成都电子科技大学研究生学位论文含研究报告撰写范例英文.docx
《成都电子科技大学研究生学位论文含研究报告撰写范例英文.docx》由会员分享，可在线阅读，更多相关《成都电子科技大学研究生学位论文含研究报告撰写范例英文.docx（16页珍藏版）》请在冰点文库上搜索。
成都电子科技大学研究生学位论文含研究报告撰写范例英文
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。
CalderόnTECHNIQUEBASEDINTEGRALEQUATIONMETHODSINCOMPUTATIONALELECTROMAGNETICS
AMasterThesisSubmittedto
UniversityofElectronicScienceandTechnologyofChina
Major:
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：
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
ABSTRACT
RevealedbytheCalderόnrelationandtheCalderόnidentitiesinelectromagnetictheory,thepropertiesandrelationofdifferentintegraloperatorsinthecomputationalelectromagnetics（CEM）areutilizedtoconstructtheCalderόnpreconditioningtechniques,whichareappliedintheintegral-equation-basedmethodsinthisthesis.AthoroughandsystematicresearchhasbeenaccomplishedtocovertheCalderόnpreconditioningtechniquesfortheperfectelectricconductor（PEC）andthedielectriccases.ForthePECcase,theCalderόnpreconditioningfortheelectric-fieldintegralequation（EFIE）atmid,low,andhighfrequenciesareconstructedandstudied.Forthedielectriccases,theCalderόnpreconditioningforthePoggio-Miller-Chang-Harrington-Wu-Tsai（PMCHWT）integralequationareinvestigated,andtheCalderόntechniquefortheN-Müllerintegralequationisdeveloped.Moreover,theaccuracyimprovingtechniqueforthesecond-kindFredholmintegralequationforbothPECanddielectriccasesisalsostudiedinthisthesis.
…
Keywords:
Electromagneticscatteringandradiation,surface-integral-equation-basedMethods,Calderόnpreconditioningmethods,numericalaccuracy,Fred-
holmintegralequationsofthesecondkind
Contents
Chapter1Introduction1
1.1ResearchBackgroundandSignificance1
1.2StateofArts1
1.3ContentsandInnovationsoftheThesis2
1.4OutlineoftheThesis2
Chapter2TheoreticalBasics3
2.1IntegralEquationsinElectromagnetics3
2.2270MHzPlanWaveExcitation3
2.3TheSolutionofIntegralEquationsinElectromagnetics4
2.3.1GeneralPrincipleoftheMethodofMoments4
2.3.2GeometricalModelingandDiscretizationofObject4
2.3.2.1PlanarTriangularModel4
2.3.2.2CurvilinearTriangularModel4
2.3.3TheChoiceofBasisFunctions5
2.3.3.1PlanarRWGBasisFunctions6
2.3.3.2CurvilinearRWGBasisFunctions6
2.3.4TheSolutionofMatrixEquations6
2.3.4.1DirectAlgorithms6
2.3.4.2IterativeAlgorithms6
2.4Conclusion6
Chapter3CalderόnPreconditioneratMidFrequencies7
3.1Introduction7
3.2CalderόnRelationandCalderόnIdentities7
3.3CalderόnPreconditioneratMidFrequencies7
3.4NumericalExamples7
3.5Conclusion7
Chapter4CalderόnPreconditioningTechniqueforN-Müller8
4.1Introduction8
4.2N-MüllerIntegralEquations8
4.3TheDerivationofN-MüllerEquations8
4.4TheDiscretizationofN-MüllerEquations8
4.5NumericalExamples8
4.6Conclusion8
Chapter5Conclusions9
5.1ConcludingRemarks9
5.2FutureWork9
Acknowledgements10
References11
ResearchResultsObtainedDuringtheStudyforMasterDegree12
Chapter1Introduction
1.1ResearchBackgroundandSignificance
Integral-equation-basednumericalmethodscombinedwithfastalgorithmsarecapableofsolvingelectromagneticproblemsofcomplexstructuresandmaterialpropertieswithagoodaccuracyandahighefficiency.Theyarewidelyusedinavarietyofengineeringapplications,suchastheefficientanalysisofthreedimensionalradarscatteringproblems,thesimulationoftheinputimpedanceandtheradiationpropertiesofantennasystems,thecalculationoftheinputresponseandthetransmissionefficiencyofmicrowavecircuits,theevaluationoftheelectromagneticinterference（EMI）betweencomplexelectromagneticsystems,andthecomputeraidedelectromagneticcompatibility（EMC）designs.Theversatility,capability,accuracyandefficiencyoftheintegral-equation-basedmethodshavemadethemanimportantandcosteffectiveapproachintheanalysisanddesignofelectromagneticproblemsandapplications.
…
1.2StateofArts
Fromthe1960s,thenumericalmethodsofelectromagneticanalysishavebeenfastdevelopedbecauseoftheirversatilityandflexibility.Manywell-knownnumericalmethodshavebeenintroducedduringthattime,includingthefiniteelementmethod（FEM）[1]andthefinitedifferencetimedomainmethod（FDTD）[2,3],whicharebasedonthesolutiontotheMaxwell’sequationsindifferentialform,andthemethodofmoments（MoM）[2,4-6],whichisbasedonthesolutiontotheMaxwell’sequationsinintegralform.Especiallyfrom1990s,withthefastdevelopmentsofhighperformancecomputingsystems,thetheoriesandmethodsofcomputationalelectromagneticshavebeenadvanceddramatically.Theincreasesoftheclockspeedandthememorysizeofcomputersystemsandthedevelopmentsofhighlyefficientelectromagneticcomputingalgorithmsmakethenumericalmethodscapableofsolvingelectromagneticengineeringproblems.
…
1.3ContentsandInnovationsoftheThesis
BasedontheCalderόnrelationandtheCalderόnidentities,thisthesishasdevelopedseveralCalderόnpreconditioningtechniquesandinvestigatedtheirapplicationsintheintegral-equation-basedcomputationalelectromagneticmethods.TheresearchcontenthascoveredtheCalderόnpreconditioningtechniquesfortheperfectelectricconductor（PEC）anddielectriccases.ForthePECcase,theCalderόnpreconditionsatmid,low,andhighfrequenciesareinvestigated.Forthedielectriccase,theCalderόnpreconditioningtechniquesforthePMCHWTandN-Müllerintegralequationsaredeveloped.Thenumericalaccuracyofthesecond-kindFredholmintegralequationsareinvestigatedandimprovedinthisthesis.
…
1.4OutlineoftheThesis
Thisthesisisorganizedasfollows.
…
Chapter2TheoreticalBasics
Inthischapter,thegeneralmethodsofconstructingthecommonlyusedintegralequationsinelectromagneticsareintroducedbasedonthesurfaceequivalenceprincipleandthevolumeequivalenceprinciple.
…
2.1IntegralEquationsinElectromagnetics
Intheintegral-equation-basedcomputationalelectromagneticmethods,theunknownfunctionsintheelectromagneticproblemssuchasthescatteringorradiationfieldsaremodeledintermsoftheequivalentsurfaceorvolumeelectric/magneticsourcesbyapplyingthesurfaceorvolumeequivalenceprinciples,respectively.
…
2.2270MHzPlanWaveExcitation
Inordertoinvestigatetheitsperformanceinhandlingelectricallyverylargeproblemswithoveronemillionunknowns,thesamenumericalexampleisrepeatedagainbyincreasingthefrequencyto270MHz,andkeepingtheincidentangleandpolarizationoftheplanewaveunchanged.Tohaveabetterinsight,thememoryconsumptionandCPUtimerequirementsoftheEFIE,theCP-CFIE（0.8）,andtheCP-AEFIEalgorithmsaregiveninTable2-1.
Table2-1ComparisonofComputationalDataofDifferentAlgorithms
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.
…
2.3TheSolutionofIntegralEquationsinElectromagnetics
2.3.1GeneralPrincipleoftheMethodofMoments
Theintegralequationsconstructedintheprecedingsectioncanbesolvedwithadequatenumericalmethods.Oneofthemostcommonlyusedmethodsinsolvingintegralequationsisthemethodofmoments（MoM）introducedbyR.F.Harringtonin1968[5].ThegeneralprincipleandkeypointsofMoMwillbereviewedinthissection.
…
2.3.2GeometricalModelingandDiscretizationofObject
Fromthedescriptionintheprecedingsection,itisclearthatinordertosolvefortheunknownequivalentelectromagneticcurrentsdefinedonthesurfaceorinthevolumeofanobstruction,thedefinitiondomainoftheunknowncurrents,whichisthegeometry,needstobedescribedmathematically.Thisistheso-calledgeometricalmodeling.Incomputationalelectromagnetics,geometricalmodelingisthebasicofelectromagneticmodelingandnumericalcalculation,anditsqualitywillaffecttheaccuracyofthenumericalsolutiondirectly.
…
2.3.2.1PlanarTriangularModel
Thesimplestandmostcommonlyusedelementinthegeometricalmodelingistheplanartriangle,whichisdefinedbyitsthreevertices（nodes）.
…
2.3.2.2CurvilinearTriangularModel
Thecurvedsurfaceofanobjectcanbebettermodeledwithcurvilineartriangularelementswhicharethesecond-ordercurvedsurfaces.Acurvilineartrianglecanbedefinedbysixnodes,threeofwhicharetheverticesofthetriangle,theotherthreearethemidpointsofthreecurvededges.ShowninFigure2-1isthesketchofacurvilineartriangularelement.
Thecurvedsurfaceofanobjectcanbe
升级会员 