多階層快速多極展開法於隔音牆分析之應用

Abstract

本文以多階層快速多極展開法(Multilevel Fast Multipole Method)分析圓柱聲場散射問題與隔音牆聲場問題，並以介入損失值(Insertion Loss)作為其隔音效果之判斷指標。首先，針對多階層快速多極展開法的演算架構進行介紹，其主要概念是將核函數展開成場源點分離之兩函數的級數展開式，並加入樹狀分層結構，接著利用節點間相互傳遞(translation)、展開(expansion)，以達到加快計算時間、減少記憶體使用量之目的。因為樹狀分割層數(Level)用於資料之儲存，其分割層數並無一定限制；而核函數展開部份，其展開式為一無窮級數，項數多寡之取捨將影響精確度以及計算時間，因此本文對於分割層數以及項數之影響也都詳加探討。最後，於文章中加以分析矩形、T型以及改良T型隔音牆之隔音效果，以作為將來設置隔音牆之參考依據。

The purpose of this study is to investigate the scattering problems of a cylinder and barriers when applying the Multilevel Fast Multipole Method (MLFMM), and the value of insertion loss was applied as an indicator to estimate the effects of barriers. Firstly, a detailed introduction by MLFMM was illustrated. The main idea of MLFMM is to expand the kernel function into degenerate kernels which can separate the field point and source point, and then construct the tree structure. Furthermore, the translation and expansion was used to analyse node-to-node interactions. Compared with conventional Boundary Element Method (BEM), MLFMM can accelerate the computational time and the memory requirement can also be reduced. In regard of the unlimited property of the tree structure and infinite series of the expansion, a detailed study for a number of terms and levels of tree structure were investigated. Finally, the effects of rectangular, T-shaped and the refined T-shaped barriers were also studied. This study may contribute to the design of the barriers in the near future.