Valid_CostRegSolver5.sif

!################################################
!# Validation test case for Adjoint_CostRegSolver
!#  Test regularisation from a prior 
!#   running optimisation Var should converge to prior 
!################################################
! PARAMETERS:
$name="CostReg5"
$niter = 20
!###############################################
Header
  Mesh DB "." "mesh2D"
End
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Simulation
  Coordinate System  = Cartesian 2D 
  Simulation Type = Steady State

  Steady State Max Iterations = $niter
  Steady State Min Iterations = $niter
  
  Post File = "case_$name$.vtu"
  Output intervals = 1

  max output level = 4
End
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Body 1
  Equation = 1
  Body Force = 1
  Initial Condition = 1
End
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Initial Condition 1
 Var = Variable Coordinate 1, Coordinate 2
  Real  MATC "sqrt(2.0)*tx(0)^2+sqrt(2)*tx(1)*tx(1)/2"
 ! Target value for the variable
 Ap = Variable Coordinate 1, Coordinate 2
    REAL MATC "exp( -( (tx(0)-0.5)^2 + (tx(1)-0.5)^2 ) )" 
End
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Body Force 1
 ! kw related to prior value and std.
  CostReg Nodal Prior =  Equals Ap
  CostReg Nodal std = Real 0.5
End
!!!!!!!!   !!!!!!!!!!!!!!!!!!!!!!!!!!!!
Solver 1
 Exec Solver  = never
 Equation = String "UpdateExport"
 procedure = "ElmerIceSolvers" "Adjoint_CostRegSolver"

 Exported Variable 1 = -global "CostValue"  
 Exported Variable 2 = Var
 Exported Variable 3 = DJDp
 Exported Variable 4 = Ap
End
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Solver 2
  Equation = String "CostReg"
  procedure = "ElmerIceSolvers" "Adjoint_CostRegSolver"

  !# True if cost function and gradient must be initialised to 0 in this solver
  Reset Cost Value = Logical True

  Cost Filename = File "CostFile_$name$.dat"

  Lambda=Real 1.0

  Cost Variable Name = String "CostValue" 

  Gradient Variable Name = String "DJDp"

  Optimized Variable Name = String "Var"

  A priori Regularisation = Logical TRUE
end
!!!!! Validation
Solver 3
  Equation = "Optimize_m1qn3"
  procedure = "ElmerIceSolvers" "Optimize_m1qn3Parallel"

  Cost Variable Name = String "CostValue"
  Optimized Variable Name = String "Var"
  Gradient Variable Name = String "DJDp"
  gradient Norm File = String "GradientNormAdjoint.dat"

  !Note: it may be beneficial to set this to True, which scales
  !the gradient by 1/boundary_weights. With this set to false,
  !larger elements produce larger gradients.
  Mesh Independent = Logical False

! M1QN3 Parameters
  M1QN3 dxmin = Real 1.0e-10
  M1QN3 epsg = Real  1.e-12
  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
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Equation 1
  Active Solvers (3)= 1 2 3
End