OPTIM_ETA.sif

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! PARAMETERS
!! Name of the RUN 
$name="<NAME>"
!! Regularisation parameter
$Lambda=<Lambda>
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$OBSERVATION_FILE="<OBS_FILE>"
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!! number of iterations
$niter=200
!
! Exps. definitions.
$yearinsec = 31536000.0
$rhoi = 900.0/(1.0e6*yearinsec^2)   
$rhow = 1028.0/(1.0e6*yearinsec^2)
$gravity = -9.81*yearinsec^2
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Header
  Mesh DB "." "mesh"
End
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Constants
  Water Density = Real $ rhow
  Sea Level = Real 0.0
End
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Simulation
  Coordinate System  = Cartesian 
  Simulation Type = Steady State

  Steady State Min Iterations = 1
  Steady State Max Iterations = $niter

  Post File = "OPTIM_$name$.vtu"
  Output Intervals = 25

  Restart File = "IMPORT.result"
  Restart Before Initial Conditions = logical True

  max output level = 3
End
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Body 1
  Equation = 1
  Body Force = 1
  Material = 1
  Initial Condition = 1
End
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Initial Condition 1
! alpha is the optimised variable
 alpha = Variable Mu
    REAL procedure "ElmerIceUSF" "SQRTA"
End
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Body Force 1
  Flow BodyForce 1 = Real 0.0            
  Flow BodyForce 2 = Real 0.0              
  Flow BodyForce 3 = Real $gravity

  SSAVelocity 1 = Equals Uobs 1
  SSAVelocity 2 = Equals Uobs 2
  SSAVelocity 1 Condition = Variable GroundedMask
    Real procedure "USFs_RonneFilchner" "GM_CONDITION"
  SSAVelocity 2 Condition = Variable GroundedMask
    Real procedure "USFs_RonneFilchner" "GM_CONDITION"
End
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Material 1
  Viscosity Exponent = Real $1.0e00/3.0e00
  Critical Shear Rate = Real 1.0e-10

  SSA Mean Density = Real $rhoi

  SSA Mean Viscosity = Variable alpha
      REAL procedure "ElmerIceUSF" "Asquare"

  SSA Mean Viscosity derivative = Variable alpha
      REAL procedure "ElmerIceUSF" "Asquare_d"

  SSA Friction Law = String "linear"
  SSA Friction Parameter = Real 0.0
End
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Solver 1
  Equation = "SSA"
  Variable = -dofs 2 "SSAVelocity"

  Procedure = "ElmerIceSolvers" "AdjointSSA_SSASolver"

  Linear System Solver = Direct
  Linear System Direct Method = mumps

  Nonlinear System Max Iterations = 50
  Nonlinear System Convergence Tolerance  = 1.0e-10
  Nonlinear System Newton After Iterations = 8
  Nonlinear System Newton After Tolerance = 1.0e-05
  Nonlinear System Relaxation Factor = 1.00

  Steady State Convergence Tolerance = Real 1.0e-12

  Exported Variable 1 = -global CostValue
  Exported Variable 2 = alpha
  Exported Variable 3 = -nooutput DJDEta
  Exported Variable 4 = -nooutput "Velocityb"
  Exported Variable 4 DOFs = 2
End
!!! Compute Cost function
!!!!!!!!   Has to be run before the Adjoint Solver as adjoint forcing is computed here !!!!!
!! Here the cost is the discrete sum_1^Ndata 1/2 ||u-u^obs|| evaluated at the data location (which may not correspond to mesh nodes)
Solver 2
  Equation = "Cost"
    procedure = "ElmerIceSolvers" "Adjoint_CostDiscSolver"

   Cost Variable Name = String "CostValue"  ! Name of Cost Variable
   Lambda = Real 1.0
 ! save the cost as a function of iterations (iterations,Cost,rms=sqrt(2*Cost/Ndata)
   Cost Filename = File "Cost_$name$.dat"

   Observed Variable Name = String "SSAVelocity"
   Observed Variable dimension = Integer 2

 ! netcdf files
   Observation File Name = File "<OBS_FILE>"

     X Dim Name = File "x" ![default "x"] ! name of the dimension for x
     Y Dim Name = File "y" ![default "y"] ! name of the dimension for y

     X Var Name = File "x" ![default "x"] ! name of the variable for x
     Y Var Name = File "y" ![default "y"] ! name of the variable for x

     Netcdf Var 1 Name = File "VX" ![default "vx"]
     Netcdf Var 2 Name = File "VY" ![default "vy"]


end
!!!!  Adjoint Solution
Solver 3
  Equation = "Adjoint"
  Variable = -nooutput Adjoint
  Variable Dofs = 2

  procedure = "ElmerIceSolvers" "Adjoint_LinearSolver"

!Name of the flow solution solver
  Direct Solver Equation Name = string "SSA"

   Linear System Solver = Direct
   Linear System Direct Method = mumps
End

!!!!!  Compute Derivative of Cost function / Beta
Solver 4
  Equation = "DJDEta"
    procedure = "ElmerIceSolvers" "AdjointSSA_GradientSolver"

    Flow Solution Name = String "SSAVelocity"
    Adjoint Solution Name = String "Adjoint"
    Compute DJDEta = Logical True   ! Derivative with respect to the SSA Mean Viscosity
 
end
!!!!!  Compute Regularistaion term
!   Regularisation by default is: Lambda * int_{Pb dimension} 0.5 * (d(var)/dx)**2 
!   A priori regularisation can also be used ( A priori Regularisation=True) :
!                                 Lambda * int_{Pb dimension} 0.5 *(1/sigma**2)*(var-var{a_priori})**2
!
!     OUTPUT are : J and DJDvar
Solver 5
  Equation = "DJDBeta_Reg"
    procedure = "ElmerIceSolvers" "Adjoint_CostRegSolver"

    Cost Filename=File "CostReg_$name$.dat"
    Optimized Variable Name= String "alpha"
    Gradient Variable Name= String "DJDEta"
    Cost Variable Name= String "CostValue"
    Lambda= Real $Lambda
    Reset Cost Value= Logical False  !=> DJDapha already initialized in solver DJDBeta; switch off initialisation to 0 at the beginning of this solver
    A priori Regularisation= Logical False
end
!!!!! Optimization procedure : Parallel only
Solver 6
  Equation = "Optimize_m1qn3"
  procedure = "ElmerIceSolvers" "Optimize_m1qn3Parallel"

  Cost Variable Name = String "CostValue"
  Optimized Variable Name = String "alpha"
  Gradient Variable Name = String "DJDEta"
  gradient Norm File = File "GradientNormAdjoint_$name$.dat"

  !!
  Mesh Independent = Logical False

 ! M1QN3 Parameters
  M1QN3 dxmin = Real 1.0e-10
  M1QN3 epsg = Real  1.e-5
  M1QN3 niter = Integer $niter
  M1QN3 nsim = Integer $niter
  M1QN3 impres = Integer 5
  M1QN3 DIS Mode = Logical False
  M1QN3 df1 = Real 0.5
  M1QN3 normtype = String "dfn"
  M1QN3 OutputFile = File  "M1QN3_$name$.out"
  M1QN3 ndz = Integer 20

end

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Equation 1
  Active Solvers(7) = 1 2 3 4 5 6 7
End

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Boundary Condition 1
  Target Boundaries(2) = 1 3
  
  SSAVelocity 1 = Equals Uobs 1
  SSAVelocity 2 = Equals Uobs 2

End

Boundary Condition 2
  Name = "Ice Front"
  Target Boundaries(2) = 2 4

  calving front = logical true
End