电子科技大学硕士学位论文2014范文

1、电子科技大学硕士学位论文2014范文 电子科技大学硕士学位论文2014范文电子科技大学UNIVERSITYOFELECTRONICSCIENCEANDTECHNOLOGYOFCHINA硕士学位论文MASTERTHESIS（电子科技大学图标）论文题目学科专业学号作者姓名指导教师分类号密级UDC注1学位论文（题名和副题名）（作者姓名）指导教师（姓名、职称、单位名称）申请学位级别学科专业提交论文日期论文答辩日期学位授予单位和日期电子科技大学年月日答辩委员会主席评阅人注1：注明国际十进分类法UDC的类号。 CalderόnTECHNIQUEBASEDINTEGRALEQUATIONMETHO

2、DSINCOMPUTATIONALELECTROMAGNETICS AMasterThesisSubmittedtoUniversityofElectronicScienceandTechnologyofChinaMajor:Author:Advisor:School:独创性声明本人声明所呈交的学位论文是本人在导师指导下进行的研究工作及取得的研究成果。据我所知，除了文中特别加以标注和致谢的地方外，论文中不包含其他人已经发表或撰写过的研究成果，也不包含为获得电子科技大学或其它教育机构的学位或证书而使用过的材料。与我一同工作的同志对本研究所做的任何贡献均已在论文中作了明确的说明并表示谢意。作者签名

3、：日期：年月日论文使用授权本学位论文作者完全了解电子科技大学有关保留、使用学位论文的规定，有权保留并向国家有关部门或机构送交论文的复印件和磁盘，允许论文被查阅和借阅。本人授权电子科技大学可以将学位论文的全部或部分内容编入有关数据库进行检索，可以采用影印、缩印或扫描等复制手段保存、汇编学位论文。（保密的学位论文在解密后应遵守此规定）作者签名：导师签名：日期：年月日摘要本文基于电磁理论中的Calderόn关系与Calderόn恒等式所揭示的不同积分算子之间的关系，系统地研究了Calderόn预条件技术及其在计算电磁学积分方程方法中的应用。研究内容全面覆盖了求解理想导电

4、体目标和均匀或分层均匀介质目标电磁散射与辐射问题的积分方程中的Calderόn预条件技术。在导体积分方程方面，研究了电场积分方程在中频，低频，以及高频区的Calderόn预处理方法。在介质积分方程方面，则研究了PMCHWT积分方程的Calderόn预处理方法，和N-Müller积分方程的Calderόn技术。本文对金属问题中的第二类Fredholm积分方程和介质问题中的第二类Fredholm积分方的精度改善进行了深入详尽的研究。关键词：电磁散射，面积分方程方法，Calderόn预条件方法，数值计算精度，第二类Fredholm积分方程A

5、BSTRACTRevealedbytheCalderόnrelationandtheCalderόnidentitiesinelectromagnetictheory,thepropertiesandrelationofdifferentintegraloperatorsinthecomputationalelectromagnetics(CEM)areutilizedtoconstructtheCalderόnpreconditioningtechniques,whichareappliedintheintegral-equation-basedmethodsi

6、nthisthesis.AthoroughandsystematicresearchhasbeenaccomplishedtocovertheCalderόnpreconditioningtechniquesfortheperfectelectricconductor(PEC)andthedielectriccases.ForthePECcase,theCalderόnpreconditioningfortheelectric-fieldintegralequation(EFIE)atmid,low,andhighfrequenciesareconstructedandst

7、udied.Forthedielectriccases,theCalderόnpreconditioningforthePoggio-Miller-Chang-Harrington-Wu-Tsai(PMCHWT)integralequationareinvestigated,andtheCalderόntechniquefortheN-Müllerintegralequationisdeveloped.Moreover,theaccuracyimprovingtechniqueforthesecond-kindFredholmintegralequationfor

8、bothPECanddielectriccasesisalsostudiedinthisthesis.Keywords:Electromagneticscatteringandradiation,surface-integral-equation-basedMethods,Calderόnpreconditioningmethods,numericalaccuracy,Fred-holmintegralequationsofthesecondkindContentsChapter1Introduction11.1ResearchBackgroundandSignificance11.

9、2StateofArts11.3ContentsandInnovationsoftheThesis21.4OutlineoftheThesis2Chapter2TheoreticalBasics32.1IntegralEquationsinElectromagnetics32.2270MHzPlanWaveExcitation32.3TheSolutionofIntegralEquationsinElectromagnetics42.3.1GeneralPrincipleoftheMethodofMoments42.3.2GeometricalModelingandDiscretization

10、ofObject42.3.2.1PlanarTriangularModel42.3.2.2CurvilinearTriangularModel42.3.3TheChoiceofBasisFunctions52.3.3.1PlanarRWGBasisFunctions62.3.3.2CurvilinearRWGBasisFunctions62.3.4TheSolutionofMatrixEquations62.3.4.1DirectAlgorithms62.3.4.2IterativeAlgorithms62.4Conclusion6Chapter3CalderόnPreconditi

11、oneratMidFrequencies73.1Introduction73.2CalderόnRelationandCalderόnIdentities73.3CalderόnPreconditioneratMidFrequencies73.4NumericalExamples73.5Conclusion7Chapter4CalderόnPreconditioningTechniqueforN-Müller84.1Introduction84.2N-MüllerIntegralEquations84.3TheDerivationof

12、N-MüllerEquations84.4TheDiscretizationofN-MüllerEquations84.5NumericalExamples84.6Conclusion8Chapter5Conclusions95.1ConcludingRemarks95.2FutureWork9Acknowledgements10References11ResearchResultsObtainedDuringtheStudyforMasterDegree12Chapter1Introduction1.1ResearchBackgroundandSignificanceIn

13、tegral-equation-basednumericalmethodscombinedwithfastalgorithmsarecapableofsolvingelectromagneticproblemsofcomplexstructuresandmaterialpropertieswithagoodaccuracyandahighefficiency.Theyarewidelyusedinavarietyofengineeringapplications,suchastheefficientanalysisofthreedimensionalradarscatteringproblem

14、s,thesimulationoftheinputimpedanceandtheradiationpropertiesofantennasystems,thecalculationoftheinputresponseandthetransmissionefficiencyofmicrowavecircuits,theevaluationoftheelectromagneticinterference(EMI)betweencomplexelectromagneticsystems,andthecomputeraidedelectromagneticcompatibility(EMC)desig

15、ns.Theversatility,capability,accuracyandefficiencyoftheintegral-equation-basedmethodshavemadethemanimportantandcosteffectiveapproachintheanalysisanddesignofelectromagneticproblemsandapplications.1.2StateofArtsFromthe1960s,thenumericalmethodsofelectromagneticanalysishavebeenfastdevelopedbecauseofthei

16、rversatilityandflexibility.Manywell-knownnumericalmethodshavebeenintroducedduringthattime,includingthefiniteelementmethod(FEM)1andthefinitedifferencetimedomainmethod(FDTD)2,3,whicharebasedonthesolutiontotheMaxwellsequationsindifferentialform,andthemethodofmoments(MoM)2,4-6,whichisbasedonthesolutiont

17、otheMaxwellsequationsinintegralform.Especiallyfrom1990s,withthefastdevelopmentsofhighperformancecomputingsystems,thetheoriesandmethodsofcomputationalelectromagneticshavebeenadvanceddramatically.Theincreasesoftheclockspeedandthememorysizeofcomputersystemsandthedevelopmentsofhighlyefficientelectromagn

18、eticcomputingalgorithmsmakethenumericalmethodscapableofsolvingelectromagneticengineeringproblems.1.3ContentsandInnovationsoftheThesisBasedontheCalderόnrelationandtheCalderόnidentities,thisthesishasdevelopedseveralCalderόnpreconditioningtechniquesandinvestigatedtheirapplicationsinthein

19、tegral-equation-basedcomputationalelectromagneticmethods.TheresearchcontenthascoveredtheCalderόnpreconditioningtechniquesfortheperfectelectricconductor(PEC)anddielectriccases.ForthePECcase,theCalderόnpreconditionsatmid,low,andhighfrequenciesareinvestigated.Forthedielectriccase,theCalder

20、72;npreconditioningtechniquesforthePMCHWTandN-Müllerintegralequationsaredeveloped.Thenumericalaccuracyofthesecond-kindFredholmintegralequationsareinvestigatedandimprovedinthisthesis.1.4OutlineoftheThesisThisthesisisorganizedasfollows.Chapter2TheoreticalBasicsInthischapter,thegeneralmethodsofcon

21、structingthecommonlyusedintegralequationsinelectromagneticsareintroducedbasedonthesurfaceequivalenceprincipleandthevolumeequivalenceprinciple.2.1IntegralEquationsinElectromagneticsIntheintegral-equation-basedcomputationalelectromagneticmethods,theunknownfunctionsintheelectromagneticproblemssuchasthe

22、scatteringorradiationfieldsaremodeledintermsoftheequivalentsurfaceorvolumeelectric/magneticsourcesbyapplyingthesurfaceorvolumeequivalenceprinciples,respectively.2.2270MHzPlanWaveExcitationInordertoinvestigatetheitsperformanceinhandlingelectricallyverylargeproblemswithoveronemillionunknowns,thesamenu

23、mericalexampleisrepeatedagainbyincreasingthefrequencyto270MHz,andkeepingtheincidentangleandpolarizationoftheplanewaveunchanged.Tohaveabetterinsight,thememoryconsumptionandCPUtimerequirementsoftheEFIE,theCP-CFIE(0.8),andtheCP-AEFIEalgorithmsaregiveninTable2-1.Table2-1ComparisonofComputationalDataofDi

24、fferentAlgorithms TotalMemory(Mb) CPUTime Setup(h) SolutionTime Iter.(m) Tol.(h) EFIE 3215.84 1.14 3.18 63 CP-CFIE(0.8) 6386.12 7.84 7.04 27.69 CP-AEFIE 5750.43 6.71 7.47 19.05 AllthecalculationsarecarriedoutonaHPZ400workstationwithaFedora10operatingsystem.2.3TheSolutionofIntegralEquationsinElectrom

25、agnetics2.3.1GeneralPrincipleoftheMethodofMomentsTheintegralequationsconstructedintheprecedingsectioncanbesolvedwithadequatenumericalmethods.Oneofthemostcommonlyusedmethodsinsolvingintegralequationsisthemethodofmoments(MoM)introducedbyR.F.Harringtonin19685.ThegeneralprincipleandkeypointsofMoMwillber

26、eviewedinthissection.2.3.2GeometricalModelingandDiscretizationofObjectFromthedescriptionintheprecedingsection,itisclearthatinordertosolvefortheunknownequivalentelectromagneticcurrentsdefinedonthesurfaceorinthevolumeofanobstruction,thedefinitiondomainoftheunknowncurrents,whichisthegeometry,needstobed

27、escribedmathematically.Thisistheso-calledgeometricalmodeling.Incomputationalelectromagnetics,geometricalmodelingisthebasicofelectromagneticmodelingandnumericalcalculation,anditsqualitywillaffecttheaccuracyofthenumericalsolutiondirectly.2.3.2.1PlanarTriangularModelThesimplestandmostcommonlyusedelemen

28、tinthegeometricalmodelingistheplanartriangle,whichisdefinedbyitsthreevertices(nodes).2.3.2.2CurvilinearTriangularModelThecurvedsurfaceofanobjectcanbebettermodeledwithcurvilineartriangularelementswhicharethesecond-ordercurvedsurfaces.Acurvilineartrianglecanbedefinedbysixnodes,threeofwhicharethevertic

29、esofthetriangle,theotherthreearethemidpointsofthreecurvededges.ShowninFigure2-1isthesketchofacurvilineartriangularelement.Thecurvedsurfaceofanobjectcanbebettermodeledwithcurvilineartriangularelementswhicharethesecond-ordercurvedsurfaces.Acurvilineartrianglecanbedefinedbysixnodes,threeofwhicharetheve

30、rticesofthetriangle,theotherthreearethemidpointsofthreecurvededges.ShowninFigure2-1isthesketchofacurvilineartriangularelement.Figure2-1Thesketchofacurvilineartriangularelement（a）Thecurvilineartriangleinthecoordinatesystem;(b)ThecurvilineartriangleinthecoordinatesystemUsingthefollowingcoordinatetrans

31、formation,thecurvilineartriangleintherectangularcoordinatesystem,asshowninFigure2-1(a),canbemappedontothetriangledefinedinaparametriccoordinatesystem,asshowninFigure2-1(b)(2-1)wheredenotetherectangularcoordinatesofthesixcontrollingnodesinFigure2-1a,，aretheparametriccoordinatesvaryingfrom0to1,andthey

32、satisfytherelation(2-2)From(2-2),itisclearthatonlytwovariablesoutofthesethreeareindependent.2.3.3TheChoiceofBasisFunctionsAfterthegeometricaldiscretizationoftheobjectsurfaceusingplanarorcurvilineartriangularelements,basisfunctionscanbedefinedonthesetriangularelementstoexpandtheunknownvectorfunctions

33、.2.3.3.1PlanarRWGBasisFunctionsIntroducedbyRaoWilton,andGlissonin1982,theRWGbasisfunction6isdefinedovertwoadjacenttriangularelements.2.3.3.2CurvilinearRWGBasisFunctionsInordertogiveabetterrepresentationofcurvedsurfaces,thecurvilineartriangularelementscanbeused.Correspondingly,thecurvilinearRWGbasisf

34、unctions7canbedefinedonthecurvilineartriangularelements.2.3.4TheSolutionofMatrixEquationsThematrixequationcanbesolvedwithtwotypesofalgorithms,thedirectalgorithmsandtheiterativealgorithms.Theywillbeintroducedbrieflyinthissubsection8.2.3.4.1DirectAlgorithmsThecommonlyuseddirectalgorithmsincludetheGaus

35、sianelimination,theLUdecomposition,andthesingularvaluedecomposition(SVD)9-10.2.3.4.2IterativeAlgorithmsWhenthedimensionoftheimpedancematrixisverylarge,thedirectsolutionbecomesveryexpensive.2.4ConclusionChapter3CalderόnPreconditioneratMidFrequencies3.1IntroductionTheintegralequations(IEs)areused

36、tomodeltheelectromagneticscattering,3.2CalderόnRelationandCalderόnIdentitiesInascatteringproblem,accordingtothesurfaceequivalenceprinciple,3.3CalderόnPreconditioneratMidFrequenciesBasedonthediscussionintheprecedingsection,3.4NumericalExamplesTwosimpleexamplesaregiventodemonstratethefa

37、stconvergenceoftheCalderόnpreconditioneratmidfrequencies.3.5ConclusionTheCalderόnpreconditionerfortheEFIEatmidfrequenciesisreviewedinthischapter.Chapter4CalderόnPreconditioningTechniqueforN-Müller4.1IntroductionAnalysisoflow-frequencyelectromagneticproblemshasreceivedmoreattentio

38、n,4.2N-MüllerIntegralEquationsConsidertheproblemofelectromagneticwavescatteringbyaconductingsurface,Theorem1Proof:Considertheproblemofelectromagneticwavescatteringbyaconductingsurface,theproblemisproved.4.3TheDerivationofN-MüllerEquationsThederivationbeginsfromthepreconditioningoftheEFIE,4

39、.4TheDiscretizationofN-MüllerEquationsThederivationbeginsfromthepreconditioningoftheEFIE,4.5NumericalExamplesInthissection,theperformanceoftheN-M¨ullerequationsisinvestigated.4.6ConclusionInthischapter,Chapter5Conclusions5.1ConcludingRemarksTheaccurateandefficientnumericalsolutionsoftheMaxw

40、ellsequationshaveimportantsignificancetotheanalysisofelectromagneticscatteringandradiationproblems.5.2FutureWorkTheresearchesreportedinthisdissertationhavecoveredmostimportantareasincludingtheconvergenceaccelerationofthefirst-kindintegralequationsandtheaccuracyimprovementofthesecond-kindintegralequationsforboththePECandthedielectriccases.Nevertheless,duetothetimelimitation,therearestillspacesforthefuturedevelopmentoftheCalder´on-technique-relatedmethods.AcknowledgementsOnthecompletionofthisthesis,References1W.C.Chew,J.M.Jin,E.Michielssen,etal.FastandE