Decoupling simulation accuracy from mesh quality
Decoupling simulation accuracy from mesh quality
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DOI：
10.1145/3272127.3275067
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发表时间：
2018-12
期刊：
影响因子：
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通讯作者：
T. Schneider;Yixin Hu;Jérémie Dumas;Xifeng Gao;Daniele Panozzo;D. Zorin
中科院分区：
文献类型：
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作者：
T. Schneider;Yixin Hu;Jérémie Dumas;Xifeng Gao;Daniele Panozzo;D. Zorin
对于给定的偏微分方程问题，影响有限元解精度的主要因素有三个：基阶、网格分辨率和网格单元质量。前两个因素很容易控制，而控制元件形状质量是一个挑战，对可以实现的目标有根本的限制。我们建议使用p-细化（增加元素的程度）解耦的近似误差的有限元方法从域网格质量椭圆偏微分方程。我们的技术产生一个精确的解决方案，即使在网格形状不好的元素，由于高阶元素的成本较高，运行时间稍长。我们证明，它是能够自动适应的基础上，形状不好的元素，确保高质量的啮合一致的错误，没有任何每网格参数调整。我们的建设减少到传统的固定度有限元方法在高质量的网格具有相同的性能。我们的建设减少了网格算法的负担，减少了往往昂贵的网格优化的需要，并自动补偿形状不好的元素，这是目前由于边界约束或当前的网格方法的限制。通过联合处理网格生成和有限元模拟，我们获得了一个比现有的最先进的网格划分和FEM算法的组合更有效和更强大的流水线。
For a given PDE problem, three main factors affect the accuracy of FEM solutions: basis order, mesh resolution, and mesh element quality. The first two factors are easy to control, while controlling element shape quality is a challenge, with fundamental limitations on what can be achieved. We propose to use p-refinement (increasing element degree) to decouple the approximation error of the finite element method from the domain mesh quality for elliptic PDEs. Our technique produces an accurate solution even on meshes with badly shaped elements, with a slightly higher running time due to the higher cost of high-order elements. We demonstrate that it is able to automatically adapt the basis to badly shaped elements, ensuring an error consistent with high-quality meshing, without any per-mesh parameter tuning. Our construction reduces to traditional fixed-degree FEM methods on high-quality meshes with identical performance. Our construction decreases the burden on meshing algorithms, reducing the need for often expensive mesh optimization and automatically compensates for badly shaped elements, which are present due to boundary constraints or limitations of current meshing methods. By tackling mesh generation and finite element simulation jointly, we obtain a pipeline that is both more efficient and more robust than combinations of existing state of the art meshing and FEM algorithms.