Multiple Radiators & Scatters

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簡歷

基本資料

Project title

Code/計畫編號

NSC94-2115-M019-003

Translated Name/計畫中文名

多體輻射與散射

Project Coordinator/計畫主持人

Jeng-Tzong Chen

Funding Organization/主管機關

National Science and Technology Council

Department/Unit

Department of Harbor and River Engineering

Website

https://www.grb.gov.tw/search/planDetail?id=1093457

Year

2005

Start date/計畫起

01-08-2005

Expected Completion/計畫迄

01-07-2006

Bugetid/研究經費

318千元

ResearchField/研究領域

數學

在過去幾年中，採用邊界積分方程或邊界元素法解單連通輻射及散射體的外域聲場問題時遇到虛擬頻率的問題已經充分的研究過。就數學而言，此為積分推導對外域聲場的甩解性問題。而在這個計畫中我們將把對單連通的成功經驗運用於多體輻射及散射的問題。多體輻射及散射的積分方程式及邊界元素法皆將在此計畫中完成，並甩得到總截面積（total cross section)及雙柱增益（two-cylinder gains)。同時不規則頻率在此多體問題中如何產生我們也會做詳細的探討，而且甩能的處理方案，如修正基本解法（MFSM)、Burton & Miller法、SVD補充式法及CHEEF法皆將被考慮。對於 MFSM法與CHEEF法之間的關聯我們也將建構出來。隨後我們將驗證虛擬頻率是否與輻射或散射體的形狀有關，我們將從圓形改為長方形來觀察之間的差異。對於多體輻射及散射問題的連續系統及離散系統，我們將配合退化核，傳立葉級數及循環矩陣一併考慮。對於含有一個山峰或山谷的半平面問題則甩視為一個多體輻射或散射問題的特例來處理。同時對於全平面及含山峰或山谷的半平面問題中虛擬頻率的差異性亦將探討。最後由赫姆茲方程支配的多體輻射及散射水波問題亦將被測試。 "In the past years, the NTOU BIEM/BEM group has investigated the fictitious frequencies in the exterior acoustics using BIEM/BEM for a single radiator and a scatter. Mathematically speaking, it is a problem of solvability of BIE formulation for exterior acoustics. In this project, we will extend the study to multiple radiators and scatters. Boundary integral equation will be formulated for the Helmholtz equation and BIEM/BEM will be implemented for exterior acoustics with multiple ones. The total cross section (TCS) and two-cylinder gains (TCG) will be determined. How irregular frequencies appear will be studied in detail. The possible remedies of using the modified fundamental solution method (MFSM), Burton & Miller method, SVD updating technique and CHIEF method will be considered. How the MFSM work will be investigated in detail mathematically and numerically. The number of multiplicity for rank deficiency at the root in the influence matrix will be discussed. The corresponding required number of CHIEF points and their positions will be discussed. Relations between the CHIEF method and MFSM will be constructed. Then, we will examine whether the fictitious frequency depends on the shape of any scatter and radiator and we will change the shape of cylinders to rectangular sections for observing the differences. Both the continuous system (BIEM) and discrete system (BEM) will be considered in conjunction with degenerate kernel, Fourier series and circulants. Half-plane problems with hills or canyons will be considered as a special case of multiple radiators and scatters. Then, the difference of the occurring mechanism and treatment of fictitious frequency between a single and multiple radiators (scatters) will be studied. Also, the differences of fictitious frequency between full-plane and half-plane (hill or canyon) will be addressed. Finally, the water wave problem governed by the same Helmholtz equation will be tested for multiple scatters and radiators."

Keyword(s)

多體輻射及散射
虛擬頻率
總結面積
雙柱增益
修正基本解法
SVD補充式法
Burton & Miller 法
CHIEF 法
radiator and scatter
fictitious frequency
TCS
MFSM
SVD updating technique
Burton & Miller method
CHIEF method

DSpace CRIS

Multiple Radiators & Scatters

基本資料

Description