1、SummaryofBuilt-InVariablesWithReservedNamesThissectionisanoverviewofthebuilt-inelementsofthefollowingcategoriesasdefinedbytheunderlyingCOMSOLlanguage:ConstantsVariablesFunctionsTheselanguageelementsarebuilt-inoruser-defined.Inadditionthereareoperatorsthatcannotbeuser-defined,andexpressions,whicharea

2、lwaysuser-defined.具有保留名稱的內(nèi)置變量摘要本節(jié)概述了由基礎(chǔ)COMSOL語言定義的以下類別的內(nèi)置元素：常量變量功能這些語言元素是內(nèi)置的或用戶定義的。此外，還有不能由用戶定義的運(yùn)算符，以及始終由用戶定義的表達(dá)式。ABOUTRESERVEDNAMES關(guān)于預(yù)留名稱Built-invariableshavereservednames,namesthatcannotberedefinedbytheuser.Itisnotrecommendedtouseareservedvariablenameforauser-definedvariable,parameter,orfunction.F

3、orsomeofthemostcommonreservedvariablenames,suchaspi,i,andj,thetextwhereyouenterthenameturnsorangeandyougetatooltipmessageifyouselectthetextstring.Reservedfunctionnamesarereservedonlyforfunctionnames,whichmeansthatsuchnamescanbeusedforvariableandparameternames,andviceversa.Thefollowingtableslistmostb

4、uilt-inelementsandhencethosereservednames.內(nèi)置變量具有保留名稱，用戶無法重新定義。不建議對(duì)用戶定義的變量，參數(shù)或函數(shù)使用保留的變量名。對(duì)于一些最常見的保留變量名稱，例如pi，i和j，輸入名稱變?yōu)槌壬绻x擇文本字符串，則會(huì)得到工具提示消息。保留的函數(shù)名稱僅作為函數(shù)名保留，這意味著此類名稱可用于變量和參數(shù)名稱，反之亦然。下表列出了大多數(shù)內(nèi)置元素，因此列出了這些保留名稱。CONSTANTSANDPARAMETERS常量和參數(shù)Therearethreedifferenttypesofconstants:built-inmathematicalandnume

5、ricalconstants,built-inphysicalconstants,andparameters.Parametersareuser-definedconstantsthatcanvaryoverparametersweeps.Constantsarescalarvalued.Thefollowingtableliststhebuilt-inphysicalconstants.Constantsandparameterscanhaveunits.有三種不同類型的常數(shù)：內(nèi)置的數(shù)學(xué)和數(shù)值常數(shù)，內(nèi)置的物理常數(shù)和參數(shù)。參數(shù)是用戶定義的常量，可以隨參數(shù)掃描而變化。常量是標(biāo)量值。下表列出了內(nèi)置

6、物理常量。常量和參數(shù)可以有單位。BUILT-INPHYSICALCONSTANTS內(nèi)置物理常數(shù)TABLE5-12:BUILT-INPHYSICALCONSTANTSNAMEDESCRIPTION描述g_constAccelerationofgravityN_A_constAvogadroconstantk_B_constBoltzmannconstantZ0_constCharacteristicimpedanceofvacuum(impedanceoffreespace)真空的特性阻抗(自由空間的阻抗)me_constElectronmass電子質(zhì)量e_constElementarychar

7、ge元電荷F_constFaradayconstant法拉第常數(shù)alpha_constFine-structureconstant精細(xì)結(jié)構(gòu)常數(shù)G_constGravitationalconstant萬有引力常量V_m_constMolarvolumeofidealgas(at273.15Kand1atm)理想氣體的摩爾體積(在273.15K和1atm下)mn_constNeutronmass中子質(zhì)量mu0_constPermeabilityofvacuum(magneticconstant)真空的磁導(dǎo)率(磁常數(shù))epsilon0_constPermittivityofvacuum(electr

8、icconstant)真空介電常數(shù)(電常數(shù))h_constPlancsconstant普朗克常數(shù)hbar_constPlancsconstantover2pi超過2pi的普朗克常數(shù)mp_constProtonmass質(zhì)子質(zhì)量c_constSpeedoflightinvacuum真空中的光速sigma_constStefan-Boltzmannconstant斯蒂芬一玻爾茲曼常數(shù)R_constUniversalgasconstant通用氣體常數(shù)b_constWiendisplacementlawconstant維恩位移常數(shù)BUILT-INMATHEMATICALFUNCTIONS內(nèi)置數(shù)學(xué)函數(shù)Th

9、esefunctionsdonothaveunitsfortheirinputoroutputarguments.這些函數(shù)沒有用于其輸入或輸出參數(shù)的單位。TABLE5-13:BUILT-INDESCRIPTIONMATHEMATICALFUNCTIONSNAMEabsAbsolutevalue絕對(duì)值acosInversecosine（inradians）逆余弦（以弧度表示）acoshInversehyperboliccosine反雙曲余弦acotInversecotangent(inradians)反余切(單位為弧度)acothInversehyperboliccotangent反雙曲余切ac

10、scInversecosecant(inradians)逆余弦(以弧度表示)acschInversehyperboliccosecant反雙曲余割argPhaseangle（in出12口5）相位角（以弧度表示）asecInversesecant（inradians）反正切（以弧度表示）asechInversehyperbolicsecant反雙曲正割asinInversesine(inradians)反正弦(以弧度表示)asinhInversehyperbolicsine反雙曲正弦atanInversetangent(inradians)反正切(弧度)atan2Four-quadrantinv

11、ersetangent(inradians)四象限反正切(以弧度表示)atanhInversehyperbolictangent反雙曲正切besseljBesselfunctionofthefirstkind第一類貝塞爾函數(shù)besselyBesselfunctionofthesecondkind第二類貝塞爾函數(shù)besseliModifiedBesselfunctionofthefirstkind第一類修改的貝塞爾函數(shù)besselkModifiedBesselfunctionofthesecondkind第二類修改的貝塞爾函數(shù)ceilNearestfollowingintegerconjComp

12、lexconjugate復(fù)共軛cosCosine余弦coshHyperboliccosine雙曲余弦cotCotangent余切cothHyperboliccotangent雙曲余切cscCosecant余割cschHyperboliccosecant雙曲余割erfErrorfunction誤差函數(shù)expExponential指數(shù)floorNearestpreviousintegergammaGammafunction伽馬函數(shù)imagImaginarypart虛部logNaturallogarithm自然對(duì)數(shù)log10Base-10logarithmlog2Base-2logarithmmax

13、MaximumoftwoargumentsminMinimumoftwoargumentsmodModulooperator模運(yùn)算符psiPsifunctionanditsderivatives甲函數(shù)及其導(dǎo)數(shù)rangeCreatearangeofnumbers創(chuàng)建一個(gè)數(shù)字范圍realRealpart實(shí)部roundRoundtoclosestinteger四舍五入為最接近的整數(shù)secSecant割線sechHyperbolicsecant雙曲正割signSignumfunction符號(hào)函數(shù)sinSine正弦sinhHyperbolicsine雙曲正弦sqrtSquareroot平方根tanTan

14、gent雙曲正切tanhHyperbolictangentThefollowingtablesummarizesthebuilt-invariablesandconstantsthataregenerallyavailableinallCOMSOLmodels.Someareonlyavailableincertaingeometriesorintime-dependentmodels,forexample.ThesevariablenamesarereservednamesandappearinorangeintheSettingswindowsforparametersandvariabl

15、es.下表總結(jié)了通常在所有COMSOL模型中用到的內(nèi)置變量和常量。例如，一些僅在某些幾何形狀或在瞬態(tài)模型中可用。這些變量名稱是保留的名稱，在參數(shù)和變量的設(shè)置窗口中顯示為橙色TABLE5-14:BUILT-INVARIABLESANDCONSTANTSNAMEDESCRIPTIONTYPEtTime.時(shí)間Scalar標(biāo)量freqFrequency.頻率ScalarlambdaEigenvalues.特征值ScalarphasePhaseangle.相位角ScalarnumberofdofsNumberofdegreesoffreedom.自由度數(shù)Scalarx,y,z,r,X,YZ,RPosit

16、ion.位置Field域s,s1,s2Edge/surfaceparameters.邊/面參數(shù)Fieldn,nx,ny,nz,nrEdge/surfacenormals.邊/面法線Fieldtx,ty,tz,trEdgetangents.邊緣切線Fieldtlx,t1y,t1z,t2x,t2y,t2zSurfacetangents.表面切線Fieldun,unx,uny,unzEdge/surfaceupwardnormals.邊/面向上法線Fielddn,dnx,dny,dnzEdge/surfacedownwardnormals.Fieldeps,i,j,pi,inf,Inf,nan,Na

17、NNumericalconstants.數(shù)字常量ScalarhLocalmeshelementsize(lengthofthelongestelementedge).局部網(wǎng)格兀素大小(最長(zhǎng)元素邊的長(zhǎng)度)FielddomThedomainnumber,boundarynumber,edgenumber,orpointnumber.域名，邊界號(hào)，邊緣號(hào)或點(diǎn)號(hào)FieldmeshtypeMeshtypeindexforthemeshelement;thisisthenumberofedgesintheelement.網(wǎng)格元素的網(wǎng)格類型索引;這是元素中的邊的數(shù)量FieldmeshelementMeshe

18、lementnumber.網(wǎng)格元素?cái)?shù)FieldmeshvolVolumeofthe(linearized)meshelement.(線性化)網(wǎng)格元素的體積FielddvolVolumescalefactorvariable;thisisthedeterminantoftheJacobianmatrixforthemappingfromlocal(element)coordinatestoglobalcoordinates.體積比例因子變量;這是用于從局部(元素)坐標(biāo)到全局坐標(biāo)的映射的雅可比矩陣的行列式FieldqualAmeshqualitymeasurebetween0(poorqualit

19、y)and1(perfectquality).Theabsolutevalueofthemeshelementqualityisbasedontheratiosoftheinscribedandcircumscribedcirclesorspheresradiiforthesimplexcorrespondingtoeachcorneroftheelement.Anegativevaluemeansacontradictiontothenumberingconventionformeshelementverticesandtheelementisthenreferredtoasaninvert

20、edelement.網(wǎng)格質(zhì)量測(cè)量在0(質(zhì)量差)和1(完美質(zhì)量)之間。網(wǎng)格元素質(zhì)量的絕對(duì)值基于對(duì)應(yīng)于元素的每個(gè)角的單形的內(nèi)切圓或外接圓或球的半徑的比率。負(fù)值意味著與網(wǎng)格元素頂點(diǎn)的編號(hào)慣例矛盾，然后該元素被稱為反向元素FieldreldetjacDeterminantoftheJacobianmatrixfortheFieldmappingfromthestraightmeshelementtothepossiblycurvedelementusedwhensolving.Jacobian矩陣的決定因素，用于從直的網(wǎng)格元素到解決時(shí)使用的可能彎曲的元素的映射reldetjacminTheminimu

21、mvalueofthereldetjacvariableineachelement.每個(gè)元素中reldetjac變量的最小值FieldlinearizedelemOneinsideelementsthathavebeenlinearized;zerootherwise.線性化的一個(gè)內(nèi)部元素;否則為零FieldniterCMPIterationnumberfornonlineariterations.非線性迭代的迭代數(shù)Scalargmg_levelGeometricmultigridlevel.幾何多網(wǎng)格級(jí)ScalartimestepCurrenttimestep.當(dāng)前時(shí)間步Scalarpart

22、icleindexAuniquepositiveintegertodefineeachparticleorray.ThisvariableisonlydefinedwhenusingtheGeometricalOpticsinterface,RayAcousticsinterface,oroneoftheparticletracingphysicsinterfaces.定義每個(gè)粒子或射線的唯一正整數(shù)。此變量?jī)H在使用幾何光學(xué)接口，RayAcoustics接口或粒子跟蹤物理接口之一時(shí)才定義ScalarparticlestatusAnintegerthatcorrespondstothestatusofaparticleorray,whichindicateswhethertheparticleorrayisactiveorhasbeensubjectedtocertaintypesofboundaryconditions.ThisvariableisonlydefinedwhenusingtheScalarGeometricalOpticsinterface,RayAcousticsinterface,oroneoftheparticletrac