An efficient particle locating method on unstructured meshes in two and three dimensions based on patch searching

Abstract: We present a particle locating method for unstructured meshes in two and three dimensions. Our algorithm is based on a patch searching process, and includes two steps. We first locate the given point to a patch near a vertex, and then the host element is determined within the patch domain. Here, the patch near a vertex is the domain of elements around this vertex. We prove that in the first step the patch can be rapidly identified by constructing an auxiliary Cartesian grid with a prescribed resolution. Then, the second step can be converted into a searching problem, which can be easily solved by searching algorithms. Only coordinates to particles are required in our method. We conduct a series of numerical tests in two and three dimensions to illustrate the robustness and efficiency of our method.