The scaled boundary finite element method (SBFEM) has recently been employed as an efficient means 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 SBFEM 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 certain transition elements on the subdomains' surfaces. Thus, we avoid the triangulation of surfaces employed in previous works and consequently reduce the number of surface elements and degrees of freedom. In addition, these discretizations allow coupling elements of arbitrary order such that local p-refinement can be achieved straightforwardly.

翻译：缩放边界有限元法（SBFEM）近期被用作三维结构建模的高效手段，尤其适用于几何体以体素图像形式呈现的场景。该方法对计算域进行八叉树分解，并将每个立方体单元视为一个SBFEM子域。每个子域的表面采用有限元方式进行离散化。本文通过将SBFEM的半解析概念与子域表面的特定过渡单元相结合，对这一思路进行了改进。由此避免了前人工作中采用的表面三角剖分，从而减少了表面单元数量与自由度。此外，这种离散化方法允许耦合任意阶次的单元，使得局部p型细化的实现变得直接可行。