论文标题
iSOODEMONEMOTIC GALERKIN方法中的Tchebycheffian B-Splines
Tchebycheffian B-splines in isogeometric Galerkin methods
论文作者
论文摘要
Tchebycheffian花纹是平滑的分段函数，其碎片是从（可能不同的）Tchebycheff空间中绘制出来的，这是代数多项式空间的自然概括。他们享受多项式样条案例中已知的大多数属性。特别是，在合适的假设下，Tchebycheffian花键在基础函数方面接受A表示，称为Tchebycheffian B-Splines（TB-Splines），完全类似于多项式B-Splines。一个特别有趣的子类由tchebycheffian花键组成，其零件属于恒定线性差分运算符的零空间。他们赋予将多项式与指数和三角函数与任何数量的单个形状参数相结合的自由。此外，他们最近还配备了有效的评估和操纵程序。在本文中，我们将使用属于恒定线性差异操作器的零空间的TB-Splines用作标准多项式B-Splines的有吸引力的替代品，而在同期Galerkin方法中的有吸引力的替代品。我们讨论如何根据问题驱动的选择策略来利用基础Tchebycheff空间的几何和分析特征的巨大灵活性。 TB-SPLINE为等同几何范式提供了一个广泛而健壮的环境，超出了理性NURBS模型的范围。
Tchebycheffian splines are smooth piecewise functions whose pieces are drawn from (possibly different) Tchebycheff spaces, a natural generalization of algebraic polynomial spaces. They enjoy most of the properties known in the polynomial spline case. In particular, under suitable assumptions, Tchebycheffian splines admit a representation in terms of basis functions, called Tchebycheffian B-splines (TB-splines), completely analogous to polynomial B-splines. A particularly interesting subclass consists of Tchebycheffian splines with pieces belonging to null-spaces of constant-coefficient linear differential operators. They grant the freedom of combining polynomials with exponential and trigonometric functions with any number of individual shape parameters. Moreover, they have been recently equipped with efficient evaluation and manipulation procedures. In this paper, we consider the use of TB-splines with pieces belonging to null-spaces of constant-coefficient linear differential operators as an attractive substitute for standard polynomial B-splines and rational NURBS in isogeometric Galerkin methods. We discuss how to exploit the large flexibility of the geometrical and analytical features of the underlying Tchebycheff spaces according to problem-driven selection strategies. TB-splines offer a wide and robust environment for the isogeometric paradigm beyond the limits of the rational NURBS model.
