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1、快速多極邊界元方法在大規(guī)模聲學問題中的應用*?1?1?2?李善德黃其柏張潛（1.華中科技大學數(shù)字制造裝備與技術(shù)國家重點實驗室武漢430074；2.中船重工?701?研究所武漢430064)摘要：為了克服傳統(tǒng)邊界元方法不適合進行大規(guī)模聲學問題仿真的困難，將快速多極算法應用到傳統(tǒng)邊界元方法中，對大規(guī)模聲學問題進行數(shù)值計算。由于在快速多極邊界元方法中引入基本解的多極擴展，并應用預處理后的廣義極小殘差法迭代求解器求解線性方程系統(tǒng)，使得快速多極邊界元方法的計算效率與傳統(tǒng)邊界元方法相比顯著提高，計算量和存儲量減少到O(N)量級(N為問題的自由度數(shù))。對于傳統(tǒng)邊界元方
2、法求解外部聲學問題時的非唯一解現(xiàn)象，在快速多極邊界元方法中采用改進的BurtonMiller方法獲得全頻段的唯一解。數(shù)值算例驗證了快速多極邊界元方法的準確性，表明快速多極邊界元方法的計算效率與傳統(tǒng)邊界元方法相比有數(shù)量級的提高，能夠有效求解大規(guī)模聲學問題。關(guān)鍵詞：邊界元方法快速多極算法Helmholtz方程聲學大規(guī)模中圖分類號：TB52+9Application?offast?multipole?boundary?element?method?forlargescale?acoustic?problems112LIShande?HUANG?Qibai?ZH
3、ANG?Qian?(1.State?Key?Laboratoryof?Digital?Manufacturing?Equipment?and?Technology,?HuazhongUniversityof?ScienceandTechnology,?Wuhan?430074??2.China?ShipIndustry?Corporation?No.701?Research?andDevelopment?Institute,?Wuhan?430064)Abstract:In?ordertoovercome?thedifficultyofthe?conve
4、ntionalboundaryelementmethod?(BEM)is?unsuitable?forsolving?largescale?acousticsimulations,thefastmultipole?method?(FMM)is?used?withthe?conventionalBEMforsolving?largescale?acousticproblems.Thecomputationalefficiency?ofthe?fastmultipole?BEM?(FMBEM)isimproved?significantlycomparedt
5、othe?conventionalBEMdue?tothemultipole?expansion?ofthe?fundamentalsolution?andusingthe?preconditioned?generalized?minimumresidualmethod?(GMRES)as?an?iterative?solvertosolve?systemoflinearequation.Thus,both?thecomputationalcomplexityand?memoryrequirementofthepresentFMBEMare?drasti
6、callyreduced?to?O(N),whereNisthenumberofdegreesoffreedom.In?orderto?remove?thenonuniqueproblemsoftheconventionalBEM,?theFMBEM?employs?theimproved?BurtonMillermethod?to?solve?theexterioracousticproblemsforallfrequencies.NumericalexamplesvalidatetheaccuracyoftheFMBEM,andshowthatthe
7、?presentalgorithmprovidesan?orderofmagnitudeincreaseincomputationalefficiency?compared?totheconventionalBEM.Theseexamplesclearlydemonstratethatthe?presentFMBEMis?effective?tosolve?largescale?acousticproblems.Keywords:Boundaryelementmethod?Fastmultipolemethod?Helmholtzequation?Aco
8、usticproblems?Largescale?[1～4]究。但傳統(tǒng)邊界元方法
