In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy

Kaoji Xu

will defend his dissertation

Hexahedral Mesh Generation, Optimization, and Visualization

Abstract

Hexahedral (or hex-) meshes are preferred in many medical, engineering and scientific simulation applications due to their desired numerical properties (e.g., natural tensor embedding, large tolerance for anisotropy deformation and less numerical stiffness), which usually lead to faster and more accurate simulations for those applications. In the general hex-meshing pipeline (i.e., hex-mesh generation and post-processing), each step still has its limitations despite decades of efforts. My dissertation is dedicated to address some of those limitations, including adaptive hex-mesh with simple structure for generation, and a new untangling framework for the post-processing. In addition, to help achieve structured hex-mesh generation, which is important for certain applications, I present a first visualization strategy to help us understand the structure in a hex-mesh. Finally, I propose a semi-global strategy to reduce the structure complexity of hex-meshes. Most existing techniques aim to generate a hex-mesh with a uniform element size, which may not be suitable for simulations that require higher accuracy in certain regions of interest. To address that, adaptive meshes should be utilized. However, existing adaptive mesh generation techniques typically produce hex-meshes with complex structures. To address this issue, a new framework is proposed to generate a hex-mesh with varying element sizes according to the input surface feature, while still having a simple structure. Usually, the initially created hex-meshes might not have a high quality required by simulations, sometimes they even contain inverted elements which cannot be used for simulations. To address this issue, a new framework to untangle hex-meshes with inverted elements effectively is introduced. To do so, the proposed method first untangles the hex-mesh and improves its quality via optimizing each edge-angle to its ideal degree. The same framework can be used to further improve the hex-mesh element quality after untangling. Compared to the state-of-the-art technique, the proposed method improves hex-meshes with better quality in terms of the minimum scaled Jacobian and boundary error. Beside element quality, producing hex-meshes with simple structure is important for certain applications. However, there currently lacks an understanding of the complex 3D structure of hex-meshes. To address this, an effective framework to calculate and visualize the complexity of a hex-mesh structure is introduced. This framework enable us to decode the configuration in hex-meshes structures in a multi-level fashion. It also introduces a first comprehensive complexity metric for the measurement of the quality of hex-mesh structure, which will benefit the future optimization and manipulation of hex-mesh structure to achieve a desired configuration. Based on the knowledge obtained from the above structure analysis, a new structure simplification is proposed. which cancels groups of singularities in a semi-global fashion. This strategy has been implemented for quad-mesh simplification and has a high possibility to be extended to simplifying hex-meshes. In summary, this dissertation contributes to all steps of hex-meshing pipeline, including its generation, optimization, and visualization. Based on this dissertation work, a robust and automatic work for the generation of high qualities meshes with structure adapting to the needs of application can be developed.

Date: Tuesday, April 2, 2019
Time: 3:00 - 5:00 PM
Place: PGH 550
Advisors: Dr. Guoning Chen

Faculty, students, and the general public are invited.