A generalized particle search-locate algorithm for arbitrary grids (Q1357324)

An iterative algorithm for searching and locating particles in arbitrary two-dimensional meshes is presented. Such algorithms play an essential role in implementing characteristic-Galerkin finite element methods or semi-Lagrangian difference schemes. The algorithm uses the Newton iteration method to invert the map of the mesh element onto a reference element and incorporates a criterion for the movement of the particle from one element to another element of the mesh. Numerical examples for various grids demonstrate the performance, the accuracy and the versatility of the method.