CAREER: Dynamics, Domain Conformity, and Anisotropy in the Theory and Implementation of Unstructured Mesh Generation

职业：非结构化网格生成理论和实现中的动力学、域一致性和各向异性

• 批准号: 9875170
• 负责人: Jonathan Shewchuk
• 金额: $ 24.55万
• 依托单位: University of California-Berkeley
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1999
• 资助国家: 美国
• 起止时间: 1999-08-01 至 2004-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9875170&HistoricalAwards=false
• 关键词: CAREER; Dynamics; Domain; Conformity; Anisotropy

Solutions to complex scientific simulations based on partial differential equations use discrete meshes to represent the physical (continuous) domain. Similarly, computer rendering of complex scenes uses these meshes for radiosity calculations. Existing heuristic-based methods do not produce meshes that dependable for 3-dimensional real-world problems that include moving or complex surfaces, or that exhibit anisotropic (direction-dependent) behavior. This project will design, analyze, and implement mesh generation algorithms for these domains that are practical and, where possible, provably good. The technical approach to this task is to use optimization-based smoothing and topological transformations. For anisotropic problems, the project will also develop a firm theoretical basis footing for extending Delaunay triangulations to the anisotropic case. Finally, in three dimensions the project will pursue a firm understanding of constrained Delaunay tetrahedralizations and algorithms for their construction.This project will also be active in integrating research with education. It will contribute to curriculum development and course design in support of a new Computational Engineering Science program being initiated within the College of Engineering at UC Berkeley. This effort will include courses and texts in mesh generation and conjugate gradient-like solvers.

基于偏微分方程的复杂科学模拟的解决方案使用离散网格来表示物理（连续）域。类似地，复杂场景的计算机渲染使用这些网格进行光能传递计算。现有的基于几何的方法不产生可靠的三维现实世界的问题，包括移动或复杂的表面，或表现出各向异性（方向相关）的行为的网格。这个项目将设计，分析和实现这些领域的网格生成算法，这些算法是实用的，并且在可能的情况下，可以证明是好的。该任务的技术方法是使用基于优化的平滑和拓扑变换。对于各向异性问题，该项目还将为将Delaunay三角剖分扩展到各向异性情况奠定坚实的理论基础。最后，在三维方面，该项目将寻求对约束Delaunay四面体及其构建算法的深刻理解。该项目还将积极将研究与教育相结合。它将有助于课程开发和课程设计，以支持在加州大学伯克利分校工程学院内启动的新的计算工程科学计划。这项工作将包括课程和文本在网格生成和共轭梯度样求解器。