Three-dimensional waves under ice computed with novel preconditioning methods

In this work, we present three-dimensional, nonlinear traveling wave solutions for water waves under a sheet of ice, i.e., flexural-gravity waves. The ice is modeled as a thin elastic plate on top of water of infinite depth and the equations are formulated as a boundary integral method. Depending on the velocity of the moving disturbance generating the flow, different deflection patterns of the floating ice sheet are observed. In order to compute solutions as efficiently as possible, we introduce a novel hybrid preconditioning technique used in an iterative Newton-Krylov solver. This technique is able to significantly increase the grid refinement and decrease the computational time of our solutions in comparison to methods that are presently used in the literature. We show how this approach is generalizable to three-dimensional ice wave patterns in different velocity regimes.