Parallel re-initialization of level set functions on distributed unstructured tetrahedral grids

Level set functions are employed to track interfaces in various application areas including simulation of two-phase flows and image segmentation. Often, a re-initializing algorithm is incorporated to transform a numerically instable level set function to a signed distance function. In this note, we present a parallel algorithm for re-initializing level set functions on unstructured, three-dimensional tetrahedral grids. The main idea behind this new domain decomposition approach is to combine a parallel brute-force re-initializing algorithm with an efficient way to compute distances between the interface and grid points. Time complexity and error analysis of the algorithm are investigated. Detailed numerical experiments demonstrate the accuracy and scalability on up to 128 processes.