Analysis of surface integral

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1、ARTICLEINPRESSEngineeringAnalysiswithBoundaryElements32(2008)196–209www.elsevier.com/locate/enganaboundAnalysisofsurfaceintegralequationsinelectromagneticscatteringandradiationproblemsPasiYla¨-Oijala,MattiTaskinen,SeppoJa¨rvenpa¨a¨ElectromagneticsLaboratory,HelsinkiUniversityofTechnolo

2、gy,FinlandReceived26April2007;accepted14August2007Availableonline1October2007AbstractPropertiesofvarioussurfaceintegralequationsofthefirstandsecondkindsarestudiedinelectromagneticscatteringandradiationproblems.Thesecond-kindequationsarefoundtogivebetterconditionedmatrixequationandfasterc

3、onvergingiterativesolutionsbutpoorersolutionaccuracythanthefirst-kindequations.Thesolutionaccuracyandmatrixconditioningseemtobealmostoppositepropertiesassociatedwiththesingularityofthekernelofintegraloperators.Themoresingular/smootherthekernel,themore/lessdiagonallydominantandthebetter/p

4、oorerconditionedthematrix,butthepoorer/betterthesolutionaccuracy.Accuracyoftheintegralequationsofthesecondkindcanbeimprovedbyincreasingtheorderofthebasisandtestingfunctions.However,therequiredexpansionorderseemstobeproblemdependent.Themoresingulartheunknown,thehighertheexpansionorderand

5、thefinerthediscretizationneededinordertomaintainthesolutionaccuracyofthesecond-kindequations.r2007ElsevierLtd.Allrightsreserved.Keywords:Electromagnetics;Galerkin’smethod;Integralequations;Iterativesolution;Scatteringandradiationproblems1.IntroductionbutgoodsolutionaccuracyandMFIEbehaves

6、viceversa[7,8].Hence,MFIEisbettersuitedforiterativeandfastRecentlyalotofresearchhasbeenmadeincomputa-methodsthanEFIE.However,MFIEhasbeenclearlylesstionalelectromagnetictodevelopfastsolversbasedonthepopularinpracticalsimulationsbecausethesolutionintegralequationmethods[1,2].Thesemethodsa

7、reaccuracyisoftenunsatisfactory[7].typicallybasedoniterativesolutionofamatrixequationThefundamentaldifferencebetweentheintegralequa-andinmanycasesthebottleneckinthesimulationsisthetionsofthefirstandsecondkindsistheidentityoperatorinconvergenceofiterativesolution.Hence,itisveryth