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:ThereisnoaccurateanalyticalapproachfortheacousticperformancepredictionofHelmholtzresonatorwithconicalneck,whichhasbroadbandacousticattenuationperformanceinthelowfrequencyrange.Topredicttheacousticperformanceoftheresonatoraccurately,ageneraltheorymodelbasedontheone-dimensionalanalysisapproachwithacousticlengthcorrectionsisdeveloped.Thesegmentationmethodisusedtocalculatetheacousticparametersforsoundpropagationinconicaltubes.Andthen,anapproximateformulaisdeducedtogiveaccuratecorrectionlengthsforconicaltubeswithdifierentgeometries.Thedeviationsoftheresonancefrequencybetweenthetransmissionlossresultsobtainedbythegeneraltheorywithacousticlengthscorrectionandtheresultsfromthefiniteelementmethodandexperimentsarelessthan2Hz,whichismuchbetterthantheresultsfromone-dimensionalapproachwithoutcorrections.Theresultsshowthatthemethodofacousticlengthcorrectionfortheconicalneckgreatlyimprovedtheaccuracyoftheone-dimensionalanalysisapproach,anditwillbequickandaccuratetopredictthesoundattenuationpropertyofHelmholtzresonatorwithconicalneck.
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.
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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:BasedonthetheoreticalanalysisofastandingwavetubewithflowandlateralHelmholtzresonator,arelevantexperimentalapparatusweresetup,andweresuccessfullyusedtovalidatethetheanalysisabove.Meanwhileanendcorrectionandanequivalentradiuscoefficientcoveredinthetheoreticalanalysiswerealsodeterminedbyexperiments.FurthermoreseveralresultsobtainedfromthetheoreticalanalysisandexperimentswereusedtodiscusstheeffectsofflowontheperformanceofHelmholtzresonatorandthesoundfieldinthestandingwavetube.ItisshownthatusingHelmholtzresonatorforthestandingwavetubewithflowisstillagoodmeasurefornoisereduction,eventhoughtheeffectofnoisereductioncouldbereducedbecauseofflow.
简介:在小学数学中,列方程解应用题与用算术方法解应用题是有密切联系的。它们都是以四则运算和常见的数量关系为基础,通过分析题里的数量关系,根据四则运算的意义列式解答的。但是,两种解答方法的解题思路却不同。由于数量关系的多样性和叙述方式的不同,用算术方法解答应用题,时常要用逆向思考,列式比较困难,解法的变化也比较多。用列方程的方法解答应用题,由于引进了字母表示未知数,可以使未知数直接参与运算,使题目中的数量关系更加清楚,把未知数当成已知数来用,使我们很容易理