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Graph-based data structures for refinement and derefinement algorithms based on the longest edge bisection. Applications (Spanish text).

机译:基于图的数据结构,用于基于最长边平分的优化和反优化算法。应用程序(西班牙语文本)。

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摘要

In the last years, mesh generation algorithms have been largely investigated. These algorithms are basic tools in numerical methods, as in the finite element method or in the piecewise linear approximation to a given function. The algorithms are also relevant in graphic engineering, computer graphics, surfaces and solid modeling, industrial design, visualization, CAD/CAM, etc. Furthermore, in an increasing way, the algorithms are getting used in Science and Technology Numerical Simulations; in this wide topic it is specially critical to provide algorithms with efficient performance in terms of time and space.; In the refinement and coarsening algorithms, an important point is to have a suitable data structure which makes it possible that the algorithms perform in an efficient way. This is due to the complexity of operations in the elements partitions which turn in a critical issue when the dimension increases and the number of elements grow rapidly.; This thesis investigates a new class of data structures which are based on the graph theory. The data structures are used to design new efficient versions of refinement and coarsening algorithms. We explore the main properties of the data structures in 2D. Moreover, a number of applications using the new version of the algorithms are provided.
机译:在最近几年中,网格生成算法已经得到了广泛的研究。这些算法是数值方法中的基本工具,如有限元方法或给定函数的分段线性逼近。该算法还与图形工程,计算机图形学,表面和实体建模,工业设计,可视化,CAD / CAM等相关。此外,算法在科学和技术数值模拟中得到了越来越多的应用。在这个广泛的主题中,特别重要的是要在时间和空间方面为算法提供高效的性能。在细化和粗化算法中,重要的一点是要具有合适的数据结构,这使得算法可以高效地执行。这是由于元素分区中操作的复杂性,当维度增加且元素数量迅速增长时,这成为一个关键问题。本文研究了一种基于图论的新型数据结构。数据结构用于设计细化和粗化算法的新有效版本。我们探索2D数据结构的主要属性。此外,提供了使用新版本算法的许多应用程序。

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