Hole patching in unstructured mesh and parallelization using graphics processing units.

摘要

Engineering analysis of a three-dimensional geometric model using mesh-based computational technologies requires the model to be topologically watertight. However, achieving watertight geometry is considered to be a challenging task in the field of computational engineering due to the potential presence of geometric deficiencies, such as gaps and holes on the surfaces. This dissertation aims to repair the defective geometric model with the presence of holes irrespective of their complexities. Presented in this dissertation are novel research and implementation of a hybrid surface and volume-based technique for geometry repair. It utilizes a NURBS-based surface-patching algorithm for topologically simple holes and incorporates a volumetric hole-patching algorithm for complex holes. The volume-based hole-patching algorithm solves the diffusion equation using an explicit forward difference scheme in time and a centered difference scheme in space. A robust and efficient algorithm has been developed to both identify and extract a localized hole region. An automated mesh generation process has been implemented to construct individual "column grids" for each isolated hole region. The diffusion equation is solved using finite-difference techniques to generate a scalar solution field from which isosurfaces are extracted with an isovalue that represents the repaired surfaces for the local regions. Finally, a Poisson surface reconstruction is used to create a reconstructed watertight surface.;The graphics processing unit (GPU) has emerged as the most powerful chip in a computer in the last decade but has only in the past few years received extensive attention from the research community for its use in high performance computing. This research explores a GPU-based implementation of a diffusion equation solution to better harness its computation potential and to facilitate the computational needs of geometry repair. Comparisons of the speedup gains for diffusion solutions using GPGPU with that of conventional single and multi-threaded implementations are presented, and their performance characteristics are discussed in this dissertation.