Smart octrees: Accurately integrating discontinuous functions in 3D

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• 作者：Lá ; szló ; Kudela^a ; ^{laszlo.kudela@tum.de" class="auth_mail" title="E-mail the corresponding author} ; Nils Zander^a ; Stefan Kollmannsberger^a ; Ernst Rank^a ; ^b
• 关键词：Finite Cell Method ; Numerical integration ; Marching cubes
• 刊名：Computer Methods in Applied Mechanics and Engineering
• 出版年：2016
• 出版时间：1 July 2016
• 年：2016
• 卷：306
• 期：Complete
• 页码：406-426
• 全文大小：3355 K

文摘

This paper presents an efficient and accurate method for the integration of discontinuous functions on a background mesh in three dimensions. This task is important in computational mechanics applications where internal interfaces are present in the computational domain. The proposed method creates boundary-conforming integration subcells for composed numerical quadrature, even in the presence of sharp geometric features (e.g. edges or vertices). Similar to the octree procedure, the algorithm subdivides the cut elements into eight octants. However, the octant nodes are moved onto the interface, which allows for a robust resolution of the intersection topology in the element while maintaining algorithmic simplicity. Numerical examples demonstrate that the method is able to deliver highly accurate domain integrals with a minimal number of quadrature points. Further examples show that the proposed method provides a viable alternative to standard octree-based approaches when combined with the Finite Cell Method.