COMSOL AC-DC模块

1、Mastering AC/DC and RF SimulationsMagnus OlssonContentsIntroduction to the RF and AC/DC Modules Formulations Choosing solversTips and tricks Boundary settings Handling high contrast Global constraints Force computations New transient solver tweaking the settings Handling large scale differencesCOMSO

2、L Products for Electromagnetic SimulationsCOMSOL MultiphysicsAcousticsModuleChemical Engineering ModuleStructural MechanicsModuleEarth Science ModuleHeat TransferModuleMEMS ModuleRF ModuleCAD ImportModuleMaterial LibraryAC/DCModuleVarious multiphysics combinations with electric fields not available

3、in AC/DC and RF modules(Piezoelectric, Piezoresistive, Electrokinetic, Electroosmotic, etc.)I-V termswave termsEMMaxwells EquationstttJBDBEDJH0Maxwell-Amperes lawFaradays lawGauss law, electricGauss law, magneticEquation of ContinuityPotentialsMagnetic Vector Potential, AElectric Potential, VMagneti

4、c Scalar Potential, VmmVtVHAEABFormulationsElectrostatics, unknown V:Quasi-statics, unknown H:0)(0)()(000ererrVtVVjVJJP0)(010HvJHHerrtElectric currents quasi-statics, unknown V:0)(0rmrVBMagnetostatics, no currents:FormulationsQuasi-statics, unknown V and A:Electromagnetic Waves, unknown A, E or H:ee

5、JAvAAJAvAVjjVjjrrrrr)()()()(0)()()(0110020020HH0EE0AAArrrrrrkjjkttt201002011000)()()()()(Choosing Solvers for Electromagnetic Problems Solvers for vector field problemsAll EM problemsVector problemsMixed vector-scalar(e.g. A-V)Scalar problems(V, Vm, Az, Hphi, etc.)Inherent gaugeGauge enforcedUngauge

6、dGauge expected, unenforcedGauge freedomSOR vectorVankaSOR gaugeSOR (plain)No gauge issuesSOR (plain)User decidesUser decidesPhysicsdecides&Can use direct solversCan not use direct solversCategory 1Category 2Category 3Category 4Vector or scalar problem?3D problems usually involve vector fields,

7、except:1)Electrostatics; conductive media2)Magnetostatics-no-currents (Vm)3)Quasistatics, electric currents (V)2D problems are usually purely scalar, except:1)In-Plane Electric and Induction currents (Ax, Ay ; V)2)Transient In-Plane TM waves (Ax, Ay)3)Transient In-Plane Hybrid waves (Ax, Ay; Az)In R

8、F Module,all 3D problems are vectorInherent gauge or gauge freedom?Dependent variablesStaticTime-HarmonicTransientAGauge freedomInherent gaugediv (2+i) A)=0Inherent gaugediv (A)=0 A, V Gauge freedomGauge freedomN/AAN/AN/AInherent gaugediv (A)=0E or HN/AInherent “gauge”div D=0 or div B=0N/AA vector i

9、s either Ax, Ay, Az in 3D, orAx, Ay in 2D (in-plane induction), orAr, Az in axi-2D (meridional induction)Perpendicular/azimuthal induction gives scalar equation (Az/Aphi)AC/DCRFWhen should one enforce gauge?In problems with inherent gauge:When inherent gauge degenerates in some subdomainsAvoid this

10、by using non-zero conductivity in all subdomainsIn problems with gauge freedom:When unable to adjust iterative solvers recommended for ungauged formulationsIterative solvers, inherent gaugeCategory 2: Vector formulations, inherent gauge (no gauge fixing equation)1.GMRES + GMG(precond.) + SOR/SORU Ve

11、ctor (smoothers) + direct solverThis is the standard situation for RF Module applications2.GMRES + SSOR Vector (precond.)3.GMG + SOR/SORU Vector (smoothers)Try playing with all three combinations in model “Eddy Currents 3D” (Model LibraryAC/DCGeneral Industrial Applications)Reminder: direct solvers

12、PARDISO, SPOOLES, UMFPACK will work here (given enough memory)Iterative solvers, enforced gaugeCategory 3: Enforced gauge (extra equation)1.GMRES + GMG(precond.) + Vanka/Vanka(smoothers) + direct solverUse with RF applications when unable to avoid gauging2.GMG + Vanka/Vanka(smoothers) + direct solve

13、rExample: AC/DCPower Inductor3.GMRES + Vanka (precond.)Example: AC/DCBond Wires to Chip (hands-on exercise today)Reminder: direct solvers PARDISO, SPOOLES, UMFPACK will work here (given enough memory)Iterative solvers, ungaugedCategory 4: Ungauged formulations1.FGMRES + GMG(precond.) + SOR/SORU(smoo

14、thers) +GMRES(coarse) + SSOR(precond.)Recommended for all types of ungauged formulations (static A, static A-V, time-harmonic A-V)2.FGMRES + GMG(precond.) + SOR/SORU gauge(smoothers) +GMRES(coarse) + SSOR gauge(precond.)Recommended for static A and A-V formulations3.FGMRES + GMRES(precond.) + SSOR(p

15、recond.)Recommended for time-harmonic A-V4.FGMRES + SSOR gauge(precond.)Recommended for static A formulationsTips and Tricks for Electromagnetic Problems 1: Boundary conditions Use boundary conditions to replace subdomains and to drive modelsEdge and Point conditionsLine Current (3D): Specify a know

16、n time-harmonic current through a line (a wire of zero radius)Point Current (2D): Specify a known current perpendicular to the modeling planeI0sin(t)I0sin(t)Visualizing edge tangent directionsPerfect Electric Conductor (PEC) / Magnetic InsulationPECE = 0E-fieldThe Electric Field B.C. fixes the E-fie

17、ld at the boundary, in a time-harmonic sense. The Electric Field B.C., as opposed to the PEC B.C., is rarely used.Models highly conductive media, with no losses.Zero-impedance condition.Impedance Boundary ConditionImpedance B.C.Specify , r, r, nE-fieldr02Materialr, S/m, f=300MHzCopper15.991079.4 mAl

18、uminum13.7710712 mS. S.11.1410668 mIron40001.121070.34 mModels highly conductive media, with losses. Perfect Magnetic Conductor (PMC) / Electric Insulation PMCnH = 0E-fieldThe Magnetic Field B.C. fixes the H-field at the boundary, in a time-harmonic sense. The Magnetic Field B.C., as opposed to the

19、PMC B.C., is rarely used.Symmetry boundary.High-impedance condition.Surface CurrentSurface CurrentJ = JsE-fieldModels a surface with a known current flowing tangentially. Example: Driving surface currentsScattering Boundary Condition (SBC)Incident plane waveScattered WaveAn SBC allows an incident pl

20、ane wave to pass through from any directionA scattered wave of a known wave-type will pass through an SBCComputational DomainScattering Boundary Condition, Scattered FieldSet the type of the scattered wave here.Usually, this is known only approximately.For cylindrical and spherical scattered waves,

21、also set a centerpoint and axisThis only affects the scattered field, and does not affect the incident field.Scattering Boundary Condition, Incident FieldMagnitude, (and phase)Direction of the incident plane waveThe SBC is perfectly invisible only to scattered waves that are known preciselyIncident

22、WaveScattered WaveMatched Boundary Condition (MBC)If the propagation constant of the field at the boundary is known, then use the MBC.Can also apply an incident field, if the shape of the field is known. This need not be a plane wave.If you know the exact wave vector, the Matched Boundary is transpa

23、rentScatteringBoundaryConditionMatchedBoundaryConditionAdding waves at an angle to an MBC or SBC 20expwyMust include spatial and phase variation sinexpexp20iywyxy2nPML vs. Scattering Boundary ConditionScattering Boundary ConditionPMLRadiating CylinderPort Boundary ConditionThis is the same as an MBC

24、 with two extensions:1) S-parameters2) Analytic and numeric portsPort Boundary ConditionApply an analytic or numeric solution for the shape of the fields on the boundary.See waveguide adapter model in model library for a tutorialLumped PortsPECPECLumped Portd Lumped ports are appropriate when the di

25、mensions are much smaller than the wavelength and the true incident field is unknown (TEM approximation)Example: Dipole and Yagi antennas in 3DDefault 3D ViewXY ViewPeriodic Boundary ConditionEdst=EsrcEdst=-EsrcContinuityAnti-periodcityFloquet Periodic Boundary Condition, exampleAirAirGlass2sinxcosy

26、Floquet Periodic Boundary Condition, exampleFloquet Periodic Boundary Condition, exampleMust enter Floquet periodic source term2: Handling high contrast3: Global constraints Global constraint:Example: Find induced voltage in a buried pipeline under a high voltage line Bonus: Meshing infinite element

27、s and PMLsAdvanced example: RF Inductor in axisymmetry4: Force computationsMaxwell stress tensor method - was Newton right?Bonus feature: adaption on linear functionalUsing virtual work5: Tweaking of new time solver in the nonlinear settings (MO)6: Handling large scale differencesEmbedded thin wiresLeaky shieldingLeaky shielding a common problemElectromagnetic shielding typically employs thin layers of highly conductive a