论文标题
高级校正了一类单数积分的梯形规则
High order corrected trapezoidal rules for a class of singular integrals
论文作者
论文摘要
我们为一类奇异积分的高级梯形规则的四足动物提供了一个基于高级规则的四个家庭，在该类别中，积分具有点奇异性。整数的奇异部分以泰勒系列的范围扩展，涉及增强平滑度的术语。四倍体基于梯形规则，其笛卡尔节点的正交权重接近基于扩张的奇异性，根据扩展明智地纠正。高阶精度可以通过利用奇异性周围的足够数量的校正节点来实现，以近似串联扩展中的术语。派生的四元素应用于涉及拉普拉斯层内核的表面积分的隐式边界积分公式。
We present a family of high order trapezoidal rule-based quadratures for a class of singular integrals, where the integrand has a point singularity. The singular part of the integrand is expanded in a Taylor series involving terms of increasing smoothness. The quadratures are based on the trapezoidal rule, with the quadrature weights for Cartesian nodes close to the singularity judiciously corrected based on the expansion. High order accuracy can be achieved by utilizing a sufficient number of correction nodes around the singularity to approximate the terms in the series expansion. The derived quadratures are applied to the Implicit Boundary Integral formulation of surface integrals involving the Laplace layer kernels.
