high-order accurate methods for maxwell equations - kashdan

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1、TELAVIVUNIVERSITYTheRaymondandBeverlySacklerFacultyofExactSciencesSchoolofMathematicalSciencesHIGH-ORDERACCURATEMETHODSFORMAXWELLEQUATIONSThesissubmittedforthedegree“DoctorofPhilosophy”byEugeneKashdanSubmittedtothesenateofTelAvivUniversityJune2004ThisworkwascarriedoutunderthesupervisionofProfe

2、ssorEliTurkelAcknowledgementsIwouldliketoexpressmygratitudeanddeepestappreciationtoProfessorEliTurkelforhisguidance,counselingandforhisfriendship.Withouthishelpandencouragementthisworkwouldneverhavebeendone.IwishtothankmyparentsandmysisterMayafortheirlove,supportandbeliefinmysuccess,inspiteoft

3、hethousandsofkilometersbetweenus.IwouldliketothankmycolleaguesatTelAvivUniversityfortheirgreathelp,friendshipandhoursofthescientific(andnottoomuchscientific)discussions.IshouldalsomentionthatmyPhDresearchwassupportedbytheIsraeliMinistryofSciencewiththeEshkolFellowshipforStrategicResearchinyear

4、s2000–2002andsupportedinpartbytheAbsorptionFoundation("KerenKlita")ofTelAvivUniversityallotheryears.Finally,IwouldliketoacknowledgetheuseofcomputerresourcesbelongingtotheHighPerformanceComputingUnit,adivisionoftheInterUniversityComputingCenter,whichisaconsortiumformedbyresearchuniversitiesinIs

5、rael.Contents1Introduction12Preliminaries62.1Physicalbackground...........................62.2Maxwellequationsinvariouscoordinatesystems............82.2.1Cartesiancoordinates.......................82.2.2Cylindricalcoordinates......................92.2.3Sphericalcoordinates.....................

6、..93Boundaryconditions113.1Introduction................................113.2UniaxialPMLinCartesiancoordinates.................153.2.1Construction...........................153.2.2Well-posednessandstabilityofPML..............193.3Boundaryconditionsinsphericalcoordinates..............203.3.1Sing

7、ularityatthePoles......................203.3.2ConstructionofPMLinsphericalcoordinates.........214FiniteDifferencediscretization244.1Coordinatesystem............................244.2Yeealgorithm...............................244.3Highorde