欢迎来到天天文库
浏览记录
ID:40371431
大小:377.34 KB
页数:42页
时间:2019-08-01
《FDTD:introduction to the finite-difference time-domain method》由会员上传分享,免费在线阅读,更多相关内容在学术论文-天天文库。
1、Chapter3IntroductiontotheFinite-DifferenceTime-DomainMethod:FDTDin1D3.1IntroductionThefinite-differencetime-domain(FDTD)methodisarguablythesimplest,bothconceptuallyandintermsofimplementation,ofthefull-wavetechniquesusedtosolveproblemsinelectromagnet-ics.Itcanaccuratelytackleawiderangeofp
2、roblems.However,aswithallnumericalmethods,itdoeshaveitsshareofartifactsandtheaccuracyiscontingentupontheimplementation.TheFDTDmethodcansolvecomplicatedproblems,butitisgenerallycomputationallyexpensive.Solutionsmayrequirealargeamountofmemoryandcomputationtime.TheFDTDmethodlooselyfitsintot
3、hecategoryofresonanceregiontechniques,i.e.,onesinwhichthecharacteristicdimensionsofthedomainofinterestaresomewhereontheorderofawavelengthinsize.Ifanobjectisverysmallcomparedtoawavelength,quasi-staticapproximationsgenerallyprovidemoreefficientso-lutions.Alternatively,ifthewavelengthisexce
4、edinglysmallcomparedtothephysicalfeaturesofinterest,ray-basedmethodsorothertechniquesmayprovideamuchmoreefficientwaytosolvetheproblem.TheFDTDmethodemploysfinitedifferencesasapproximationstoboththespatialandtem-poralderivativesthatappearinMaxwell’sequations(specificallyAmpere’sandFaraday’sl
5、aws).ConsidertheTaylorseriesexpansionsofthefunctionf(x)expandedaboutthepointx0withanoffsetof±δ/2:23δδ′1δ′′1δ′′′fx0+=f(x0)+f(x0)+f(x0)+f(x0)+...,(3.1)222!23!223δδ′1δ′′1δ′′′fx0−=f(x0)−f(x0)+f(x0)−f(x0)+...(3.2)222!23!2wheretheprimesindicatedifferentiation.Subtractingtheseconde
6、quationfromthefirstyields3δδ′2δ′′′fx0+−fx0−=δf(x0)+f(x0)+...(3.3)223!2LecturenotesbyJohnSchneider.fdtd-intro.tex3334CHAPTER3.INTRODUCTIONTOTHEFDTDMETHODDividingbyδproduces fx+δ−fx−δ1δ20202=f′(x)+f′′′(x)+...(3.4)δ03!220Thusthetermontheleftisequaltothederivativeofthefunctionatthep
7、ointx0plusatermwhichdependsonδ2plusaninfinitenumberofothertermswhicharenotshown.Forthetermswhicharenotshown,thenextwoulddependonδ4andallsubsequenttermswoulddependonevenhigherpowersofδ.Rearrangingslightly,thisrelationshipisoftenstatedas df(x)fx+δ−fx−δ02022=+O(δ).(3.5)dxδx=x0Th
此文档下载收益归作者所有