OPTIM_DISC.sif

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! PARAMETERS
!! Name of the RUN 
$name="<NAME>"
!! Regularisation parameter
$Lambda=<Lambda>
!! max. number of iterations
$niter=50

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$OBSERVATION_FILE="<OBS_FILE>"
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$yearinsec = 365.25*24*60*60
$rhoi = 917.0/(1.0e6*yearinsec^2)  ! MPa - a - m
$rhow = 1028.0/(1.0e6*yearinsec^2)
$gravity = -9.81*yearinsec^2
$mu=1.8e8*1.0e-6*(2.0*yearinsec)^(-1.0/3.0)

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Header
  Mesh DB "." "mesh2D"
End
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Simulation
  Coordinate System  = Cartesian 3D
  Simulation Type = Steady State

  ! Internal extrusion
  Extruded Mesh Levels=5

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

  Post File = "OPTIM_$name$_.vtu"
  OutPut Intervals = 25

  max output level = 3
End

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!! Bodies
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Body 1
  Equation = 1
  Body Force = 1
  Material = 1
  Initial Condition = 1
End
! Top surface
Body 2
  Equation = 2
  Initial Condition = 2
End
! Bottom Surface
Body 3
  Equation = 3
  Initial Condition = 3
End

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!! Initial Conditions
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Initial Condition 1
  Velocity 1 = Real 0.0
  Velocity 2 = Real 0.0
  Velocity 3 = Real 0.0
End

! Top surface
Initial Condition 2
 Zs = Variable coordinate 1, Coordinate 2
      REAL procedure "MacAyeal_USFs" "Zs"
End

! Bottom Surface
Initial Condition 3
!! Slip Coefficient
 ! True value
 BetaS = Variable coordinate 1, Coordinate 2
     REAL procedure "MacAyeal_USFs" "betaSquare"
 ! Initial guess
 alpha = Real -6.0

! Topography
 Zb = Variable coordinate 1, Coordinate 2
     REAL procedure "MacAyeal_USFs" "Zb"
End

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!!  Body Forces
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Body Force 1
  Flow BodyForce 1 = Real 0.0            
  Flow BodyForce 2 = Real 0.0              
  Flow BodyForce 3 = Real $gravity
End

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!! Materials
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Material 1
  Density = Real $rhoi
  Viscosity Model = String "power law"

  Viscosity = Real $mu

  Viscosity Exponent = Real $1.0e00/3.0e00
  Critical Shear Rate = Real 1.0e-10
End

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!! Solvers
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!! Before simulation
Solver 1
  Exec Solver = before simulation
  Equation = "MapCoordinate"
  Procedure = "StructuredMeshMapper" "StructuredMeshMapper"

  Active Coordinate = Integer 3

  Top Surface Variable Name = String "Zs"
  Bottom Surface Variable Name = String "Zb"

  Displacement Mode = Logical False
  Correct Surface = Logical True
  Minimum Height = Real 1.0
End

!! Always

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!! Velocity solution
!!  body 1 (bulk)
!!!!!!!!!!!!!!!!!!!!!
Solver 2
  Equation = "Navier-Stokes"

  Stabilize = logical True
  flow model = Stokes

! Linear system
  Linear System Solver = Iterative
  Linear System Iterative Method = GCR
  Linear System Preconditioning= ILU0
  Linear System Convergence Tolerance= 1.0e-10
  Linear System Max Iterations = 1000

! non linear iterations
! system self adjoint if Newton is used for the last iterations
  Nonlinear System Max Iterations = Integer 100
  Nonlinear System Convergence Tolerance  = Real 1.0e-7
  Nonlinear System Newton After Iterations = Integer 10
  Nonlinear System Newton After Tolerance = Real 1.0e-04
  Nonlinear System Relaxation Factor = Real 1.0
  Nonlinear System Reset Newton = Logical True

  Steady State Convergence Tolerance = Real 1.0e-12

! Create variables required for the optimisation
  Exported Variable 1 = -global CostValue 
  Exported Variable 2 = -nooutput "Velocityb"
  Exported Variable 2 DOFs = 4
End

!!!!!!!!!!!!!!!!!!!!!
!! Cost Function
!!  body 2 (top)
!!!!!!!!!!!!!!!!!!!!!
Solver 3
  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 "Flow Solution"
   Observed Variable dimension = Integer 2

 ! ASCII File with data: x,y,u,v
   Observation File Name = File "$OBSERVATION_FILE$"


 !! Exported Variables
 Exported Variable 1 = Zs
end

!!!!!!!!!!!!!!!!!!!!!!!!
!!  Adjoint 
!!  body 1 (bulk)
!!!!!!!!!!!!!!!!!!!!!!!!
Solver 4
  Equation = "Adjoint"
  Variable = -nooutput Adjoint
  Variable Dofs = 4

  procedure = "ElmerIceSolvers" "Adjoint_LinearSolver"

!Name of the flow solution solver
  Direct Solver Equation Name = string "Navier-Stokes"

! linear system
  Linear System Solver = Iterative
  Linear System Iterative Method = GCR
  Linear System Preconditioning= ILU0
  Linear System Convergence Tolerance= 1.0e-10
  Linear System Max Iterations = 1000

End

!!!!!!!!!!!!!!!!!!!!!!!!
!!  Derivative / beta
!!  body 3 (bottom)
!!!!!!!!!!!!!!!!!!!!!!!!
Solver 5
 Equation = "DJDBeta"
    procedure = "ElmerIceSolvers" "AdjointStokes_GradientBetaSolver"

    Flow Solution Name = String "Flow Solution"
    Adjoint Solution Name = String "Adjoint"
    Gradient Variable Name = String "DJDalpha"

  !! Exported Variables
    Exported Variable 1 = alpha
    Exported Variable 2 = DJDalpha
    Exported Variable 3 = BetaS
    Exported Variable 4 = Zb
End

!!!!!!!!!!!!!!!!!!!!!!!!
!!  Regularisation
!!  body 3 (bottom)
!!!!!!!!!!!!!!!!!!!!!!!!
Solver 6
  Equation = "DJDBeta_Reg"
    procedure = "ElmerIceSolvers" "Adjoint_CostRegSolver"

    Cost Filename=File "CostReg_$name$.dat"
    Optimized Variable Name= String "alpha"
    Gradient Variable Name= String "DJDalpha"
    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

!!!!!!!!!!!!!!!!!!!!!!!!
!!  Optimisation
!!  body 3 (bottom)
!!!!!!!!!!!!!!!!!!!!!!!!
Solver 7
  Equation = "Optimize_m1qn3"
  procedure = "ElmerIceSolvers" "Optimize_m1qn3Parallel"

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

  !!
  Mesh Independent = Logical FALSE

 ! M1QN3 Parameters
  M1QN3 dxmin = Real 1.0e-10
  M1QN3 epsg = Real  1.e-6
  M1QN3 niter = Integer $niter
  M1QN3 nsim = Integer $niter
  M1QN3 impres = Integer 5
  M1QN3 DIS Mode = Logical True
  M1QN3 df1 = Real 0.5
  M1QN3 normtype = String "dfn"
  M1QN3 OutputFile = File  "M1QN3_$name$.out"
  M1QN3 ndz = Integer 20

end

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!! Equations
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! bulk
Equation 1
  Active Solvers(3) = 1 2 4
End
! Top
Equation 2
  Active Solvers(1) = 3
End
! bottom
Equation 3
  Active Solvers(3) = 5 6 7
End

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!! Boundary Conditions
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Boundary Condition 1
  Name = "Side Walls"
  Target Boundaries(2) = 1 3
  
  Velocity 1 = Real 0.0
  Velocity 2 = Real 0.0
End

Boundary Condition 2
  Name = "Inflow"
  Target Boundaries = 4 

  Velocity 1 = Variable Coordinate 2
      REAL procedure "MacAyeal_USFs" "Inflow"
  Velocity 2 = Real 0.0

End

Boundary Condition 3
  Name = "OutFlow"
  Target Boundaries = 2

  Velocity 1 = Variable Coordinate 2
      REAL procedure "MacAyeal_USFs" "Outflow"
  Velocity 2 = Real 0.0
End

Boundary Condition 4
  Name = "bottom"
  Body Id = 3

  Normal-tangential Velocity = True
  Velocity 1 = Real 0.0e0

  Slip Coefficient 2 = Variable alpha
    REAL procedure "ElmerIceUSF" "TenPowerA"

  Slip Coefficient 3 = Variable alpha
    REAL procedure "ElmerIceUSF" "TenPowerA"

  Slip Coefficient derivative = Variable alpha
    REAL procedure "ElmerIceUSF" "TenPowerA_d"
End

Boundary Condition 5
  Name = "top"
  Body Id = 2
End