求解流固系統衍生之有理特徵值問題數值方法的比較

Abstract

求解聲場限制在一具有消散聲能吸音牆壁的空間所衍生之阻尼 上的波動方式。由有限元素法，我們由節點基底的壓力空間將問題離 散和建出有理特徵問題(REP)的矩陣。之後，我們概述三種數值方法， nonlinear Arnoldi method [18]、nonlinear Jacobi-Davidson method [19] 和 trimmed linearization method [7]，求解有理特徵問題(REP)。最後， 數值證據顯示選擇trimmed linearization method [7]是最好的方法求解 有理特徵問題(REP)，在高精準度的要求下。

For computing damped vibration modes of an acoustic fluid confined in a cavity with absorbing walls capable of dissipating acoustic energy. By finite elements, we discrete the problem from the node-based pressure space and construct the rational eigenvalue problem (REP) with coefficients matrices. Then, We summarize three numerical methods, nonlinear Arnoldi method [18], nonlinear Jacobi-Davidson method [19] and trimmed linearization method [7], for solving the rational eigenvalue problem (REP).Finally, numerical evidence shows that choosing the trimmed linearization method is the best way for solving the REP, in high-efficiency requirement.