Embedded or immersed boundary methods (IBM) are powerful mesh-based techniques that permit to solve partial differential equations (PDEs) in complex geometries circumventing the need of generating a mesh that fits the domain boundary, which is indeed very difficult and has been the main bottleneck of the simulation pipeline for decades. Embedded methods exploit a simple background mesh that covers the domain and the difficulties are (1) the imposition of boundary conditions, (2) the ill-conditioning generated by poorly intersected elements and (3) the lack of resolution required in boundary layers. Whereas several methods are available in the literature to address the first two difficulties, the third one still deserves attention. Meshless methods, Chimera grids or adaptive h or p-refinement strategies have been proposed but none of them include alignment techniques.

中文翻译：

---

嵌入式有限元方法的各向异性变分网格自适应


嵌入式或浸没式边界方法 （IBM） 是一种强大的基于网格的技术，允许在复杂的几何结构中求解偏微分方程 （PDE），从而避免了生成适合域边界的网格的需求，这确实非常困难，并且几十年来一直是仿真管道的主要瓶颈。嵌入式方法利用覆盖域的简单背景网格，困难是 （1） 施加边界条件，（2） 相交不良的单元产生的不良条件，以及 （3） 边界层缺乏所需的分辨率。虽然文献中有几种方法可以解决前两个困难，但第三个仍然值得关注。已经提出了无网格方法、Chimera 网格或自适应 h 或 p 细化策略，但它们都没有包括对齐技术。