Automatic construction of boundary parametrizations for geometric multigrid solvers
Automatic construction of boundary parametrizations for geometric multigrid solvers
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DOI：
10.1007/s00791-006-0013-1
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发表时间：
2006-03-01
影响因子：
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通讯作者：
Sander, Oliver
中科院分区：
文献类型：
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作者：
Krause, Rolf;Sander, Oliver
提出了一种自动构造边界和界面表面参数化的算法。从描述计算域的高分辨率三角曲面开始，我们迭代简化曲面，产生具有相同拓扑类型的边界的粗略近似。在简化过程中，我们构造了一个函数，该函数定义在粗糙表面上，其图像为原始表面。该函数允许访问原始表面的正确形状和表面法线以及在其上定义的任何类型的数据。这些信息可以用于几何多网格求解器进行自适应网格细化。我们的算法在所有类型的输入表面上运行稳定，包括那些描述由几种材料组成的域的输入表面。我们已经在不同的领域成功地使用了我们的方法，并讨论了结构力学和生物力学的例子。
We present an algorithm that constructs parametrizations of boundary and interface surfaces automatically. Starting with high-resolution triangulated surfaces describing the computational domains, we iteratively simplify the surfaces yielding a coarse approximation of the boundaries with the same topological type. While simplifying we construct a function that is defined on the coarse surface and whose image is the original surface. This function allows access to the correct shape and surface normals of the original surface as well as to any kind of data defined on it. Such information can be used by geometric multigrid solvers doing adaptive mesh refinement. Our algorithm runs stable on all types of input surfaces, including those that describe domains consisting of several materials. We have used our method with success in different fields and we discuss examples from structural mechanics and biomechanics.