同心圓環二維 Helmholtz 特徵方程問題真假根探討

Abstract

本文針對同心圓環之 Helmholtz 特徵值問題，採用實部對偶邊界元素法求得真假特徵值。以離散化系統由邊界元素法中影響係數矩陣循環的特性解析一同心圓環空間聲場真假特徵值發生的機制；在數值解方面，則發展實部對偶邊界元素法程式並配合奇異值分解法萃取真根與過濾假根。最後，比較兩者與有限元素法的結果均相當符合。In this paper, the real-part dual BEM was employed to solve the Helmholtz eigenproblems of annular domain. The circulant and degenerate kernel were used to study the true and spurious eigensolutions in discrete system for simulating the continuous system. The numerical program of real-part dual BEM was also developed to distinguish the true and spurious eigensolutions by using the singular value decomposition technique. Good agreement can be made.