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1、218IEEETRANSACTIONSONMICROWAVETHEORYANDTECHNIQUES,VOL.60,NO.2,FEBRUARY2012ParAFEMCap:AParallelAdaptiveFinite-ElementMethodfor3-DVLSIInterconnectCapacitanceExtractionGenlongChen,HengliangZhu,Member,IEEE,TaoCui,ZhimingChen,XuanZeng,Member,IEEE,andWeiCaiAbstract—Parasitic
2、extractionisoneofthekeytechniquesinI.INTRODUCTIONverylargescaleintegrationdesignthathasbeenwidelyusedtobuildtheequivalent-circuitmodelofinterconnects.Inthispaper,aSTHEverylargescaleintegration(VLSI)technologyparalleladaptivefinite-elementmethod(AFEM)forcapacitanceAscale
3、sdowntonanoscaleandthecircuitfrequencyextractionoflarge-scaleinterconnects(ParAFEMCap)isdevel-reachesgigahertz,interconnectsplayamoreandmoreimpor-opedtoprovideextremelyhighparallelscalabilityandnumericaltantroleintoday’sintegratedcircuits(ICs).Theparasiticeffectsaccura
4、cy.First,theproposedParAFEMCaphasthepotentialofofinterconnectscouldgreatlydeterioratetheperformanceofhighparallelscalabilitybytakingadvantagesofseveraladvancedparalleltechniques,suchasparalleladaptivemeshrefinementandthecircuitsandleadtomanysignalintegrityproblems.Paras
5、iticdynamicloadbalancing.Tothebestoftheauthors’knowledge,extractionofinterconnects,whichbuildstheequivalent-circuitthisisthefirstcapacitanceextractionfieldsolverthatisabletomodelforinterconnectsbyvariousnumericalapproaches,runinparallelonhundredsandeventhousandsofCPUcore
6、s.thereforebecomesoneofthekeystepsinICdesign[1].TheSecond,theproposedParAFEMCapisbasedontheAFEM,whichproblemofparasiticextractionofinterconnectshasbeenisproventoconvergetotheexactsolutionoftheelectromagneticproblemsinatheoreticallyquasi-optimalrate.Thesolutionpre-studi
7、edforalmostthreedecades.MostoftheresearchmainlycisionofParAFEMCapcaneasilybecontrolledbyvaryingthefallintothreecategories,namely:1)capacitanceextraction[2];thresholdfortheaposteriorierrorestimator,whilethecomputa-2)inductanceextraction[3],[4];and3)full-waveimpedancetio
8、naltimecaneasilybereducedbyincreasingthenumberofCPUextraction[5],[6].Theinductanceextractionandfull-wavecores.Moreove
