In this paper, we will focus on adaptive meshing and re-meshing. We present an original approach, based on Quadtree and Octree, to construct the initial mesh and refine it using mixed-elements. We propose a fast algorithm using a determined set of Patterns to handle transitions between fine and coarse regions, and to closely approximate surface boundaries. An optimized structure for storing edges permits to efficiently manage neighbor information, dramatically reducing the balancing time. Results, both in 2D and 3D, exhibit the multiple possibilities for local refinements. Comparisons in terms of accuracy, number of elements in the resulting mesh, and computation time, clearly position our method as a competitive alternative to generate a conform adapted mesh, which can be used with standard numerical methods.

在本文中，我们将重点介绍自适应网格划分和重新网格划分。我们提出一种基于Quadtree和Octree的原始方法来构造初始网格并使用混合元素对其进行优化。我们提出了一种快速算法，该算法使用确定的一组模式来处理精细区域和粗糙区域之间的过渡，并近似逼近表面边界。用于存储边缘的优化结构允许有效管理邻居信息，从而大大减少了平衡时间。2D和3D的结果都显示出进行局部改进的多种可能性。在准确性，结果网格中的元素数量和计算时间方面的比较清楚地将我们的方法定位为竞争性替代方法，可以生成符合标准的网格，可以与标准数值方法一起使用。