Boundary Element Simulation of Linear Water Waves in a Model Basin

  • Clemens Hofreither
  • Ulrich Langer
  • Satyendra Tomar
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5910)

Abstract

We 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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Clemens Hofreither
    • 1
  • Ulrich Langer
    • 2
  • Satyendra Tomar
    • 3
  1. 1.DK Computational MathematicsJKU LinzLinzAustria
  2. 2.Institute of Computational MathematicsJKU LinzLinzAustria
  3. 3.Johann Radon Institute for Computational and Applied Mathematics (RICAM)LinzAustria

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