Density gradient‐based adaptive refinement of analysis mesh for efficient multiresolution topology optimization
Density gradient‐based adaptive refinement of analysis mesh for efficient multiresolution topology optimization
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DOI：
10.1002/nme.6863
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发表时间：
2021-10
影响因子：
2.9
通讯作者：
F. Mezzadri;Xiaoping Qian
中科院分区：
文献类型：
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作者：
F. Mezzadri;Xiaoping Qian
在拓扑优化中，问题的有限元分析通常是求解过程中计算量最大的任务。为了提高这一阶段的效率，在这篇文章中，我们提出了一个粗糙的分析网格表示零密度梯度的区域。该设计而是以均匀网格表示。我们通过讨论密度梯度的拓扑意义以及它如何帮助避免在设计和分析网格之间的投影或插值过程中丢失信息来激发基于密度梯度的自适应细化。我们还研究了网格的自适应性及其检测设计拓扑变化的能力。并进行了后验误差分析。此外，我们提供了理论和数值上的考虑减少的自适应分析网格的自由度的数量相对于统一的情况。这转化为更快的分析解决方案，正如我们数值显示的那样。最后，我们解决了几个测试问题，包括我们在计算机集群上并行解决的大型3D问题，证明了我们的程序在大规模计算和迭代求解器中的适用性。
In topology optimization, the finite‐element analysis of the problem is generally the most computationally demanding task of the solution process. In order to improve the efficiency of this phase, in this article we propose to represent regions with zero density gradient by a coarser analysis mesh. The design is instead represented in a uniform mesh. We motivate the density gradient‐based adaptive refinement by discussing the topological meaning of the density gradient and how it can help avoid loss of information during projections or interpolations between design and analysis meshes. We also study the adaptiveness of the mesh and its ability to detect the topology change of the design. An a posteriori error analysis is performed as well. Furthermore, we provide theoretical and numerical considerations on the reduction of the number of degrees of freedoms of the adaptive analysis mesh with respect to the uniform case. This translates into a faster solution of the analysis, as we show numerically. Finally, we solve several test problems, including large 3D problems that we solve in parallel on computer cluster, demonstrating the applicability of our procedure in large scale computing and with iterative solvers.