I have a simple model of a single wire surrounded by a hollow cylinder out of steel. The cylinder is surrounded by air.

The boundary conditions in z-direction is chosen like the model is infinitely long. When I apply a linear permeability to the model everything works as aspected. But when I try to add a nonlinear H-B Curve the model doesn't converge. Have anyone an idea what the problem is? (i tried already: another mesh and other dimesnions of the geometry, another H-B Curve, different solver and preconditioner, another H-B Curve).

Thank you in advance!

The SIF-File:

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```
Header
CHECK KEYWORDS Warn
Mesh DB "." "."
Include Path ""
Results Directory ""
End
Simulation
Max Output Level = 10
Coordinate System = Cartesian
Coordinate Mapping(3) = 1 2 3
Simulation Type = Steady state
Steady State Max Iterations = 1
Output Intervals = 1
Timestepping Method = BDF
BDF Order = 1
Solver Input File = inf.sif
Post File = inf.ep
Coordinate Scaling = 1e-3
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 Property 1"
Equation = 1
Material = 1
Body Force = 1
End
Body 2
Target Bodies(1) = 2
Name = "Body Property 2"
Equation = 2
Material = 3
End
Body 3
Target Bodies(1) = 3
Name = "Body Property 3"
Equation = 2
Material = 2
End
Body 4
Target Bodies(1) = 4
Name = "Body Property 4"
Equation = 2
Material = 3
End
Solver 3
Equation = MgDynPost
Procedure = "MagnetoDynamics" "MagnetoDynamicsCalcFields"
Potential Variable = AV
Calculate Electric Field = True
Calculate Magnetic Field Strength = True
Exec Solver = Always
Stabilize = True
Bubbles = False
Lumped Mass Matrix = False
Optimize Bandwidth = 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 = CG
Linear System Max Iterations = 10000
Linear System Convergence Tolerance = 1.0e-10
BiCGstabl polynomial degree = 2
Linear System Preconditioning = Diagonal
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 1
Equation = Static Current Conduction
Calculate Volume Current = True
Procedure = "StatCurrentSolve" "StatCurrentSolver"
Variable = Potential
Exec Solver = Before Simulation
Stabilize = True
Bubbles = False
Lumped Mass Matrix = False
Optimize Bandwidth = 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 = CG
Linear System Max Iterations = 10000
Linear System Convergence Tolerance = 1.0e-10
BiCGstabl polynomial degree = 2
Linear System Preconditioning = Diagonal
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 4
Equation = Result Output
Procedure = "ResultOutputSolve" "ResultOutputSolver"
Output Format = Vtu
Output File Name = inf
Exec Solver = After Timestep
End
Solver 2
Equation = MgDyn
Procedure = "MagnetoDynamics" "WhitneyAVSolver"
Variable = AV
Fix Input Current Density = True
Exec Solver = Always
Stabilize = True
Bubbles = False
Lumped Mass Matrix = False
Optimize Bandwidth = True
Steady State Convergence Tolerance = 1.0e-5
Nonlinear System Convergence Tolerance = 1.0e-7
Nonlinear System Max Iterations = 200
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 = CG
Linear System Max Iterations = 10000
Linear System Convergence Tolerance = 1.0e-8
BiCGstabl polynomial degree = 2
Linear System Preconditioning = None
Linear System ILUT Tolerance = 1.0e-3
Linear System Abort Not Converged = False
Linear System Residual Output = 1
Linear System Precondition Recompute = 1
End
Equation 1
Name = "Wire"
Active Solvers(4) = 3 1 4 2
End
Equation 2
Name = "Air+Core"
Active Solvers(3) = 3 4 2
End
Material 1
Name = "Copper"
Electric Conductivity = 59.59e6
Relative Permeability = 1
Density = 8960.0
End
Material 2
Name = "Steel"
Electric Conductivity = 1.449e6
H-B Curve = Variable "nonlin"
Real Cubic Monotone
include HB_M330
End
Density = 7850.0
End
Material 3
Name = "Air"
Electric Conductivity = 0
Relative Permeability = 1
Density = 1.205
End
Body Force 1
Name = "BodyForce 1"
Current Density 1 = Equals Volume Current 1
Current Density 3 = Equals Volume Current 3
Current Density 2 = Equals Volume Current 2
End
Boundary Condition 1
Target Boundaries(1) = 2
Name = "Ground"
Potential = 0
AV {e} 2 = 0
AV {e} 1 = 0
End
Boundary Condition 2
Target Boundaries(1) = 10
Name = "Potential"
AV {e} 2 = 0
AV {e} 1 = 0
Current Density = 7.96e7
End
Boundary Condition 3
Target Boundaries(1) = 8
Name = "Border"
AV {e} = 0
End
Boundary Condition 4
Target Boundaries(6) = 1 3 4 9 11 12
Name = "inf"
AV {e} 2 = 0
AV {e} 1 = 0
End
```

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```
0 0
0.100 30
0.150 35
0.200 39
0.250 43
0.300 48
0.350 52
0.400 56
0.450 60
0.500 64
0.550 68
0.600 72
0.650 76
0.700 81
0.750 85
0.800 90
0.850 96
0.900 103
1.000 120
1.050 131
1.100 145
1.150 162
1.200 185
1.250 218
1.300 262
1.350 331
1.400 477
1.450 770
1.500 1300
1.550 2142
1.600 3294
1.650 4721
1.700 6338
1.75 8000
1.8 11000
1.85 15000
1.9 22000
1.95 35000
2 50000
2.05 80000
2.1 150000
2.15 500000
2.2 1000000
```