Fast parallel solver for the levelset equations on unstructured meshes. (4th July 2014) - Fu, Zhisong; Yakovlev, Sergey; Kirby, Robert M.; Whitaker, Ross T.
Summary The levelset method is a numerical technique that tracks the evolution of curves and surfaces governed by a nonlinear partial differential equation (levelset equation). It has applications within various research areas such as physics, chemistry, fluid mechanics, computer vision, and microchip fabrication. Applying the levelset method entails solving a set of nonlinear partial differential equations. This paper presents a parallel algorithm for solving the levelset equations on unstructured 2D and 3D meshes. By taking into account constraints and capabilities of different computing architectures, the method is suitable for both the coarse‐grained parallelism found on CPU‐based systems and the fine‐grained parallelism of modern massively single instruction, multiple data architectures such as graphics processors. In order to solve the levelset equations efficiently, we combine the narrowband scheme with a domain decomposition that is adapted for several different architectures. We also introduce a novel parallelism strategy, which we call hybrid gathering, which allows regular and lock‐free computations of local differential operators. Finally, we provide the detailed description of the implementation and data structures for the proposed strategies, as well as performance data for both CPU and graphics processing unit implementations. Copyright © 2014 John Wiley & Sons, Ltd.