Poly-Spline Finite-Element Method
Poly-Spline Finite-Element Method
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DOI：
10.1145/3313797
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发表时间：
2018-04
期刊：
影响因子：
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通讯作者：
T. Schneider;Jérémie Dumas;Xifeng Gao;M. Botsch;Daniele Panozzo;D. Zorin
中科院分区：
文献类型：
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作者：
T. Schneider;Jérémie Dumas;Xifeng Gao;M. Botsch;Daniele Panozzo;D. Zorin
我们介绍了一种集成网格和有限元方法的流水线，能够求解由边界表示包围的体积中的偏微分方程组。我们构造了一个包含少量星形多面体的混合六面体占优网格，并在其元素的基础上构造了一组高阶基，结合了三次B-样条、三次六面体和调和单元。我们证明了我们的方法在精化的情况下是立方收敛的，而与由三次六面体组成的类似密度的六面体网格相比，需要大约50%的自由度。我们在一大批模型上验证了我们的方法，这些模型由我们的算法自动处理，只需要用户在他们的表面上提供边界条件。
We introduce an integrated meshing and finite-element method pipeline enabling solution of partial differential equations in the volume enclosed by a boundary representation. We construct a hybrid hexahedral-dominant mesh, which contains a small number of star-shaped polyhedra, and build a set of high-order bases on its elements, combining triquadratic B-splines, triquadratic hexahedra, and harmonic elements. We demonstrate that our approach converges cubically under refinement, while requiring around 50% of the degrees of freedom than a similarly dense hexahedral mesh composed of triquadratic hexahedra. We validate our approach solving Poisson’s equation on a large collection of models, which are automatically processed by our algorithm, only requiring the user to provide boundary conditions on their surface.