This article proposes a generic approach to obtain semi-analytical mesh sensitivities and shows how to compute mesh updates for any tetrahedral mesher. The proposed strategy allows sensitivities to be computed for a given mesh or first improve an initial mesh and then compute sensitivities. The strategy is based on a modification of Persson and Strang's mesher, Distmesh, analogizing the mesh to a simple truss structure. The boundary of the mesh is maintained using Lagrangian multipoint constraints. An analytical relationship between the mesh and the boundary permits the nodes to move freely along the boundary. This links the mesh directly to the parameterized geometry. We demonstrate the approach's ability to produce accurate, smooth and continuous mesh sensitivities and update the mesh. We use the resulting sensitivities to predict mesh updates corresponding to geometry updates. Four examples are given that show the method can accurately describe linear and nonlinear convex and concave domains. An example is given that also demonstrates the ability to generate accurate mesh sensitivities for a mesh created using the third party mesher GMSH.

中文翻译：

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获得四面体网格生成器的半解析网格灵敏度/速度的通用策略

本文提出了一种获得半解析网格灵敏度的通用方法，并展示了如何计算任何四面体网格生成器的网格更新。所提出的策略允许计算给定网格的灵敏度，或者首先改进初始网格，然后计算灵敏度。该策略基于 Persson 和 Strang 的网格生成器 Distmesh 的修改，将网格类比为简单的桁架结构。使用拉格朗日多点约束来维护网格的边界。网格和边界之间的解析关系允许节点沿边界自由移动。这将网格直接链接到参数化几何。我们展示了该方法产生准确、平滑和连续的网格敏感性并更新网格的能力。我们使用由此产生的灵敏度来预测与几何更新相对应的网格更新。给出了四个例子，表明该方法可以准确地描述线性和非线性凸凹域。给出的示例还演示了为使用第三方网格生成器 GMSH 创建的网格生成准确网格灵敏度的能力。