19683.時空離散dg法求解超材料中的麥克斯韋方程組

1、分類號024221學(xué)校代碼1—05—42密級學(xué)號非密201202100840時空離散DG法求解超材料中的麥克斯韋方程組Space—timeDiscreteDGMethodforSolvingMaxwell’SEquationsinMetamaterials研究生姓名：操超超指導(dǎo)教師姓名、職稱：謝資清教授學(xué)科專業(yè)：計算數(shù)學(xué)研究方向：偏微分方程數(shù)值解湖南師范大學(xué)學(xué)位評定委員會辦公室二零一五年五月ABSTRACTWiththerapiddev

2、elopmentofmetamaterialsinrecentyears，scientistsbecomemoreandmoreinterestedinthestudyofthemInthispaperwemainlyfocusonthenumericalmethodsforsolvingatypicalmodel—Drudemodel，whichdescribesthe’propagationofelectromagneticwave

3、sinmetamaterialsInspiredbytheworkin【22，2a]，weadoptspace—timediscretediscontinuousGalerkinmethodfortheMaxwellsystemcomposedoffourdifferentialequationsBoththeL2stabilityanderrorestimatealeverified，ie，theL2errorrateintimeis

4、D(Tr1)andtheL2errorrateinspaceisO(h憊m／)Moreover，thenumericalexamplesin2Dand3DvalidatethetheoreticalresultsActuallythenumericMresultsshowthattheL2errorrateinspaceisO(hk1)，whichisbetterthanthetheoreticalpredictionFurther，t

5、henumericaltestsin2DdemonstratethatthenumericalfluxintimeatnodessuperconvergesatarateO(r2什11Further，weprovethattheCG—DGschemeproposedin[23】forsolvingMaxwellequationsindispersivemediaisconvergentKeywords：metamaterials；max