Higher‐order accurate integration of implicit geometries
Higher‐order accurate integration of implicit geometries
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DOI：
10.1002/nme.5121
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发表时间：
2016-05
影响因子：
2.9
通讯作者：
T. Fries;Samir Omerovic
中科院分区：
文献类型：
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作者：
T. Fries;Samir Omerovic
提出了一种统一的隐式定义几何高阶精确积分策略。该几何由高阶水平集函数表示。其任务是在零水平集上或在水平集函数的符号所定义的子域中进行积分。在三维中，这要么是表面上的积分，要么是体积内的积分。一个起点是通过高阶界面元对零级集合进行识别和网格化。对于体积积分，提出了特殊的子单元，其中单元面与零级集合上已识别的界面单元重合。将标准高斯点映射到界面元素或体积子元素。所得到的积分点可以例如用于虚拟区域方法和扩展有限元方法。对于六面体网格的情况，该方法的一部分也可以被视为高阶行进立方体算法。版权所有©2015 John Wiley&Sons，Ltd.
A unified strategy for the higher‐order accurate integration of implicitly defined geometries is proposed. The geometry is represented by a higher‐order level‐set function. The task is to integrate either on the zero‐level set or in the sub‐domains defined by the sign of the level‐set function. In three dimensions, this is either an integration on a surface or inside a volume. A starting point is the identification and meshing of the zero‐level set by means of higher‐order interface elements. For the volume integration, special sub‐elements are proposed where the element faces coincide with the identified interface elements on the zero‐level set. Standard Gauss points are mapped onto the interface elements or into the volumetric sub‐elements. The resulting integration points may, for example, be used in fictitious domain methods and extended finite element methods. For the case of hexahedral meshes, parts of the approach may also be seen as a higher‐order marching cubes algorithm. Copyright © 2015 John Wiley & Sons, Ltd.