A Finite Element Method for Fully Nonlinear Water Waves

@article{Cai1998AFE,
  title={A Finite Element Method for Fully Nonlinear Water Waves},
  author={Xing Cai and Hans Petter Langtangen and Bj{\o}rn Fredrik Nielsen and Aslak Tveito},
  journal={Journal of Computational Physics},
  year={1998},
  volume={143},
  pages={544-568}
}
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 fixed 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… 

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