A new approach to model and compute the metric tensor corresponding to a-priori prescribed surface and volume boundary layers is presented. This is achieved by the use of sources that model the combined anisotropic metric. Algorithms are presented to both evaluate the resulting metric value at any point in space and the efficient approximation of the minimum and maximum metric over an axis-aligned box which enables fast evaluation of the anisotropic metric independent of the approach used for mesh generation.

The ability to model and evaluate the anisotropic sizing independently ensure that mesh generation algorithms that use it can produce meshes that correctly and predictably capture the sizing fields induced by the user prescribed boundary layer attributes. The method is unique in producing globally smooth representations of the final anisotropic metric including the influence of implicit anisotropy due to boundary curvature and any prescribed isotropic sizes. As a result, it addresses robustness and size smoothness issues in legacy approaches that decouple the surface and volume mesh generation stages.

The value of the new method is demonstrated by several examples that include both surface and volume boundary layers prescribed on geometries with curved boundaries.

提出了一种建模和计算与先验规定的表面和体积边界层相对应的度量张量的新方法。这是通过使用对组合各向异性度量进行建模的源来实现的。提出了既可以评估空间上任何一点的度量标准值，又可以有效地近似最小化和最大度量在轴对齐框上的算法，从而可以独立于网格生成方法而快速评估各向异性度量。

独立地建模和评估各向异性尺寸的能力确保使用它的网格生成算法可以生成可正确且可预测地捕获由用户指定的边界层属性引起的尺寸字段的网格。该方法在产生最终各向异性度量的全局平滑表示方面具有独特性，包括边界曲率和任何规定的各向同性尺寸所引起的隐含各向异性的影响。结果，它解决了传统方法中鲁棒性和尺寸平滑性的问题，这些方法使表面网格物体和体积网格物体的生成阶段分离。

通过几个示例证明了新方法的价值，这些示例包括在具有弯曲边界的几何体上指定的表面边界层和体积边界层。