论文标题
边界积分方程的数值分析拉普拉斯方程的外部迪里奇问题
Numerical analysis on boundary integral equation to exterior Dirichlet problem of Laplace equation
论文作者
论文摘要
本文研究了用于修改的单层方法的数值分析，以解决拉普拉斯方程的外部迪里奇问题。我们完成了具有三角学基础的Petrov-Galerkin和Galerkin-Colocation方法的收敛性和误差分析，用于在分析边界上诱导修改的SYMM积分方程。此外，利用复合的梯形正交公式和三角插值来处理修改的对数内核中的奇异性，我们建立了实现的数值程序。在这些数值示例中，我们比较了不同的彼得罗夫 - 加盖尔金和盖素 - 同行方法的效果和效率。
This paper investigate on numerical analysis on modified Single-layer approach to exterior Dirichlet problem of Laplace equation. We complete the convergence and error analysis of Petrov-Galerkin and Galerkin-Collocation methods with trigonometric basis for the induced modified Symm's integral equation of the first kind on analytic boundary. Besides, utilizing the composite trapezial quadrature formula and trigonometric interpolation to handle the singularity in modified logarithmic kernel, we establish the numerical procedure for implementation. On these numerical examples, we compare the effect and efficiency of different Petrov-Galerkin and Galerkin-Collocation methods.
