简介：TheHelmholtzequationissometimessupplementedbyconditionsthatincludethespecificationoftheboundaryvalueofthedivergenceoftheunknown.Inthispaper,westudythevectorHelmholtzproblemindomainsofbothC~(1,1)andLipschitz.Wees-tablisharigorousvariationalanalysissuchasequivalence,existenceanduniqueness.Andweproposefiniteelementapproximationsbasedontheuncoupledsolutions.Fi-nallywepresentaconvergenceanalysisanderrorestimates.

简介：WeconsiderthenumericalsolutionfortheHelmholtzequationinR~2withmixedboundaryconditions.Thesolvabilityofthismixedboundaryvalueproblemisestab-lishedbytheboundaryintegralequationmethod.BasedontheGreenformula,weexpressthesolutionintermsoftheboundarydata.Thekeytothenumericalreal-izationofthismethodisthecomputationofweaklysingularintegrals.Numericalperformancesshowthevalidityandfeasibilityofourmethod.Thenumericalschemesproposedinthispaperhavebeenappliedintherealizationofprobemethodforinversescatteringproblems.

简介：有Helmholtz方程的外面的问题的二个盒子。如果0双线性的形式是强制的，并且如果<0它是散布问题。我们给无限的元素方法的一条新途径，它使我们能象角落问题一样解决这些外面的问题。散布问题的一个数字例子被给。[从作者抽象]

简介：ThereisnoaccurateanalyticalapproachfortheacousticperformancepredictionofHelmholtzresonatorwithconicalneck,whichhasbroadbandacousticattenuationperformanceinthelowfrequencyrange.Topredicttheacousticperformanceoftheresonatoraccurately,ageneraltheorymodelbasedontheone-dimensionalanalysisapproachwithacousticlengthcorrectionsisdeveloped.Thesegmentationmethodisusedtocalculatetheacousticparametersforsoundpropagationinconicaltubes.Andthen,anapproximateformulaisdeducedtogiveaccuratecorrectionlengthsforconicaltubeswithdifierentgeometries.Thedeviationsoftheresonancefrequencybetweenthetransmissionlossresultsobtainedbythegeneraltheorywithacousticlengthscorrectionandtheresultsfromthefiniteelementmethodandexperimentsarelessthan2Hz,whichismuchbetterthantheresultsfromone-dimensionalapproachwithoutcorrections.Theresultsshowthatthemethodofacousticlengthcorrectionfortheconicalneckgreatlyimprovedtheaccuracyoftheone-dimensionalanalysisapproach,anditwillbequickandaccuratetopredictthesoundattenuationpropertyofHelmholtzresonatorwithconicalneck.

简介：这份报纸在外表涉及放射波浪地的重建一在上述的领域的边界的部分上从Cauchy数据的知识围住二维或三维的领域。它被Cauchy问题为Helmholtz方程描述。由使用Dirichlet-to-Neumann地图，这个问题与紧缩的操作员被转变成一个操作员方程。我们严厉地认为紧缩的操作符的单个值的asymptotic行为正当。然后，有规则化的一个设计方法被使用解决操作员方程，并且规则化方法的集中被讨论。最后，几个数字例子被举说明途径。结果证明算法是有效的。

简介：NonlinearMHDKelvin-Helmholtz（K-H）instabilityinapipeistreatedwiththederiva-tiveexpansionmethodinthepresentpaperThelinearstabilityproblemwasdiscussedinthepastbyChandrasekhar（1961）andXuetal.（1981）.Nagano（1979）discussedthenonlinearMHDK-Hinstabilitywithinfinitedepth.Heusedthesingularperturbationmethodandextrapolatedtheob-tainedsecondordermodifierofamplitudevs.frequencytoseekthenonlineareffectontheinstabilitygrowthrateγ.However,inourview,suchanextrapolationisinappropriate.Becausewhentheinstabili-tysetsin,thegrowthratesofhigher,ordertermsontherighthandsideofequationswillexceedthecor-respondingsecularproducingterms,sotheexpansionwillstillbecomemeaninglessevenifthesecularproducingtermsareeliminated.Mathematicallyspeaking,it’simpossibletoderiveformula（39）whenγ02isnegativeinNagano’spaper.Moreover,evenasearlyasγ02→O+,theexpansionbe-comesinvalidbecausethe2ndordermodifierγ2（inhisformula（56））tendstoinfinity.Thisweak-nessisremovedinthispaper,andtheresultisextendedtothecaseofapipewithfinitedepth.

简介：Spectralelementmethodiswellknownashigh-ordermethod,andhaspotentialbetterparallelfeatureascomparedwithlowordermethods.Inthispaper,aparallelpreconditionedconjugategradientiterativemethodisproposedtosolvingthespectralelementapproximationoftheHelmholtzequation.Theparallelalgorithmisshowntohavegoodperformanceascomparedtononparallelcases,especiallywhenthestiffnessmatrixisnotmemorized.Aseriesofnumericalexperimentsinonedimensionalcaseiscarriedouttodemonstratetheefficiencyoftheproposedmethod.

简介：ALegendrespectralelement/LaguerrecoupledmethodisproposedtonumericallysolvetheellipticHelmholtzproblemonthehalfline.Rigorousanalysisiscarriedouttoestablishtheconvergenceofthemethod.Severalnumericalexamplesareprovidedtoconfirmthetheoreticalresults.TheadvantageofthismethodisdemonstratedbyanumericalcomparisonwiththepureLaguerremethod.

简介：ThereareNdomainsDj.（j=0,1,……,N-1）ofdifferentphysicalparametersinthewholespaceandtheirinterfaces.Sjj+1arenon-horizontallysmoothcurvedsurfaces.ThefollowingboundaryproblemiscalledHelmholtzboundaryproblem:Theanalyticalsolutionoftheaboveproblemisgiveninthispaper.

简介：ThispaperisconcernedwiththeCauchyproblemforthemodifiedHelmholtzequationinaninfinitestripdomain0

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简介：Forapracticalsuperconductingquantuminterferencedevice(SQUID)basedmeasurementsystem,theTesla/voltcoefficientmustbeaccuratelycalibrated.Inthispaper,weproposeahighlyefficientmethodofcalibratingaSQUIDmagnetometersystemusingthreeorthogonalHelmholtzcoils.TheTesla/voltcoefficientisregardedasthemagnitudeofavectorpointingtothenormaldirectionofthepickupcoil.Byapplyingmagneticfieldsthroughathree-dimensionalHelmholtzcoil,theTesla/voltcoefficientcanbedirectlycalculatedfrommagnetometerresponsestothethreeorthogonallyappliedmagneticfields.Calibrationwithalternatingcurrent(AC)fieldisnormallyusedforbettersignal-to-noiseratioinnoisyurbanenvironmentsandtheresultsarecomparedwiththedirectcurrent(DC)calibrationtoavoidpossibleeffectsduetoeddycurrent.Inourexperiment,acalibrationrelativeerrorofabout6.89×10-4isobtained,andtheerrorismainlycausedbythenon-orthogonalityofthreeaxesoftheHelmholtzcoils.ThemethoddoesnotneedprecisealignmentofthemagnetometerinsidetheHelmholtzcoil.Itcanbeusedforthemultichannelmagnetometersystemcalibrationeffectivelyandaccurately.

简介：介绍在光滑的开的弧上为Helmholtz方程建议了第一个客气的不可分的方程的一个数字答案的研究。照方法使用了；数字例子。

简介：这份报纸涉及多域光谱方法，基于内部惩罚不连续的Galerkin(IPDG)明确的表达，为经由一个准确通报或球形的Dirichlet-to-Neumann(DtN)边界截断的外面的Helmholtz问题调节。一条有效反复的途径被建议本地化全球DtN边界条件，它为scatterers的复杂几何学便于多域方法，和处理的实现。在不连续的Galerkin明确的表达下面，建议方法允许在不同子域上使用不同的度的多项式基础功能，并且更重要地，明确的波浪数字依赖估计光谱计划能被导出，它为多域是以某种方式难以置信的连续Galerkin明确的表达。[从作者抽象]

简介：AlateralHelmholtzresonatoraddedtoastandingwavetubewithoutflowhasbeenvalidatedasamethodofnoisereductionforcombustionnoiseradiatedfromcombustionchannelofrocketsorturbines.Butinfactthereisaflowwithlowvelocityinthecombustionchannel.ThereforethetheoreticalanalysiscarriedoutisaimedatsoundfieldofstandingwavetubewithflowandwithlateralHelmholtzresonator.Certainlyarelevantmath-physicalmodelshouldfirstbeformulated.Herethreekeyproblemsneedtobesolved:(1)ToformulatethediscontinuityconditionatthejointbetweenthestandingwavetubeandHelmholtzresonatorinthecaseofflow.(2)TodeterminetheacousticimpedanceofHelmholtzresonator,consideringtheeffectsofflow,viscousandmulti_hole.(3)Toformulatethereflectionconditionattheendofthestandingwavetube.SomeformulasforanalysisofthesoundfieldinthetubewithflowandwithlateralHelmholtzresonatorarededuced.Thesetheoreticalworkshavebeenvalidatedbyexperiments.

简介：在这篇论文，我们在ℝ_d为随机的Helmholtz方程考虑有限元素方法和不连续的Galerkin方法(d=2，3)。集中分析和为数字答案介绍的错误估计斧子。说明的近似斧子的精确性上的噪音的效果。数字实验斧子执行了验证我们的理论结果。

简介：BasedonthetheoreticalanalysisofastandingwavetubewithflowandlateralHelmholtzresonator,arelevantexperimentalapparatusweresetup,andweresuccessfullyusedtovalidatethetheanalysisabove.Meanwhileanendcorrectionandanequivalentradiuscoefficientcoveredinthetheoreticalanalysiswerealsodeterminedbyexperiments.FurthermoreseveralresultsobtainedfromthetheoreticalanalysisandexperimentswereusedtodiscusstheeffectsofflowontheperformanceofHelmholtzresonatorandthesoundfieldinthestandingwavetube.ItisshownthatusingHelmholtzresonatorforthestandingwavetubewithflowisstillagoodmeasurefornoisereduction,eventhoughtheeffectofnoisereductioncouldbereducedbecauseofflow.

简介：Inthisletterthethree-dimensionalnonlinearHelmholtzequationisinvestigated,whichdescribeselectro-magneticwavepropagationinanonlinearKerr-typemediumsuchthatsixteenfamiliesofnewJacobiellipticfunctionsolutionsareobtained,byusingourextendedJacobianellipticfunctionexpansionmethod.Whenthemodulusm→1or0,thecorrespondingsolitarywavesincludingbrightsolitons,darksolitonsandnewlinesolitonsandsinglyperiodicsolutionscanbealsofound.

简介：可压缩流体界面不稳定性的小扰动研究中，往往首先规定具体的状态方程形式，然后给出色散关系。这使得所给出的结果仅适用于该状态方程的具体形式，具有特殊性。由于这种特殊性，使得某些机理的讨论变得复杂，且结论相互矛盾。

简介：采用低耗散WENO（weightedessentialnon-oscillatory）格式及锐界面方法模拟可压缩Kelvin-Helmholtz不稳定性问题.由于物质界面被描述成一种接触间断,该方法可精确求解切向速度间断.基于优化模板对原始光滑指标进行正规化后,得到一种低耗散WENO格式.修正后的方法显著降低了普通流动区域的过衰减问题,保持了良好的激波捕捉性能,并可获得与混合格式相当的求解精度.不同于以往求解单一流体或易混界面时,通过初始设定有限宽度的剪切层或快速数值耗散以抑制高波数模态,该方法允许高波数扰动的发展.计算结果表明,高波数扰动展现出与以往理想Kelvin-Helmholtz不稳定性问题数值模拟或线化理论结果不同的特征,但与有限厚度的剪切层结果相符.