基于Burton-Miller边界积分方程的二维声学波动问题对角形式快速多极子边界元及其应用

论述了二维声学问题的快速多极子边界元（FMBEM）方程及实现步骤．概述了核函数展开理论,并对FMBEM的4个重要组成部分:源点矩计算、源点矩转移、源点矩至本地展开转移、本地展开转移进行了详细的描述．提出了一种有利于四叉树建立的数据结构．推导了一种比直接数值计算更精确、稳定和高效的解析源点矩计算公式．数值算例验证了FMBEM的正确性和高效性．最后,使用FMBEM对轨道二维声学辐射模型进行了模拟计算．     

IMPLICITY LINEAR COLLOCATION METHOD AND ITERATED IMPLICITY LINEAR COLLOCATION METHOD FOR THE NUMERICAL SOLUTION OF HAMMERSTEIN FREDHOLM INTEGRAL EQUATIONS ON 2D IRREGULAR DOMAINS

In this work, we adapt and compare implicity linear collocation method and iterated implicity linear collocation method for solving nonlinear two dimensional Fredholm integral equations of Hammerstein type using IMQ-RBFs on a non-rectangular domain. IMQs show to be the most promising RBFs for this kind of equations. The proposed methods are mesh-free and they are independent of the geometry of domain. Convergence analysis of the proposed methods together with some benchmark examples is provided which support their reliability and numerical stability.