二维非光滑散射体声波散射场数值解

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1、二维非光滑散射体声波散射场数值解二维非光滑散射体声波散射场数值解赵海峰，刘继军东南大学数学系，南京,210096摘要：在实际应用领域,给定入射波和不可穿透散射体,声波散射问题的研究有着重要意义.如果散射体的边界不光滑,采用标准的算法,如有限元FEM或边界元BEM,边界角点会影响算法的精度.考虑散射体边界带有角点的声学散射问题.在二维情况,此模型可以用Helmholtz方程外问题描述.散射体角点的奇异性会影响算法的数值结果.本文通过引入人工边界条件避免角点附近散射场的计算,并引入完全匹配层PML将散射问题截

2、断为有界域问题,其中PML层的外边界赋予零边值Dirichlet条件.最后用间断Galerkin有限元求解此边值问题.数值结果表明算法是有效的.关键词：散射波,非光滑散射体,间断Galerkin有限元,完全匹配层,数值算法.中图分类号：O241.8Onnumericalsolutiontoacousticwavescatteringbya2-dimensionalnon-smoothobstacleZhaoHaifeng,LiuJijunDepartmentofMathematics,SoutheastU

3、niversity,Nanjing,210096Abstract:Forgivenincidentwaveandanimpenetrableobstacle,thewavescatteringproblemsareofgreatimportanceinappliedarea.Incaseoftheobstacleboundarybeingnonsmooth,thenumericalsolutionofscatteredwaveoutsideoftheobstaclebystandardschemessuc

4、hasFEMandBEMwillbecontaminatedduetothesingularityofscatteredwaveattheobstaclecorner.Considertheacousticwavescatteringbyanobstaclewithacorneronitsboundary.In2-dimensionalcase,thisproblemisgovernedbyanexteriorproblemfortheHelmholtzequation,whichismuchcompli

5、catedforstablenumericalcomputationduetotheexistenceofobstaclecorner.Weintroduceanarti?cialboundaryconditionABCtoeliminatethesingularityofscatteredwaveatthecornerandintroduceaperfectlymatchedlayerPMLtotruncatetheunboundeddomainwherethezeroDirichletboundary

6、conditionissetupontheouterboundaryofPML.ThenthediscontinuousGalerkinmethodisappliedtosolvethisboundaryvalueproblem.Finally,somenumericalexamplesarepresentedtoshowthevalidityoftheproposedscheme.基金项目：ThisworkissupportedbyResearchFoundfortheDoctoralProgramof

7、HigherEducationofChinaNo.201XXXXXXXXXX8作者简介：Correspondenceauthor：LiuJijun（1965-），male，Professor，majorresearchdirection：inversescatterings,medicalimaging,industrymathematics.Email:jjliu@.-1-Keywords:Wavescattering,non-smoothobstacle,discontinuousGalerkinme

8、thod,perfectlymatchedlayer,numerics.0IntroductionForgivenincidentacousticwaves,thewavescatteringproblemsbyanobstacleDareofgreatimportance.Undersomeassumptions,thescatteringprocesscanbedescribedbyanexteriorproblemfor