SGER: Exploratory Research on a New Advancing Front Approach for Numerical Grid Generation

由于并行处理极大地减少了网格生成后物理分析的成本和时间，因此减少生成数值网格所需的成本和时间是一个新兴的需求。此外，在生物医学、生物工程和纳米科学竞技场中的新兴应用需要新的网格生成方法。这些应用需要更高精度的表面表示，并且通常涉及高度柔性/可变形的表面，并且需要更高程度的自动化。提出了一种新的推进前沿方法，将解决这些新出现的要求，数值网格生成。此外，所提出的方法可以用于其他相关领域，如在图像处理中识别感兴趣的表面，在计算几何学的“表面修复”，并在计算流体流动涉及移动/变形边界。提出的配方解决结构化和非结构化/混合网格。拟议的努力将导致一个软件产品，将开发和使用的概念证明使用简单的几何形状的帮助和参与的研究生和本科生，谁将彻底接触到现代软件设计原则的实际使用，以及数学和数值分析。在这次调查过程中积累的科学知识和经验将通过会议介绍、学生演讲者的参与、期刊出版物以及互联网上提供的方式向社区传播。

Cutting down the cost and the time necessary for generating numerical grids is an emerging requirement since parallel processing has enormously cut down the cost and time of physical analysis after a grid is generated. Besides, emerging applications in the biomedical, bioengineering and nanosciences arena demand new approaches to grid generation. These applications demand higher accuracy of surface representation and typically involve highly flexible/deformable surfaces and require a higher degree of automation. A new advancing front approach is proposed here that will address these emerging requirements on numerical grid generation. Moreover, the proposed approach can be used in other related areas such as in image processing for identifying surfaces of interest, in computational geometry for "surface repair", and, in computing fluid flows involving moving/deforming boundaries. The formulation presented addresses both structured and unstructured/hybrid grids. The proposed effort will result in a software product that will be developed and used for proof of concept using simple geometries with the help and involvement of graduate and undergraduate students, who will be thoroughly exposed to the practical use of modern software design principles as well as mathematical and numerical analyses. Scientific knowledge and experience accrued during the course of this investigation will be disseminated to the community through conference presentations, with the involvement of student presenters, and journal publications, as well as be made available over the Internet.