| Summary: | Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2010. === Cataloged from PDF version of thesis. === Includes bibliographical references (p. 58-60). === The numerical approximation of the Poisson equation can often be found as a subproblem to many more complex computations. In the case of Lagrangian approaches of flow equations, the Poisson equation often needs to be solved on an irregular point distribution. Currently, mainly unstructured mesh-based approaches are used. Meshfree methods present a way to approximate differential operators on unstructured point clouds without the need for mesh generation. In this thesis, a 3d meshfree finite difference Poisson solver is presented. Its performance has been studies based on numerical convergence, parallel efficiency, and computational cost. Practical application of the solver is presented in a simulation of a potential flow field in a wall-bounded domain. === by Anna Vasilyeva. === S.M.
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