ambrose and Yang Liu).