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### No Convergence with H-B Curve

Posted: 25 Nov 2016, 12:05
Hi Elmer-Users,

I have a simple model of a single wire surrounded by a hollow cylinder out of steel. The cylinder is surrounded by air.
model_sw.png (62.68 KiB) Viewed 3384 times
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).

The SIF-File:

Code: Select all

``````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
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
``````
the H-B Curve:

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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``````

### Re: No Convergence with H-B Curve

Posted: 25 Nov 2016, 16:29
Hi

There seems to be some discrepancy between the Newton iteration control that the solver uses vs. what ElmerGUI assumes. I just changed the code to also consider the legacy control of Newton linearization as in FlowSolver and HeatSolver etc. As for now you should use in the Solver section

Code: Select all

``````Newton-Rhapson iteration = Logical True
``````
-Peter

### Re: No Convergence with H-B Curve

Posted: 25 Nov 2016, 23:47
Thank you!

### Re: No Convergence with H-B Curve

Posted: 28 Nov 2016, 11:04
Some question to understand that keyword: How is the Newton Raphson iteration used? I think the system is still solved via CG?