Propagating Geometry Information to Finite Element Computations
Propagating Geometry Information to Finite Element Computations
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DOI：
10.1145/3468428
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发表时间：
2019-10
期刊：
影响因子：
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通讯作者：
L. Heltai;W. Bangerth;M. Kronbichler;A. Mola
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文献类型：
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作者：
L. Heltai;W. Bangerth;M. Kronbichler;A. Mola
连续介质力学模拟中的传统工作流程是几何描述-例如使用构造性实体几何（CSG）或计算机辅助设计（CAD）工具获得-形成网格生成器的输入。然后将网格用作有限元、有限体积和有限差分求解器的唯一输入，此时不再访问原始的“底层”几何。然而，许多现代技术（例如，自适应网格细化和使用高阶几何近似方法）确实需要有关底层几何的信息才能实现其全部潜力。我们已经进行了详尽的研究，典型的有限元代码使用几何信息，以确定几何工具将提供什么样的信息的目标。我们的研究表明，几乎所有的几何相关的需求内的模拟器可以满足只有两个“原语”：由模拟软件的几何描述所构成的基本查询。然后，我们表明，它是可能的，以提供这些原语的所有常用的方式，在常见的工业工作流程中描述的几何形状，并说明我们的解决方案，使用一些例子。
The traditional workflow in continuum mechanics simulations is that a geometry description —for example obtained using Constructive Solid Geometry (CSG) or Computer Aided Design (CAD) 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, “underlying” geometry. However, many 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 nearly all geometry-related 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 frequently used ways in which geometries are described in common industrial workflows, and illustrate our solutions using a number of examples.