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@INPROCEEDINGS{Blommaert:202242,
      author       = {Blommaert, M. and Dekeyser, W. and Baelmans, M. and Gauger,
                      N. R. and Reiter, D.},
      title        = {{A} {P}ractical and in {P}arts {A}djoint {B}ased {G}radient
                      {C}omputation {M}ethodology for {E}fficient {O}ptimal
                      {M}agnetic {D}ivertor {D}esign in {N}uclear {F}usion
                      {R}eactors},
      reportid     = {FZJ-2015-04531},
      year         = {2015},
      abstract     = {Divertor particle and power exhaust system design is still
                      a key issue to be resolved to evolve from experimental
                      fusion reactors to commercial power plants. In particular
                      the excessive heat load to the divertor geometry structure
                      needs to be tackled. The divertor design process is assisted
                      by computationally extremely demanding codes simulating the
                      complex physics of the plasma edge. In order to reduce
                      design costs, advanced adjoint based automated design
                      methods from aerodynamics have recently been adapted for use
                      in divertor shape design. A similar methodology is sought to
                      enable these adjoint based methods for magnetic
                      configuration design. However, adjoint sensitivities of the
                      plasma edge grid generator are difficult to obtain, as those
                      grids are aligned with the magnetic field to overcome
                      numerical noise arising from the strongly anisotropic plasma
                      flow. First of all, this results in computational grid
                      boundaries that change with varying magnetic fields. A
                      second difficulty is the necessity to use a curvilinear
                      coordinate system attached to the magnetic field that is
                      implied by the grid generator.A Practical and in Parts
                      Adjoint Based Gradient Computation Methodology for Efficient
                      Optimal Magnetic Divertor Design in Nuclear Fusion
                      ReactorsIn this paper, these difficulties are overcome by
                      using a combined finite differences/continuous adjoint
                      gradient computation. An adjoint plasma edge simulation is
                      used to overcome the high computational cost of the plasma
                      edge simulations during gradient calculations. At the same
                      time, the computationally less demanding yet more difficult
                      grid generator adjoint sensitivities are avoided by making
                      use of a finite difference approach to differentiate the
                      remaining terms within a Lagrangian multiplier approach.
                      Moreover, an extensive analytical derivation of the partial
                      derivatives of the plasma edge equations with respect to the
                      geometrical parameters is avoided by using the finite
                      difference approach through the forward plasma edge solver
                      as well. Specific attention is hereby needed for the
                      implementation of the boundary conditions.},
      month         = {Jun},
      date          = {2015-06-03},
      organization  = {2nd Frontiers of Computational
                       Physics, Zurich (Switzerland), 3 Jun
                       2015 - 5 Jun 2015},
      cin          = {IEK-4},
      cid          = {I:(DE-Juel1)IEK-4-20101013},
      pnm          = {174 - Plasma-Wall-Interaction (POF3-174) / HITEC -
                      Helmholtz Interdisciplinary Doctoral Training in Energy and
                      Climate Research (HITEC) (HITEC-20170406)},
      pid          = {G:(DE-HGF)POF3-174 / G:(DE-Juel1)HITEC-20170406},
      typ          = {PUB:(DE-HGF)1},
      url          = {https://juser.fz-juelich.de/record/202242},
}