Using exact geometry information in finite element computations
Using exact geometry information in finite element computations
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发表时间：
2019-10
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通讯作者：
L. Heltai;W. Bangerth;M. Kronbichler;A. Mola
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作者：
L. Heltai;W. Bangerth;M. Kronbichler;A. Mola
Continuum Mechanics模拟中的传统工作流程是，使用建设性固体几何或计算机辅助设计工具获得的几何描述形成了网格发电机的输入。然后将网格用作有限元，有限量和有限差求解器的唯一输入，此时，该求解器不再可以访问原始几何形状。但是，许多更现代的技术（例如，自适应网格的改进和使用高阶几何近似方法）确实确实需要有关基础几何形状的信息，以实现它们的全部潜力。我们对典型有限元代码使用几何信息的详尽研究进行了详尽的研究，目的是确定必须提供哪些信息几何工具。我们的研究表明，仅两个``primitives''即可满足模拟器内部的所有几何需求：模拟软件对几何描述提出的基本查询。然后，我们证明可以以所有常用的几何形状在常见的工业工作流程中描述几何形状的所有常用方式提供这些原语。我们使用自适应网格细化的示例来说明我们的解决方案，以进行复杂的几何形状。
The traditional workflow in continuum mechanics simulations is that a geometry description -- obtained using Constructive Solid Geometry or Computer Aided Design tools -- forms the input for a mesh generator. The mesh is then used as the sole input for the finite element, finite volume, and finite difference solver, which at this point no longer has access to the original geometry. However, many more modern techniques -- for example, adaptive mesh refinement and the use of higher order geometry approximation methods -- really do need information about the underlying geometry to realize their full potential. We have undertaken an exhaustive study of where typical finite element codes use geometry information, with the goal of determining what information geometry tools would have to provide. Our study shows that all geometry needs inside the simulators can be satisfied by just two ``primitives'': elementary queries posed by the simulation software to the geometry description. We then show that it is possible to provide these primitives in all of the commonly used ways in which geometries are described in common industrial workflows. We illustrate our solutions using examples from adaptive mesh refinement for complex geometries.