The scaled boundary finite element method (SBFEM) has recently been employed as an efficient tool to model three-dimensional structures, in particular when the geometry is provided as a voxel-based image. To this end, an octree decomposition of the computational domain is deployed, and each cubic cell is treated as an SBFE subdomain. The surfaces of each subdomain are discretized in the finite element sense. We improve on this idea by combining the semi-analytical concept of the SBFEM with a particular class of transition elements on the subdomains’ surfaces. Thus, a triangulation of these surfaces as executed in previous works is avoided, and consequently, the number of surface elements and degrees of freedom is reduced. In addition, these discretizations allow coupling elements of arbitrary order such that local p-refinement can be achieved straightforwardly.

中文翻译：

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结合SBFEM和超限元形状函数的三维图像建模

缩放边界有限元方法 (SBFEM) 最近已被用作建模三维结构的有效工具，特别是当几何作为基于体素的图像提供时。为此，部署了计算域的八叉树分解，并将每个立方单元视为一个 SBFE 子域。每个子域的表面都是在有限元意义上离散的。我们通过将 SBFEM 的半解析概念与子域表面上特定类别的过渡元素相结合来改进这一想法。因此，避免了在以前的工作中对这些表面进行三角剖分，从而减少了表面元素的数量和自由度。此外，