论文标题
$ c^s $ -Smooth ISOOGENOMETRICEMETRIC条样条空间在平面多斑点参数化上
$C^s$-smooth isogeometric spline spaces over planar multi-patch parameterizations
论文作者
论文摘要
全球$ c^s $ -Smooth（$ s \ geq 1 $）在多斑点几何上的等几何样条空间是ISOODEMORTION分析框架中的当前研究主题。在这项工作中，我们将最近的方法[25,28]和[31-33]扩展了$ c^1 $ - 平滑的和$ c^2 $ -SMOOTH ISOOTOMETRICEMEMETRIC SPINEMEMETRICITRIC SPLINE SPACES上的特定平面多块几何形状，以$ C^S $ C^S $ -SMOTHMOTH-SMOMOTH ISOOTOMETRIC MOTORPATCH ISOOMOTOMETRIC MULTI-PATCH spline $ spome $ smooty $ smife $ smife $ s usiptersys $ s $ s smife s $ s s smife s smpempers $ s。更准确地说，对于任何$ s \ geq 1 $，我们研究了$ c^s $ - 平滑的等单样条样条函数，定义在平面，双线性参数化的多斑点域，并生成一个特定的$ c^s $ -s $ -smooth-smooth子空间。我们进一步介绍了此$ c^s $ smooth子空间的基础的构建，该子空间由简单且在本地支持的功能组成。此外，我们使用$ c^s $ smooth条样条件函数在双线性参数化的多块域上执行$ l^2 $近似，其中获得的数值结果表明构建的$ c^s $ -smooth子空间的最佳近似能力。
The design of globally $C^s$-smooth ($s \geq 1$) isogeometric spline spaces over multi-patch geometries is a current and challenging topic of research in the framework of isogeometric analysis. In this work, we extend the recent methods [25,28] and [31-33] for the construction of $C^1$-smooth and $C^2$-smooth isogeometric spline spaces over particular planar multi-patch geometries to the case of $C^s$-smooth isogeometric multi-patch spline spaces of an arbitrary selected smoothness $s \geq 1$. More precisely, for any $s \geq 1$, we study the space of $C^s$-smooth isogeometric spline functions defined on planar, bilinearly parameterized multi-patch domains, and generate a particular $C^s$-smooth subspace of the entire $C^s$-smooth isogeometric multi-patch spline space. We further present the construction of a basis for this $C^s$-smooth subspace, which consists of simple and locally supported functions. Moreover, we use the $C^s$-smooth spline functions to perform $L^2$ approximation on bilinearly parameterized multi-patch domains, where the obtained numerical results indicate an optimal approximation power of the constructed $C^s$-smooth subspace.
