A nite element method for fullynonlinear water waves

We introduce a numerical method for fully nonlinear, three-dimensional water surface waves, described by standard potential theory. The method is based on a transformation of the dynamic water volume onto a xed domain. Regridding at each time step is thereby avoided. The transformation introduces an elliptic boundary value problem which is solved by a preconditioned conjugate gradient method. Moreover, a simple domain imbedding precedure is introduced to solve problems with an obstacle in the water volume. Numerical experiments are presented and they show nice convergence properties of the iterative solver as well as convergence of the entire solution towards a reference solution computed by another scheme.