论文标题
基于双变量样条的准式插值的立方体规则，用于弱奇异积分
Cubature rules based on bivariate spline quasi-interpolation for weakly singular integrals
论文作者
论文摘要
在本文中，我们介绍了新的立方体规则，目的是准确整合弱奇异的双重积分。特别是，我们专注于从ISOOGETRIC分析范式中使用搭配方法的3D拉普拉斯边界值问题的边界积分方程的离散化。在这种设置中，可以将集成剂的常规部分定义为张量产品b-spline和一般函数的乘积。该规则是通过首先使用样条准插值方法来得出的，以近似此类功能，然后将众所周知的样条产品算法扩展到双变量设置。通过这种方式，确保效率确保，由于任何样条准插入方案的位置与B-Spline因子的AD-HOC处理能力相结合。数值集成是通过利用集成的元素间连续性来对B-Spline因子的全部支持进行的。
In this paper we present a new class of cubature rules with the aim of accurately integrating weakly singular double integrals. In particular we focus on those integrals coming from the discretization of Boundary Integral Equations for 3D Laplace boundary value problems, using a collocation method within the Isogeometric Analysis paradigm. In such setting the regular part of the integrand can be defined as the product of a tensor product B-spline and a general function. The rules are derived by using first the spline quasi-interpolation approach to approximate such function and then the extension of a well known algorithm for spline product to the bivariate setting. In this way efficiency is ensured, since the locality of any spline quasi-interpolation scheme is combined with the capability of an ad--hoc treatment of the B-spline factor. The numerical integration is performed on the whole support of the B-spline factor by exploiting inter-element continuity of the integrands
