同心圓環二維Helmholtz方程特徵值問題 真假根探討

Abstract

本文針對同心圓環之Helmholtz特徵值問題利用實部對偶邊界元素法來求得真假特徵值。在解析解方面，以離散系統模擬連續系統，並利用邊界元素法中影響係數矩陣循環的特性來求得一同心圓環形聲場空間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分辨真根與過濾假根。最後，比較兩者的結果均相當符合。In this paper, the real-part dual BEM was employed to solve the Helmholtz eigenproblems of annular domain. The circulant was 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.