Optimizing domain parameterization in isogeometric analysis based on Powell-Sabin splines
Optimizing domain parameterization in isogeometric analysis based on Powell-Sabin splines
复制标题
DOI：
10.1016/j.cam.2015.03.024
复制
发表时间：
2015-12
期刊：
影响因子：
--
通讯作者：
H. Speleers;C. Manni
中科院分区：
文献类型：
--
作者：
H. Speleers;C. Manni
我们解决的问题，构建一个高品质的参数化给定的平面物理域，定义通过一组有限的边界曲线。我们寻找一个几何地图表示的Powell-Sabin B-样条。Powell-Sabin样条是定义在三角剖分上的C1二次样条，因此参数域可以是任何多边形。几何贴图由以下三个步骤生成。首先，确定参数域的形状和对应的三角测量，使得其角的数量与物理域的角的数量相匹配。其次，选择与Powell-Sabin B样条表示相关的边界控制点，使它们参数化物理域的边界曲线。第三，通过求解基于温斯洛泛函的灵活优化问题来获得剩余的内部控制点。建议的域参数化过程中示出的上下文中的等距伽辽金离散Powell-Sabin样条数值。事实证明，从参数域的一般性所产生的灵活性对参数化的质量以及计算的近似解的精度具有有益的影响。
We address the problem of constructing a high-quality parameterization of a given planar physical domain, defined by means of a finite set of boundary curves. We look for a geometry map represented in terms of Powell–Sabin B-splines. Powell–Sabin splines are C 1 quadratic splines defined on a triangulation, and thus the parameter domain can be any polygon. The geometry map is generated by the following three-step procedure. First, the shape of the parameter domain and a corresponding triangulation are determined, in such a way that its number of corners matches the number of corners of the physical domain. Second, the boundary control points related to the Powell–Sabin B-spline representation are chosen so that they parameterize the boundary curve of the physical domain. Third, the remaining inner control points are obtained by solving a nimble optimization problem based on the Winslow functional. The proposed domain parameterization procedure is illustrated numerically in the context of isogeometric Galerkin discretizations based on Powell–Sabin splines. It turns out that the flexibility rising from the generality of the parameter domain has a beneficial effect on the quality of the parameterization and also on the accuracy of the computed approximate solution.