A Generic Paradigm for Accelerating Laplacian-Based Mesh Smoothing on the GPU

Abstract

General purpose computing on Graphics Processor Units (GPGPU) can significantly reduce computational cost by performing massively parallel computing. The benefits of GPGPU have been exploited in mesh generation and mesh optimization. Mesh smoothing is one of the most popular approaches that are capable of improving mesh quality by repositioning nodes in meshes without altering the topology of meshes. In this paper, specifically aiming at Laplacian-based mesh smoothing, a generic paradigm for exploiting the power of GPU-acceleration is developed to improve the computational efficiency. The data layouts for representing mesh data structures on the GPU are first discussed; and then a practical solution to dealing with the data dependencies in the iterative smoothing procedure is introduced. Two forms of iteration in Laplacian smoothing (LS) are also analyzed, including the form that needs to swap intermediate nodal coordinates and the other form that does not swap data. In addition, the standard LS is implemented to demonstrate the effectiveness of the presented paradigm. Experimental results show that: on single and double precision, the GPU implementations developed using the data structures represented by aligned array-of-structures layout achieve the best efficiency. It is also demonstrated that the form that needs to swap intermediate nodal coordinates is always slower than the one that does not swap data.