Parallel Correction for Hierarchical Re-Distancing Using the Fast Marching Method

Abstract

Topography simulation is typically implemented with the level-set method which uses the level-set function to represent the interface. The signed-distance property, capturing the distances from the entire simulation domain towards the interface, has to be regularly restored during a simulation in order to update the distances relative to the evolution of the interface. The restoring process is called ‘re-distancing’ and the most established algorithm is the Fast Marching Method. For Cartesian grids, which are commonly used, high-performance applications require an adaptive resolution for geometric features, such as narrow trenches or sharp corners. Among the most important challenges is the need to utilize the solution in higher resolved regions to correct the solution in the embedding coarser regions. We present a parallelized bottom-up (i.e. from finest to coarsest resolution levels) correction technique for hierarchical re-distancing using the Fast Marching Method, which increases the accuracy of the discretized level-set function on the coarser grids. The coarser grids are corrected by interpolation on grid points covered by finer regions and a partial restart of the Fast Marching Method for the remaining grid points, thus minimizing the computational effort. This parallel correction step has been integrated into a recently developed parallel re-distancing algorithm, is implemented in C++ using OpenMP, and is evaluated for different geometries. The correction step significantly reduces the error in the signed-distance function, introducing a performance penalty of less than 10%.