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

由于并行处理大大降低了生成网格后物理分析的成本和时间，因此降低生成数值网格所需的成本和时间是一个新兴的要求。此外，生物医学、生物工程和纳米科学领域的新兴应用需要新的网格生成方法。这些应用需要更高的表面表示精度，通常涉及高度灵活/可变形的表面，需要更高程度的自动化。本文提出了一种新的前沿方法，以解决数值网格生成的这些新要求。此外，所提出的方法可用于其他相关领域，例如用于识别感兴趣的表面的图像处理，用于“表面修复”的计算几何，以及用于计算涉及移动/变形边界的流体流动。提出的公式既适用于结构化网格，也适用于非结构化/混合网格。在研究生和本科生的帮助和参与下，提出的努力将产生一个软件产品，该软件产品将被开发并用于使用简单的几何图形来证明概念，这些学生将彻底接触到现代软件设计原则以及数学和数值分析的实际应用。在这项调查过程中积累的科学知识和经验将通过会议报告（由学生发言）和期刊出版物向社区传播，并在互联网上提供。

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.