Automatic and Adaptive Mesh Generation with Applications to Scientific Computing

自动和自适应网格生成及其在科学计算中的应用

• 批准号: 9902091
• 负责人: Gary Miller
• 金额: $ 32.41万
• 依托单位: Carnegie-Mellon University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1999
• 资助国家: 美国
• 起止时间: 1999-09-01 至 2003-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9902091&HistoricalAwards=false
• 关键词: Automatic; Adaptive; Mesh; Generation; Applications

This project combines the expertise developed in the numerical analysis community with that developed in algorithm design community to solve scientific problems governed by partial differential equations. Most of the effort will incorporate the analytical techniques from the numerical analysis area with the combinatorial techniques from the algorithms area. Central to this project is the design and analysis of new and novel meshing algorithms well suited for use with numerical techniques such as the finite element or finite volume methods. Special attention will be given to meshing in three dimensions. In particular, extension of algorithms developed under prior NSF grants will be constructed. These extensions include analyzable methods for both mesh refinement and coarsening. The more general problem of adaptive meshing for problems that are changing with time, such as solutions to singular and degenerate parabolic equations, will also be studied. The use of triangles and tetrahedra that may have small angles but no angles approaching 180 degrees will also be undertaken. Fundamental to the project is the development of good methods to estimate the eigenvalues of graphs. These tools will be used to estimate convergence rates for preconditioned iterative system solvers, to estimate interpolation error for particular mesh algorithms, to compute error estimates for control volume methods, and to analyze spectral separator methods.

这个项目结合了数值分析领域的专业知识和算法设计领域的专业知识，以解决偏微分方程式所支配的科学问题。大部分工作将把数值分析领域的分析技术与算法领域的组合技术结合起来。这个项目的核心是设计和分析新的和新的网格划分算法，这些算法非常适合用于数值技术，如有限元或有限体积法。将特别注意三维啮合。特别是，将构建在先前NSF拨款下开发的算法的扩展。这些扩展包括网格细化和粗化的可分析方法。对于随时间变化的问题，例如奇异和退化抛物型方程的解，还将研究更一般的自适应网格划分问题。还将使用可能有小角度但没有接近180度的角度的三角形和四面体。这个项目的基础是开发好的方法来估计图的特征值。这些工具将被用来估计预条件迭代系统求解器的收敛速度，估计特定网格算法的内插误差，计算控制体积方法的误差估计，以及分析谱分离方法。