The method of fundamental solutions for two-dimensional exterior acoustics

Abstract

In this paper, the method of fundamental solutions is applied to solve for to exterior acoustic radiation problem. By using the fundamental solution, the coefficients of influence matrices are easily determined according to a two-point function. This method also results in the irregular frequency as well as the boundary element method does. The position of irregular frequency depends on the location where sources are located. To avoid this numerical instability, Burton & Miller technique is employed to deal with the problem. Based on the circulant properties and degenerate kernels, an analytical study in discrete system of a cylinder radiator is demostrated. 本文中以提出基本解法來解二維外域輻射聲場的問題。藉由基本解，影響係數矩陣由二點函數輕易的得到。這個方法會有虛擬頻率的問題，這就與採用邊界元素法解外域聲場所產生的虛擬頻率問題一般。但是不規則頻率的產生位置則與所佈源點的位置有關。為了避免這個數值不穩定的問題，Burton & Miller 的技巧可用來避免虛擬頻率的發生。藉由循環矩陣及退化核函數，一個對於圓柱的輻射聲場問題，我們以離散系統成功的解析證明此論點。