Abstract
AbstractWe present the Galerkin boundary element method (BEM) for the numerical simulation of free-surface water waves in a model basin. In this work, as a first step we consider the linearized model of this time-dependent three-dimensional problem. After time discretization by an explicit Runge-Kutta scheme, the problem to be solved at each time step corresponds to the evaluation of a Dirichlet-to-Neumann map on the free surface of the domain. We use the Galerkin BEM for the approximate evaluation of the Dirichlet-to-Neumann map. To solve the resulting large, dense linear system, we use a data-sparse matrix approximation method based on hierarchical matrix representations. The proposed algorithm is quasi-optimal. Finally, some numerical results are given.KeywordsBoundary Element MethodModel BasinLinear WaterGalerkin Boundary Element MethodHierarchical MatriceThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Published Version
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