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On the simulation of image-based cellular materials in a meshless style
Computers & Mathematics with Applications ( IF 2.9 ) Pub Date : 2021-09-15 , DOI: 10.1016/j.camwa.2021.08.021
S.M. Mirfatah 1 , B. Boroomand 1
Affiliation  

A meshfree method on fixed grids is devised for simulation of Poisson's equation on 3D image-based cellular materials. The non-boundary fitted discretization of such jagged voxel models of complex geometries is accomplished through embedding the micro-CT scan image in a Cartesian grid of nodes. The computational nodes inside the solid voxels are found by a simple point-in-membership test. Using a set of modified singular functions around the voids, along with the library-rational-exponential basis functions (EBFs) satisfying the governing differential equation, an enriched spatial solution is locally constructed on a generic computational cloud/cell (GCC) of nodes containing the voids. Within each GCC, the boundary conditions are satisfied through a weighted least-squares approximation. Finally, by establishing point-wise compatibility between the solutions of the GCCs a well-conditioned small linear system of equations is resulted. The results are compared with those of the finite element method (FEM) using extremely fine meshes with an excessive number of nodes.



中文翻译:

基于图像的蜂窝材料的无网格模拟

设计了一种固定网格上的无网格方法,用于在基于 3D 图像的细胞材料上模拟泊松方程。这种复杂几何形状的锯齿状体素模型的非边界拟合离散化是通过将微 CT 扫描图像嵌入到笛卡尔节点网格中来实现的。实体体素内的计算节点是通过简单的成员点测试找到的。使用围绕空隙的一组修改奇异函数,以及满足控制微分方程的库-有理-指数基函数 (EBF),在包含节点的通用计算云/单元 (GCC) 上本地构建了丰富的空间解决方案空隙。在每个 GCC 内,边界条件通过加权最小二乘近似来满足。最后,通过在 GCC 的解之间建立逐点兼容性,产生了条件良好的小型线性方程组。将结果与使用具有过多节点的极细网格的有限元方法 (FEM) 的结果进行比较。

更新日期:2021-09-15
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