Adaptive Timestepping

Numerical methods and mathematical models of Elmer
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mzenker
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Joined: 07 Dec 2009, 11:49
Location: Germany

Adaptive Timestepping

Post by mzenker » 29 Nov 2010, 19:29

Hi,

I try to use adaptive timestepping on a problem with coupled Statcurrent and Heat Equation solvers involving phase change. I have run the problem before without adaptive timestepping. It worked OK, but I found that I need to take very small timesteps in order to achieve resonable results. Then I have just added

Adaptive Timestepping = Logical True
Adaptive Time Error = Real 1e-5

in the Simulation section. My problem is that now the solver seems to run forever.
I have read in the Models Manual that adaptive timestepping is possible when the BDF timestepping method of order 1 is used, which is the case.
What could I have done wrong? Is there an example where adaptive timestepping is used?
I have found nothing the tutorials and just one example under "tests" where a "Runge-Kutta" timestepping method (?) is used.

Maybe someone could shed some light on this and give me a hint what I could do to get more information and get my simulation to work...

Thank you,

Matthias

mzenker
Posts: 1902
Joined: 07 Dec 2009, 11:49
Location: Germany

Re: Adaptive Timestepping

Post by mzenker » 01 Dec 2010, 13:45

Hi,

still trying to get the adaptive timestepping to work, I have experienced a solver crash. After some iterations, I get the error message:

Fortran runtime error: Attempting to allocate already allocated array

I use the latest binary for Windoze (svn4844-2010-11-25).
In the attachment there is a test case which reproduces the crash. To load the project with ElmerGUI, all solver xml files fro bin/edf-extra have to be copied to bin/edf.

I would be very grateful if someone from the Elmer team could have a look on my case, and try to find out why the solver crashed, and what I can do to get the adaptive timestepping to work...

Thank you,

Matthias
Attachments
Adaptive_crash.zip
(96.07 KiB) Downloaded 118 times

Juha
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Posts: 357
Joined: 21 Aug 2009, 15:11

Re: Adaptive Timestepping

Post by Juha » 02 Dec 2010, 09:55

Hi,

thanks for the bug report, the memory (de)allocation trouble has been resolved in the current SVN.

Looking at the adaptive timestepping (after the fix), it seems to work much as expected.
Just your simulation needs pretty small timesteps at the beginning to get to the desider accuracy.
Anyway the sif file below seems to work reasonably (for me):

1) added material table values to both ends (Temp=0 & 250) to account for
iteration overshoots

2) Let the timestepping resolve (most) the nonliearities (Relaxation Factor=1, Steady Max Iter=2)

3) Use Explicit Euler timestepping for speed

4) Use somewhat stricter criteria for adaptive timestepping convergence (1e-4)

Note that the first few steps take most of the time...

Regards, Juha

Code: Select all

Header
  CHECK KEYWORDS Warn
  Mesh DB "." "."
  Include Path ""
  Results Directory ""
End

Simulation
  Max Output Level = 3
  Coordinate System = Cartesian
  Coordinate Mapping(3) = 1 2 3
  Simulation Type = Transient
  Steady State Max Iterations = 2
  Output Intervals = 1
  Timestepping Method = explicit euler
  BDF Order = 1
  Runge-Kutta Order = 2

  Timestep intervals = 100
  Timestep Sizes = 0.05
  Solver Input File = case.sif
  Post File = case_ee_t.ep

  Adaptive Timestepping = Logical True
  Adaptive Min Timestep = 1e-6
  Adaptive Time Error = 1e-4
  Adaptive Keep Smallest = 3
  Coordinate Scaling = Real 0.001
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) = 11
  Name = "Test Material"
  Equation = 1
  Material = 1
  Body Force = 1
  Initial condition = 1
End

Solver 1
  Equation = Static Current Conduction
  Calculate Volume Current = True
  Procedure = "StatCurrentSolve" "StatCurrentSolver"
  Variable = -dofs 1 Potential
  Calculate Joule Heating = 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-8
  Nonlinear System Max Iterations = 1
  Nonlinear System Newton After Iterations = 1
  Nonlinear System Newton After Tolerance = 1.0e-3
  Nonlinear System Relaxation Factor = 1
  Linear System Solver = Iterative
  Linear System Iterative Method = BiCGStabL
  Linear System Max Iterations = 10
  Linear System Convergence Tolerance = 1.0e-8
  Linear System Preconditioning = ILU2
  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 = Heat Equation
  Variable = -dofs 1 Temperature
  Procedure = "HeatSolve" "HeatSolver"
  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-8
  Nonlinear System Max Iterations = 1
  Nonlinear System Newton After Iterations = 1
  Nonlinear System Newton After Tolerance = 1.0e-3
  Nonlinear System Relaxation Factor = 1
  Linear System Solver = Iterative
  Linear System Iterative Method = BiCGStabL
  Linear System Max Iterations = 10
  Linear System Convergence Tolerance = 1.0e-8
  Linear System Preconditioning = ILU2
  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 = "Equation 1"
  Phase Change Model = Spatial 2
  Active Solvers(2) = 1 2
End

Material 1
  Name = "TestMaterial (phase and conductivity change)"
  Enthalpy = Variable Temperature;Real;0 60; 10 42117000; 20 84012000; 50 209410000; 70 293070000; 99 417000000; 101 2675800000; 150 2776600000; 250 4.62767e+09; End;
  Electric Conductivity = Variable Temperature
   Real
     0 0.2
     20 0.2
     90 0.2
     98 0.15
     99 0.1
     100 0.05
     101 0.005
     110 0.005
     250 0.005
  End
  Heat Conductivity = 0.5
  Heat Capacity = 3600
  Density = 1000
End

Body Force 1
  Name = "BodyForce 1"
  Joule Heat = True
End

Initial Condition 1
  Name = "InitialCondition 1"
  Temperature = 20
End

Boundary Condition 1
  Target Boundaries(1) = 12
  Name = "Electrode"
  Potential = 100
End

Boundary Condition 2
  Target Boundaries(1) = 13
  Name = "Ground"
  Potential = 0
End

Boundary Condition 3
  Target Boundaries(1) = 14
  Name = "Temperature limit"
  Temperature = 20
End

Boundary Condition 4
  Target Boundaries(1) = 15
  Name = "Temperature limit"
  Temperature = 20
End

Juha
Site Admin
Posts: 357
Joined: 21 Aug 2009, 15:11

Re: Adaptive Timestepping

Post by Juha » 02 Dec 2010, 10:28

Hi,

seems better (timewise at least) taking Steady Max Iterations=1, when Explicit Euler is used.
Juha

mzenker
Posts: 1902
Joined: 07 Dec 2009, 11:49
Location: Germany

Re: Adaptive Timestepping

Post by mzenker » 02 Dec 2010, 12:43

Hi Juha,

thank you for your reply and the helpful hints. I will try them out when a new Windows binary is available.

In the meantime, I would like to expand my knowledge on FEM methods. I would never have found out by myself what you have suggested (timestepping method = explicit Euler - what is that, and why is it better here? etc. etc.). Unfortunately I have not found much information in the Elmer manuals, which is maybe normal since they are not textbooks on FEM. I think I should look for a good textbook on FEM. Do you have a recommendation?

Thank you,

Matthias

raback
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Re: Adaptive Timestepping

Post by raback » 02 Dec 2010, 13:47

Hi
mzenker wrote:
I would never have found out by myself what you have suggested (timestepping method = explicit Euler - what is that, and why is it better here? etc. etc.).
Time integration methods such as the explicit Euler are not limited to just to FEM. In fact in FEM the time discretization is the only one that is done with the Finite Difference method. There are also Finite Element discretizations for time but that's another story.

Generally implicit time integration methods are superior with FEM since they are unconditionally stable (of course there could be nonlinearities that spoil this stability). The explicit methods aren't and therefore you often need to severily limit the timestep. However, in this case the evaluation of the effective heat capacity is done using the previous temperature field so it is by construction explicit and goes well together the explicit time integration method as well.

-Peter

mzenker
Posts: 1902
Joined: 07 Dec 2009, 11:49
Location: Germany

Re: Adaptive Timestepping

Post by mzenker » 02 Dec 2010, 16:53

Hi Peter,

thank you for this explanation. I see that I still have much to learn in this field.

Can you recommend some literature for further reading? What is your "FEM bible", if any? ;)

Thanks again,

Matthias

hazelsct
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Joined: 05 Oct 2009, 17:02
Location: Boston, MA, USA
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Re: Adaptive Timestepping

Post by hazelsct » 03 Dec 2010, 01:27

Hello,

While it's not a "Bible" by any stretch, I worked on some reading material for an introductory course in modeling a few years back, including FEM. You can find the reading at: http://hdl.handle.net/1721.1/50265 , scroll down and click on "View/Open", then "Selected lecture notes" -> "Continuum Methods (CM) (PDF)".

Or you can just download the .zip archive with all of the files.

Either way, the time-stepping algorithm stuff is in chapter 3. Unfortunately it is limited to implicit, explicit and semi-implicit algorithms, with no BDF.

-Adam

mzenker
Posts: 1902
Joined: 07 Dec 2009, 11:49
Location: Germany

Re: Adaptive Timestepping

Post by mzenker » 06 Dec 2010, 20:27

Hi all,

thanks to Adam's lecture notes, I know more about time discretisation now, and I will go on filling my knowledge gaps... ;)

Now I am eager to try the fixed adaptive timestepping on my problem. When can we expect the next Windows binary... ?

Thank you,

Matthias

mzenker
Posts: 1902
Joined: 07 Dec 2009, 11:49
Location: Germany

Re: Adaptive Timestepping

Post by mzenker » 15 Dec 2010, 17:53

Thanks to the new binary, I just have made the first successful run using adaptive timestepping. :)

Now I am going to explore the new possibilities...

Thank you again,

Matthias

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