论文标题
分数laplacian- 3D中奇异双积分的正交规则
Fractional Laplacian - Quadrature rules for singular double integrals in 3D
论文作者
论文摘要
在本文中，提出了三个维度分数拉普拉斯的刚度矩阵有效计算的正交规则。这些规则基于达菲转换，这是删除奇点的常见工具。在这里，这种转变适应了三个维度的分数laplacian的需求。这种达菲转化产生的积分是在较小的域上的常规积分。我们在高斯点的数量上介绍了界限，以确保与有限元误差相同的误差估计。本文中介绍的方法可以轻松地适用于具有代数奇异性的三个维度的其他奇异双积分。
In this article, quadrature rules for the efficient computation of the stiffness matrix for the fractional Laplacian in three dimensions are presented. These rules are based on the Duffy transformation, which is a common tool for singularity removal. Here, this transformation is adapted to the needs of the fractional Laplacian in three dimensions. The integrals resulting from this Duffy transformation are regular integrals over less-dimensional domains. We present bounds on the number of Gauss points to guarantee error estimates which are of the same order of magnitude as the finite element error. The methods presented in this article can easily be adapted to other singular double integrals in three dimensions with algebraic singularities.
