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1、AlthoughtopologywasrecognizedbyGaussandMaxwelltoplayapivotalroleintheformulationofelectromagneticboundaryvalueproblems,itisalargelyunexploitedtoolfor eldcomputation.ThedevelopmentofalgebraictopologysinceMaxwellprovidesaframeworkforlinkingdatastructures,algorithms,a
2、ndcomputationtotopologicalaspectsofthree-dimensionalelectromagneticboundaryvalueproblems.ThisbookattemptstoexposethelinkbetweenMaxwellandamodernapproachtoalgorithms.The rstchapterslayouttherelevantfactsabouthomologyandcoho-mology,stressingtheirinterpretationsinelec
3、tromagnetism.Thesetopologicalstructuresaresubsequentlytiedtovariationalformulationsinelectromagnet-ics,the niteelementmethod,algorithms,andcertainaspectsofnumericallinearalgebra.Arecurringthemeistheformulationofandalgorithmsfortheproblemofmakingbranchcutsforcomputi
4、ngmagneticscalarpotentialsandeddycurrents.Anappendixbridgesthegapbetweenthematerialpresentedandstandardexpositionsofdi erentialforms,Hodgedecompositions,andtoolsforrealizingrepresentativesofhomologyclassesasembeddedmanifolds.MathematicalSciencesResearchInstitutePub
5、lications48ElectromagneticTheoryandComputationATopologicalApproachMathematicalSciencesResearchInstitutePublications1Freed/Uhlenbeck:InstantonsandFour-Manifolds,secondedition2Chern(ed.):SeminaronNonlinearPartialDi erentialEquations3Lepowsky/Mandelstam/Singer(eds.):V
6、ertexOperatorsinMathematicsandPhysics4Kac(ed.):In niteDimensionalGroupswithApplications5Blackadar:K-TheoryforOperatorAlgebras,secondedition6Moore(ed.):GroupRepresentations,ErgodicTheory,OperatorAlgebras,andMathematicalPhysics7Chorin/Majda(eds.):WaveMotion:Theory,Mo
7、delling,andComputation8Gersten(ed.):EssaysinGroupTheory9Moore/Schochet:GlobalAnalysisonFoliatedSpaces10{11Drasin/Earle/Gehring/Kra/Marden(eds.):HolomorphicFunctionsandModuli12{13Ni/Peletier/Serrin(eds.):NonlinearDi usionEquationsandTheirEquilibriumStates14Goodman/d
8、elaHarpe/Jones:CoxeterGraphsandTowersofAlgebras15Hochster/Huneke/Sally(eds.):CommutativeAlgebra16Ihara/Ribet/Serre(eds.):GaloisGroupsoverQ17Concu
