外域 Helmholtz 方程虛擬頻率問題之探討

Abstract

本文主要目的係以理論探討虛擬頻率發生的機制，並採用對偶積分方程的直接法及間接法作解析證明，研究結果顯示虛擬頻率發生的位置與使用的數值方法及使用的核函數及奇異源分佈的位置有關，而與外域問題所給定的邊界條件型式無關，並以一維Helmholtz方程為範例證明此一結論。 The principal objective of this paper is to understand the occurring mechanism of the fictitious frequencies by using analytical approach. Both the direct and indirect methods of the dual boundary integral equations are applied to demonstrate it. The present study indicates that the occurring positions of the fictitious frequencies depend on the numerical method, the kernel function and the distribution position of singularity. It is found that the fictitious eigenvalues are independent of the boundary conditions of the exterior problem. To verify this, a one-dimensional Helmholtz equation is used to demonstrate it.