论文标题
在无界域上的3D潜在问题的搭配IGA-BEM
A collocation IGA-BEM for 3D potential problems on unbounded domains
论文作者
论文摘要
在本文中，用边界元素方法（BEM）解决了在3D无界域上定义的潜在问题的数值解决方案，因为这样只能在边界上研究该问题，因此可以避免任何无限域的有限近似。考虑了等几何分析（IGA）设置，尤其是b-spline和NURBS功能。为了利用使用样条空间来利用所有可能的好处，一个重要的一点是开发了特定的立方体公式，以弱和几乎奇异的积分。我们针对此目的的建议是基于样条式准插值和使用样条产品公式的建议。除此之外，还引入了强大的奇异性提取程序作为初步步骤，并采用了有效的逐函数组装阶段。一系列数值示例证实了数值解决方案达到了预期的收敛顺序。
In this paper the numerical solution of potential problems defined on 3D unbounded domains is addressed with Boundary Element Methods (BEMs), since in this way the problem is studied only on the boundary, and thus any finite approximation of the infinite domain can be avoided. The isogeometric analysis (IGA) setting is considered and in particular B-splines and NURBS functions are taken into account. In order to exploit all the possible benefits from using spline spaces, an important point is the development of specific cubature formulas for weakly and nearly singular integrals. Our proposal for this aim is based on spline quasi-interpolation and on the use of a spline product formula. Besides that, a robust singularity extraction procedure is introduced as a preliminary step and an efficient function-by-function assembly phase is adopted. A selection of numerical examples confirms that the numerical solutions reach the expected convergence orders.
