Exploration of recursive skeletonization for accelerating nonlinear potential flow wave propagation

  • Harris, Jeffrey (Ecole des Ponts ParisTech)

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Many models for nonlinear dispersive wave modeling, whether based on finite elements, finite differences, boundary elements, spectral elements, or other discretizations, depend on the solution of the Laplace equation. For larger grids, depending on the approach, moderate to large grids require additional algorithms to obtain results in a reasonable amount of time, whether based on choice of preconditioner, the use of low-rank approximations, the fast multipole method, or other approaches. In each case, an improvement is noted to computational speed, but at the cost of increased complexity. Alternatively, a more recent approach is recursive skeletonization, which can easily be applied to the system matrix used for a Laplace solver, to act as a preconditioner, to solve the linear problem, or with some extensions, a direct 3D solver. In this work, we look at some of the ways recursive skeletonization, could be used help in the computational effort required for nonlinear potential flow problems. The resulting model is validated to show that a simulation becomes notably faster without adding significant error, and can be extended to different potential flow models. Results for both 2D and 3D applications with nonlinear wave propagation are considered.