论文标题
快速评估平面领域的牛顿潜力
Rapid evaluation of Newtonian potentials on planar domains
论文作者
论文摘要
对一般二维域对牛顿电位的准确评估对于Poisson方程和体积积分方程的数值解决方案很重要。在本文中，我们提出了一种简单有效的高级算法，用于计算由非结构化网格离散的平面域上计算牛顿电位。该算法基于使用格林的第三个身份将牛顿电势转换为网格元素边界上的层电位集合的集合，这可以通过helsing-ojala方法轻松评估。我们算法的一个重要组成部分是在单一基础上使用高阶（最新阶）双变量多项式插值，我们为此提供了广泛的理由。通过几个数值实验来说明我们的算法的性能。
The accurate and efficient evaluation of Newtonian potentials over general 2-D domains is important for the numerical solution of Poisson's equation and volume integral equations. In this paper, we present a simple and efficient high-order algorithm for computing the Newtonian potential over a planar domain discretized by an unstructured mesh. The algorithm is based on the use of Green's third identity for transforming the Newtonian potential into a collection of layer potentials over the boundaries of the mesh elements, which can be easily evaluated by the Helsing-Ojala method. One important component of our algorithm is the use of high-order (up to order 20) bivariate polynomial interpolation in the monomial basis, for which we provide extensive justification. The performance of our algorithm is illustrated through several numerical experiments.
