! Luiz Souza, Jun/2020 ! Testing an axisymmetric problem in 3D (cilyndrical magnet centered ! at origen) ! Save output on ZY plane for comparison with actual axisymmetric FEMM ! solution ! Check changes in the Magnetic Vector Potential as the Lagrange Gauge ! Penalization Coefficient (kLagr) changes ! One conclusion: no numerically significant change in the vector ! potential with kLagr = 1, 2, 10, 1e8 when using Piola transform ! Compute the divergence of the vector potential (does it get closer ! to zero as kLagr increases?) ! Ref. for sif file format: Solver Manual, Chapter 2 echo on $dx = 76.2e-3 $dy = 1.5875e-3 $dz = 1.5875e-3 $xmin = 0 $ymin = 0 $zmin = 0 $xmax = 76.2e-3 $ymax = 76.2e-3 $zmax = 88.9e-3 ! Lagrange Gauge Penalization Coefficient $kLagr = 0 $grifname = "magneticplane_no_Lagr_gauge_noPiola" Header CHECK KEYWORDS Warn Mesh DB "." "fine_mesh" Include Path "" Results Directory "" End Simulation Max Output Level = 5 Coordinate System = Cartesian 3D Coordinate Mapping(3) = 1 2 3 Simulation Type = Steady state Steady State Max Iterations = 1 Output Intervals = 1 Timestepping Method = BDF BDF Order = 1 Coordinate Scaling = 1 Solver Input File = case.sif Post File = singlemag_sphere.ep End Constants Gravity(4) = 0 -1 0 9.82 Stefan Boltzmann = 5.67e-08 Permittivity of Vacuum = 8.8542e-12 Boltzmann Constant = 1.3807e-23 Unit Charge = 1.602e-19 End Body 1 Target Bodies(1) = 1 Name = "Body 1" Equation = 1 Material = 1 End Body 2 Target Bodies(1) = 2 Name = "Body 2" Equation = 1 Material = 2 End Solver 1 Equation = MgDyn Procedure = "MagnetoDynamics" "WhitneyAVSolver" Exec Solver = Always Stabilize = True Bubbles = False Optimize Bandwidth = False Lumped Mass Matrix = False Variable = String AV Use Lagrange Gauge = False ! True ! Lagrange Gauge Penalization Coefficient = Real $kLagr Use Piola Transform = False ! True Steady State Convergence Tolerance = 1.0e-5 Nonlinear System Convergence Tolerance = 1.0e-7 Nonlinear System Max Iterations = 20 Nonlinear System Newton After Iterations = 3 Nonlinear System Newton After Tolerance = 1.0e-3 Nonlinear System Relaxation Factor = 1 Linear System Solver = Iterative Linear System Iterative Method = BiCGStab Linear System Max Iterations = 500 Linear System Convergence Tolerance = 1.0e-10 BiCGstabl polynomial degree = 2 Linear System Preconditioning = ILUT Linear System ILUT Tolerance = 1.0e-3 Linear System Abort Not Converged = False Linear System Residual Output = 1 Linear System Precondition Recompute = 1 End Solver 2 Equation = MgDynPost Calculate Divergence = Logical True Calculate Magnetic Field Strength = False Potential Variable = String AV Calculate Magnetic Vector Potential = Logical True Procedure = "MagnetoDynamics" "MagnetoDynamicsCalcFields" Exec Solver = After Timestep Stabilize = False Bubbles = False Lumped Mass Matrix = False Optimize Bandwidth = False Steady State Convergence Tolerance = 1.0e-5 Nonlinear System Convergence Tolerance = 1.0e-7 Nonlinear System Max Iterations = 20 Nonlinear System Newton After Iterations = 3 Nonlinear System Newton After Tolerance = 1.0e-3 Nonlinear System Relaxation Factor = 1 Linear System Solver = Iterative Linear System Iterative Method = BiCGStab Linear System Max Iterations = 500 Linear System Convergence Tolerance = 1.0e-10 BiCGstabl polynomial degree = 2 Linear System Preconditioning = ILUT Linear System ILUT Tolerance = 1.0e-3 Linear System Abort Not Converged = False Linear System Residual Output = 1 Linear System Precondition Recompute = 1 End ! from Elmer Models Manual, chapter 43, August 23, 2019 !Calculate Magnetic Vector Potential = Logical True ! Target Variable = AV !Magnetic Vector Potential Solver 3 Name = "Divergence" Procedure = "DivergenceSolver" "DivergenceSolver" Equation = "Divergence Solver" Calculate Magnetic Vector Potential = Logical True Variable = String DivA Exec Solver = After Timestep ! After Simulation Target Variable = Magnetic Vector Potential Linear System Solver = "Iterative" Linear System Iterative Method = "cg" Linear System Preconditioning = None Linear System Max Iterations = 500 Linear System Convergence Tolerance = 1.0e-10 End Solver 4 Exec Solver = after all Equation = SaveGridData Procedure = "SaveGridData" "SaveGridData" Grid Dx = Real $dx Grid Dy = Real $dy Grid Dz = Real $dz Max Coordinate 1 = Real $xmax Max Coordinate 2 = Real $ymax Max Coordinate 3 = Real $zmax Min Coordinate 1 = Real $xmin Min Coordinate 2 = Real $ymin Min Coordinate 3 = Real $zmin Check For Duplicates = Logical True Binary Output = Logical False Filename Prefix = String $grifname Vtu Format = Logical False ! True Table Format = Logical True Scalar Field 1 = String DivA Vector Field 1 = String Magnetic Flux Density Vector Field 2 = String Magnetic Vector Potential End Equation 1 Name = "Magnetic WhitneyAV, Post, Div" Active Solvers(4) = 1 3 2 4 End Material 1 Name = "ND52magnet_plusZ" Heat expansion Coeff(3,3) = Real -0.8e-6 0 0 \ 0 -0.8e-6 0 \ 0 0 5.2e-6 H-B Curve = Variable "nonlin" Real Cubic Monotone include nd52HB.txt End Poisson ratio = 0.24 Mesh Poisson ratio = 0.24 Heat Capacity = 400 Electric Conductivity = 5.56e5 Youngs modulus = 160.0e9 Heat Conductivity = 7.6 Density = 7450 Electric Conductivity = 5.56e5 Relative Permeability = 1.05 Relative Permittivity = 1.0 Magnetization 3 = Real 956180.0 End Material 2 Name = "Air" Sound speed = 343.0 Viscosity = 1.983e-5 Heat expansion Coefficient = 3.43e-3 Heat Capacity = 1005.0 Relative Permeability = 1.00000037 Heat Conductivity = 0.0257 Density = 1.205 Relative Permittivity = 1.00059 End Boundary Condition 1 Target Boundaries(1) = 4 Name = "zero potential" AV {e} = Real 0.0 AV = Real 0.0 End