Import the content of the dune-tnnmg-examples modules

It is preferable to not have this in a separate module: The code gets forgotten and slowly rots...

Import the content of the dune-tnnmg-examples modules
23a38ca9 · oliver.sander_at_tu-dresden.de · d642d297 · 23a38ca9 · 23a38ca9 · 23a38ca9
Commit 23a38ca9 authored Sep 4, 2020 by oliver.sander_at_tu-dresden.de
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -13,5 +13,6 @@ dune_project()
 add_subdirectory("doc")
 add_subdirectory("dune")
+add_subdirectory("examples")
 finalize_dune_project(GENERATE_CONFIG_H_CMAKE)
--- a/doc/CMakeLists.txt
+++ b/doc/CMakeLists.txt
 add_subdirectory(doxygen)
+add_subdirectory(manual)
--- a/doc/manual/.gitignore
+++ b/doc/manual/.gitignore
+*.atfi
+*.aux
+*.bbl
+*.blg
+*.log
+*.out
+dune-tnnmg-manual.pdf
--- a/doc/manual/CMakeLists.txt
+++ b/doc/manual/CMakeLists.txt
+dune_add_latex_document(
+  SOURCE dune-tnnmg-manual.tex
+  FATHER_TARGET doc
+  INSTALL ${CMAKE_INSTALL_DOCDIR})
--- a/doc/manual/dune-tnnmg-manual.bib
+++ b/doc/manual/dune-tnnmg-manual.bib
+@article{bastian_et_al:dune1:2008,
+    author      = {Bastian, P. and Blatt, M. and Dedner, A. and Engwer, C. and Kl\"ofkorn, R. and Ohlberger, M. and Sander, O.},
+    title       = {A Generic Interface for Adaptive and Parallel Scientific Computing. {P}art {I}: Abstract Framework},
+    journal     = {Computing},
+    year        = {2008},
+    volume      = {82},
+    number      = {2--3},
+    pages       = {103--119}
+}
+@article{bastian_et_al:dune2:2008,
+    author      = {Bastian, P. and Blatt, M. and Dedner, A. and Engwer, C. and Kl\"ofkorn, R. and Kornhuber, R. and Ohlberger, M. and Sander, O.},
+    title       = {A Generic Interface for Adaptive and Parallel Scientific Computing. {P}art {II}: Implementation and Tests in {DUNE}},
+    journal     = {Computing},
+    year        = {2008},
+    volume      = {82},
+    number      = {2--3},
+    pages       = {121--138}
+}
+@InProceedings{blatt_bastian:06,
+author = {Markus Blatt and Peter Bastian},
+title = {The Iterative Solver Template Library},
+booktitle = {Applied Parallel Computing. State of the Art in Scientific Computing},
+series = {Lecture Notes in Scientific Computing},
+volume = {4699},
+publisher = {Springer Verlag},
+pages = {666--675},
+year = {2007}
+}
+@www{dune-web,
+  key = {{\sc DUNE}},
+  title =     {{Distributed and Unified Numerics Environment}},
+  url = {http://dune-project.org/}
+}
+@www{dune-extensions,
+  key = {External {\sc DUNE} Modules},
+  howpublished = {\url{www.dune-project.org/downloadext.html}}
+}
+@www{dune_solvers,
+    title = {The dune-solvers module},
+    howpublished = {\url{https://git.imp.fu-berlin.de/agnumpde/dune-solvers}}
+}
+@www{dune_pdelab,
+    title = {The dune-pdelab module},
+    howpublished = {\url{https://www.dune-project.org/modules/dune-pdelab}}
+}
+@inproceedings{graeser_sack_sander:tnnmg:2009,
+    author      = {Gr\"aser, C. and Sack, U. and Sander, O.},
+    title       = {Truncated Nonsmooth {N}ewton Multigrid Methods for Convex Minimization Problems},
+    booktitle   = {Domain Decomposition Methods in Science and Engineering XVIII},
+    editor      = {Bercovier, M. and Gander, M. and Kornhuber, R. and Widlund, O.},
+    series      = {LNCSE},
+    publisher   = {Springer},
+    year        = {2009},
+    pages       = {129--136}
+}
+@article{graeser_kornhuber:multigrid_obstacle:2009,
+    author      = {Gr\"aser, C. and Kornhuber, R.},
+    title       = {Multigrid Methods for Obstacle Problems},
+    year        = {2009},
+    journal     = {J. Comp. Math.},
+    volume      = {27},
+    number      = {1},
+    pages       = {1-44}
+}
+@Article{graeser_kornhuber_sack:ac_anisotropic:2009,
+    author = {C. Gr\"aser and R. Kornhuber and U. Sack},
+    title = {Adaptive Multigrid Methods for Anisotropic {A}llen--{C}ahn Equations with Logarithmic Potential},
+    journal = {},
+    pages = {},
+    volume = {},
+    number = {},
+    year = {2009},
+    note = {in preparation}
+}
+@book{kornhuber:adapt_mmg_for_nonlin_var_prob:1997,
+    author = {Kornhuber, R.},
+    title = {Adaptive Monotone Multigrid Methods for Nonlinear Variational Problems},
+    year = {1997},
+    publisher = {Teubner},
+    address = {Stuttgart},
+    edition = {1.}
+}
+@Book{glowinski:1984,
+  author =    "R. Glowinski",
+  title =        "Numerical Methods for Nonlinear Variational Problems",
+  publisher =    {Springer Verlag},
+  year =         {1984},
+  series =    {Series in Computational Physics}
+}
+@book{ekeland_temam:1976,
+  author = {Ekeland, I. and Temam, R.},
+  title = {Convex Analysis},
+  year = {1976},
+  publisher = {North-Holland}
+}
+@Book{kikuchi_oden:1988,
+author = {N. Kikuchi and J. Oden},
+title = {Contact Problems in Elasticity},
+publisher = {SIAM},
+year = {1988}
+}
+@Book{Braess:1997,
+  author =    {Dietrich Braess},
+  title =        {Finite Elemente},
+  publisher =    {Springer},
+  year =         {1997},
+  edition =   {2nd},
+}
+@article{bastian_et_al:1997,
+AUTHOR =  "P. Bastian and K. Birken and K. Johannsen and S. Lang and
+               N. N{eu\ss } and  H. Rent{z--Reicher}t and C. Wieners",
+TITLE =   "{UG} -- a flexible Software toolbox for solving
+               partial differential equations",
+JOURNAL = CVS,
+YEAR =    "1997",
+VOLUME =  "1",
+PAGES =   "27--40"
+}
+@mastersthesis{Hardering2010_diplom,
+    author      = {Hardering, H.},
+    title       = {Analysis and Numerical Approximation of Capillary Surfaces},
+    type        = {Diplomarbeit},
+    school      = {Freie Universit\"at Berlin},
+    year        = {2010}
+}
+@phdthesis{Sander2008_phd,
+    author      = {Sander, O.},
+    title       = {Multidimensional Coupling in a Human Knee Model},
+    year        = {2008},
+    school      = {Freie Universit\"at Berlin}
+}
+@inproceedings{GraeserSackSander2009,
+    author      = {Gr{\"a}ser, C. and Sack, U. and Sander, O.},
+    title       = {Truncated Nonsmooth {N}ewton Multigrid Methods for Convex Minimization Problems},
+    booktitle   = {Domain Decomposition Methods in Science and Engineering XVIII},
+    editor      = {Bercovier, M. and Gander, M. and Kornhuber, R. and Widlund, O.},
+    series      = {LNCSE},
+    volume      = {70},
+    publisher   = {Springer},
+    year        = {2009},
+    pages       = {129--136}
+}
+@article{GraeserKornhuberSack2011,
+    author      = {Gr{\"a}ser, C. and Kornhuber, R. and Sack, U.},
+    title       = {Time discretizations of anisotropic {A}llen--{C}ahn equations},
+    year        = {2013},
+    journal     = {IMA J. Numer. Anal.},
+    volume      = {33},
+    number      = {4},
+    pages       = {1226--1244},
+    doi         = {10.1093/imanum/drs043}
+}
--- a/doc/manual/dune-tnnmg-manual.tex
+++ b/doc/manual/dune-tnnmg-manual.tex
--- a/doc/manual/gfx/blocking-tree-elasticity.pdf
+++ b/doc/manual/gfx/blocking-tree-elasticity.pdf
--- a/doc/manual/gfx/blocking-tree-elasticity.svg
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--- a/doc/manual/gfx/poisson_result.png
+++ b/doc/manual/gfx/poisson_result.png
--- a/dune/tnnmg/functionals/CMakeLists.txt
+++ b/dune/tnnmg/functionals/CMakeLists.txt
@@ -13,5 +13,6 @@ install(FILES
    stronglyconvexfunctional.hh
    sumfunctional.hh
    sumfunctionalconstrainedlinearization.hh
+    trescafrictionfunctional.hh
    zerofunctional.hh
    DESTINATION ${CMAKE_INSTALL_INCLUDEDIR}/dune/tnnmg/functionals)
--- a/dune/tnnmg/functionals/trescafrictionfunctional.hh
+++ b/dune/tnnmg/functionals/trescafrictionfunctional.hh
+// -*- tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 2 -*-
+// vi: set ts=8 sw=2 et sts=2:
+#ifndef DUNE_TNNMG_EXAMPLES_TRESCAFRICTIONFUNCTIONAL_HH
+#define DUNE_TNNMG_EXAMPLES_TRESCAFRICTIONFUNCTIONAL_HH
+#include <dune/common/bitsetvector.hh>
+#include <dune/common/typeutilities.hh>
+#include <dune/common/typetraits.hh>
+#include <dune/matrix-vector/algorithm.hh>
+#include <dune/solvers/common/interval.hh>
+#include <dune/solvers/common/resize.hh>
+#include <dune/tnnmg/functionals/nonsmoothconvexfunctional.hh>
+#ifndef NEW_TRESCA_FRICTION_FUNCTIONAL
+#include <dune/tnnmg/problem-classes/nonlinearity.hh>
+#endif
+#ifdef NEW_TRESCA_FRICTION_FUNCTIONAL
+template <class V, class R=double>
+class ShiftedTrescaFrictionFunctional;
+/** \brief Coordinate restriction of a Tresca friction functional
+ *
+ *  \tparam V global vector type
+ *  \tparam R Range type
+ *  \tparam I Index type used to access individual vector entries
+ */
+template <class V, class R, class I = std::size_t>
+class TrescaFrictionCoordinateRestriction
+{
+public:
+  using GlobalVector = V;
+  using GlobalIndex = I;
+  using Vector = std::decay_t<decltype(std::declval<GlobalVector>()[std::declval<GlobalIndex>()])>;
+  using Range = R;
+  TrescaFrictionCoordinateRestriction(const GlobalVector& coefficients,
+                                      const GlobalVector& origin,
+                                      GlobalIndex index)
+  : coefficients_(&coefficients),
+    origin_(origin),
+    index_(index)
+  {}
+  Range operator()(const Vector& v) const
+  {
+    DUNE_THROW(Dune::NotImplemented, "Evaluation of TrescaFrictionCoordinateRestriction not implemented");
+  }
+  GlobalIndex index() const
+  {
+    return index_;
+  }
+  const auto& coefficients() const
+  {
+    return (*coefficients_)[index_];
+  }
+  template<class Origin,
+    std::enable_if_t<! Dune::IsNumber<Origin>::value, int> = 0>
+  friend ShiftedTrescaFrictionFunctional<Vector, Range>
+    shift(const TrescaFrictionCoordinateRestriction& f, const Origin& origin)
+  {
+    return ShiftedTrescaFrictionFunctional<Vector, Range>(f.coefficients(),
+                                                          f.origin_[f.index_],   // origin of the functional before this shift
+                                                          origin);   // new additional shift, with reference semantics
+  }
+protected:
+  const GlobalVector* coefficients_;
+  const GlobalVector origin_;
+  const GlobalIndex index_;
+};
+/** \brief Coordinate restriction of a Tresca friction functional
+ *
+ *  \tparam blocksize The number of scalar entries of one vector block
+ *  \tparam R Range type
+ *  \tparam I Index type used to access individual vector entries
+ */
+template <int blocksize, class R, class I>
+class TrescaFrictionCoordinateRestriction<Dune::FieldVector<double,blocksize>, R, I>
+{
+  /** \todo Use the implementation in TrescaFrictionFunctional instead */
+  template <int dim>
+  static Dune::FieldVector<double,dim-1> tangentialPart(const Dune::FieldVector<double,dim>& v)
+  {
+    Dune::FieldVector<double,dim-1> result;
+    std::copy(v.begin()+1,v.end(),result.begin());
+    return result;
+  }
+public:
+  using GlobalVector = Dune::FieldVector<double,blocksize>  ;
+  using GlobalIndex = I;
+  using Vector = std::decay_t<decltype(std::declval<GlobalVector>()[std::declval<GlobalIndex>()])>;
+  using Range = R;
+  TrescaFrictionCoordinateRestriction(const GlobalVector& coefficients,
+                                      const GlobalVector& origin,
+                                      GlobalIndex index)
+  : coefficients_(&coefficients),
+    origin_(origin),
+    index_(index)
+  {}
+  Range operator()(const Vector& v) const
+  {
+    // BUG: This code here omits all contributions from other than the local blocks
+    // AFAICT that's okay, because this method is not used by the actual solver.
+    auto tmp = origin_;
+    tmp[index_] += v;
+    assert(coefficients_->size()==1);
+    return (*coefficients_)[0] * tangentialPart(tmp).two_norm();
+  }
+  GlobalIndex index() const
+  {
+    return index_;
+  }
+  const auto& coefficients() const
+  {
+    return (*coefficients_)[index_];
+  }
+  Dune::Solvers::Interval<double> domain() const
+  {
+    // Our domain is the entire space
+    return Dune::Solvers::Interval<double>{-std::numeric_limits<double>::infinity(),
+                                            std::numeric_limits<double>::infinity()};
+  }
+  Dune::Solvers::Interval<double> subDifferential(double z) const
+  {
+    constexpr double tolerance = 1e-15;
+    Dune::Solvers::Interval<double> dJ = 0.0;
+    if (index_!=0)
+    {
+      // Compute current tangential displacement
+      auto displacement = origin_;
+      displacement[index_] += z;
+      double tangentialNorm = tangentialPart(displacement).two_norm();
+      if (tangentialNorm < tolerance)
+      {
+        dJ[0] -= (*coefficients_)[0];
+        dJ[1] += (*coefficients_)[0];
+      }
+      else
+        dJ += (*coefficients_)[0] * displacement[index_] / tangentialNorm;
+    }
+    return dJ;
+  }
+protected:
+  const GlobalVector* coefficients_;
+  const GlobalVector origin_;
+  const GlobalIndex index_;
+};
+/** \brief Shifted Tresca friction functional
+ *
+ *  \tparam V global vector type
+ *  \tparam R Range type
+ */
+template <class V, class R>
+class ShiftedTrescaFrictionFunctional
+{
+public:
+  using Vector = V;
+  using Range = R;
+  ShiftedTrescaFrictionFunctional(const Vector& coefficients,
+                                  const Vector& origin,
+                                  const Vector& offset)
+  : coefficients_(&coefficients),
+    origin_(origin),
+    offset_(&offset)
+  {}
+  Range operator()(const Vector& v) const
+  {
+    DUNE_THROW(Dune::NotImplemented, "Evaluation of ShiftedTrescaFrictionFunctional not implemented");
+  }
+  void updateOrigin()
+  {
+    // Does not do anything, because no information is precomputed
+  }
+  void updateOrigin(std::size_t i)
+  {
+    // Does not do anything, because no information is precomputed
+  }
+  template<class Index>
+  friend TrescaFrictionCoordinateRestriction<Vector, Range, Index>
+    coordinateRestriction(const ShiftedTrescaFrictionFunctional& f, const Index& i)
+  {
+    auto tmp = f.origin_;
+    tmp += *f.offset_;
+    return TrescaFrictionCoordinateRestriction<Vector, Range, Index>(*f.coefficients_, tmp, i);
+  }
+protected:
+  const Vector* coefficients_;
+  const Vector origin_;
+  const Vector* offset_;
+};
+/** \brief Directional restriction of the Tresca friction functional
+ *
+ *  \tparam V Global vector type
+ *  \tparam R Range type
+ */
+template <class V, class R=double>
+class TrescaFrictionDirectionalRestriction
+{
+  /** \todo Use the implementation in TrescaFrictionFunctional instead */
+  template <int dim>
+  static Dune::FieldVector<double,dim-1> tangentialPart(const Dune::FieldVector<double,dim>& v)
+  {
+    Dune::FieldVector<double,dim-1> result;
+    std::copy(v.begin()+1,v.end(),result.begin());
+    return result;
+  }
+public:
+  using GlobalVector = V;
+  using Vector = typename GlobalVector::field_type;
+  using Range = R;
+  TrescaFrictionDirectionalRestriction(const GlobalVector& coefficients,
+                                       const GlobalVector& origin,
+                                       const GlobalVector& direction)
+  : coefficients_(&coefficients),
+    origin_(&origin),
+    direction_(&direction)
+  {}
+  Range operator()(const Vector& v) const
+  {
+    Range result = 0.0;
+    auto globalPos = *origin_;
+    globalPos.axpy(v, *direction_);
+    // Norm part (i.e., the actual friction)
+    for (size_t row=0; row<origin_->size(); ++row)
+    {
+      auto p = (*origin_)[row];
+      p.axpy(v, (*direction_)[row]);
+      result += (*coefficients_)[row] * tangentialPart(p).two_norm();
+    }
+    return result;
+  }
+  Dune::Solvers::Interval<double> domain() const
+  {
+    // Our domain is the entire space
+    return Dune::Solvers::Interval<double>{-std::numeric_limits<double>::infinity(),
+                                            std::numeric_limits<double>::infinity()};
+  }
+  Dune::Solvers::Interval<double> subDifferential(double z) const
+  {
+    // \todo It should be possible to set this globally
+    double tolerance = 1e-15;
+    Dune::Solvers::Interval<double> dJ = 0.0;
+    for(size_t row=0; row<origin_->size(); ++row)
+    {
+      auto p = (*origin_)[row];
+      p.axpy(z,(*direction_)[row]);
+      double tangentialNorm = tangentialPart(p).two_norm();
+      if (tangentialNorm >= tolerance){
+        for (std::size_t j=1; j<(*origin_)[row].size(); j++) {
+          dJ[0] += (*coefficients_)[row][0] * (p[j]*(*direction_)[row][j]) / tangentialNorm;
+          dJ[1] += (*coefficients_)[row][0] * (p[j]*(*direction_)[row][j]) / tangentialNorm;
+        }
+      } else {
+        for (std::size_t j=1; j<(*origin_)[row].size(); j++) {
+          dJ[0] += (*coefficients_)[row][0] * (*direction_)[row][j];
+          dJ[1] -= (*coefficients_)[row][0] * (*direction_)[row][j];
+        }
+      }
+    }
+    return dJ;
+  }
+protected:
+  const GlobalVector* coefficients_;
+  const GlobalVector* origin_;
+  const GlobalVector* direction_;
+};
+/** \brief Functional of linear elasticity with one-sided contact and Tresca friction
+ *
+ *  \tparam V Vector type
+ *  \tparam R Range type
+ */
+template <class V, class R=double>
+class TrescaFrictionFunctional
+{
+  template <int dim>
+  static Dune::FieldVector<double,dim-1> tangentialPart(const Dune::FieldVector<double,dim>& v)
+  {
+    Dune::FieldVector<double,dim-1> result;
+    std::copy(v.begin()+1,v.end(),result.begin());
+    return result;
+  }
+public:
+  using Vector = V;
+  using Range = R;
+  TrescaFrictionFunctional(const Vector& coefficients)
+  : coefficients_(coefficients)
+  {}
+  Range operator()(const Vector& v) const
+  {
+    Range result = 0.0;
+    // Norm part (i.e., the actual friction)
+    for (size_t row=0; row<v.size(); ++row)
+      result += coefficients_[row][0] * tangentialPart(v[row]).two_norm();
+    return result;
+  }
+  const Vector& coefficients() const
+  {
+    return coefficients_;
+  }
+  friend auto directionalRestriction(const TrescaFrictionFunctional& f, const Vector& origin, const Vector& direction)
+  {
+    return TrescaFrictionDirectionalRestriction<Vector, Range>(f.coefficients_,
+                                                              origin, direction);
+  }
+  friend ShiftedTrescaFrictionFunctional<Vector, Range>
+    shift(const TrescaFrictionFunctional& f, const Vector& origin)
+  {
+    Vector zero;
+    Dune::Solvers::resizeInitialize(zero, origin, 0.0);
+    return ShiftedTrescaFrictionFunctional<Vector, Range>(f.coefficients_, std::move(zero), origin);
+  }
+protected:
+  const Vector coefficients_;
+};
+#else
+// { trescafunctional_header_begin }
+template <int dim>
+class TrescaFrictionFunctional
+  : public Dune::TNNMG::NonsmoothConvexFunctional<Dune::FieldVector<double,dim>, Dune::FieldMatrix<double,dim,dim> >
+// { trescafunctional_header_end }
+{
+public:
+  typedef Dune::FieldVector<double,dim>      LocalVectorType;
+  typedef Dune::FieldMatrix<double,dim,dim>  LocalMatrixType;
+private:
+  // { trescafunctional_tangentialpart_begin }
+  static Dune::FieldVector<double,dim-1> tangentialPart(const LocalVectorType& v)
+  {
+    Dune::FieldVector<double,dim-1> result;
+    std::copy(v.begin()+1,v.end(),result.begin());
+    return result;
+  }
+  // { trescafunctional_tangentialpart_end }
+public:
+  typedef Nonlinearity<LocalVectorType, LocalMatrixType> NonlinearityType;
+  typedef typename NonlinearityType::VectorType VectorType;
+  typedef typename NonlinearityType::MatrixType MatrixType;
+  typedef typename NonlinearityType::IndexSet IndexSet;
+  TrescaFrictionFunctional(const std::vector<double> coefficients,
+                          const Dune::BitSetVector<1>& frictionNodes,
+                          double tolerance = 1e-15) :
+    coefficients_(coefficients),
+    tolerance_(tolerance),
+    frictionNodes_(frictionNodes)
+    {}
+  // { trescafunctional_energy_begin }
+  double operator()(const VectorType& v) const
+  {
+    double result = 0.0;
+    for(size_t row=0; row<v.size(); ++row)
+      if (frictionNodes_[row][0])
+        result += coefficients_[row] * tangentialPart(v[row]).two_norm();
+    return result;
+  }
+  // { trescafunctional_energy_end }
+  /** \brief Add the gradient of the Tresca friction potential to a given vector
+   *
+   * Note: the gradient of |v| is v/|v|
+   */
+  // { trescafunctional_addgradient_begin }
+  void addGradient(const VectorType& v, VectorType& gradient) const
+  {
+    for(size_t row=0; row<v.size(); ++row)
+    {
+      if (not frictionNodes_[row][0])
+        continue;
+      double tangentialNorm = tangentialPart(v[row]).two_norm();
+      // Do nothing if we are at a nondifferentiable point
+      if (tangentialNorm < tolerance_)
+        continue;
+      for (int j=1; j<dim; j++)
+        gradient[row][j] += coefficients_[row] * v[row][j] / tangentialNorm;
+    }
+  }
+  // { trescafunctional_addgradient_end }
+  /** \brief Add the Hessian of the Tresca friction potential to a given matrix
+   *
+   * Note: Entry ij of the Hessian of |v| is - \frac{v_i v_j}{\norm{v}^3} + \frac{\delta_{ij}}{\norm{v}}
+   */
+  // { trescafunctional_addhessian_begin }
+  void addHessian(const VectorType& v, MatrixType& hessian) const
+  {
+    for(size_t row=0; row<v.size(); ++row)
+    {
+      if (not frictionNodes_[row][0])
+        continue;
+      double tangentialNorm = tangentialPart(v[row]).two_norm();
+      // Do nothing if we are at the nondifferentiable point
+        if (tangentialNorm < tolerance_)
+          continue;
+      for (int i=1; i<dim; i++)
+        for (int j=1; j<dim; j++)
+          hessian[row][row][i][j] += coefficients_[row] * (- v[row][i] * v[row][j] / (tangentialNorm*tangentialNorm*tangentialNorm) + (i==j) / tangentialNorm);
+    }
+  }
+  // { trescafunctional_addhessian_end }
+  void addHessianIndices(IndexSet& indices) const {}
+  /** \brief Compute the subdifferential of the nonlinearity restricted to the line u + t v.
+   *
+   * \param[out] subdifferential the resulting subdifferential
+   * \param u base point
+   * \param v direction
+   */
+  // { trescafunctional_directional_subdiff_begin }
+  virtual void directionalSubDiff(const VectorType& u, const VectorType& v, Dune::Solvers::Interval<double>& subdifferential)
+  {
+    subdifferential[0] = 0.0;
+    subdifferential[1] = 0.0;
+    for(size_t row=0; row<u.size(); ++row)
+    {
+      if (not frictionNodes_[row][0])
+        continue;
+      double tangentialNorm = tangentialPart(u[row]).two_norm();
+      if (tangentialNorm >= tolerance_){
+        for (int j=1; j<dim; j++) {
+          subdifferential[0] += coefficients_[row] * (u[row][j]*v[row][j]) / tangentialNorm;
+          subdifferential[1] += coefficients_[row] * (u[row][j]*v[row][j]) / tangentialNorm;
+        }
+      } else {
+        for (int j=1; j<dim; j++) {
+          subdifferential[0] -= coefficients_[row] * v[row][j];
+          subdifferential[1] += coefficients_[row] * v[row][j];
+        }
+      }
+    }
+  }
+  // { trescafunctional_directional_subdiff_end }
+  /** \brief Compute the subdifferential of the nonlinearity restricted to the
+   * line u_pos' +t e_(i,j) at t=0.
+   *
+   * Here e_(i,j) is the (i,j)-th Euclidean unit vector,
+   * and u_pos' is the internal position vector u_pos with the (i,j)-the entry replaced by x.
+   * If the nonlinearity decouples in the Euclidean directions this is simply the (i,j)-th
+   * component of the subdifferential.
+   *
+   * \param i global index
+   * \param j local index
+   * \param x value of the (i,j)-th entry of position to evaluate the nonlinearity at
+   * \param[out] D the subdifferential
+   */
+  // { trescafunctional_subdiff_begin }
+  virtual void subDiff(int i, double x, Dune::Solvers::Interval<double>& D, int j) const
+  {
+    D[0] = 0.0;
+    D[1] = 0.0;
+    if (not frictionNodes_[i][0])
+      return;
+    if (j!=0)
+    {
+      // Compute current tangential displacement
+      LocalVectorType displacement = u_[i];
+      displacement[j] = x;
+      double tangentialNorm = tangentialPart(displacement).two_norm();
+      if (tangentialNorm < tolerance_)
+      {
+        D[0] = - coefficients_[i];
+        D[1] =   coefficients_[i];
+      } else
+        D[0] = D[1] = coefficients_[i] * displacement[j] / tangentialNorm;
+    }
+  }
+  // { trescafunctional_subdiff_end }
+  /** \brief Return the regularity of the nonlinearity restricted to the
+   * line u_pos' +t e_(i,j) at t=0.
+   *
+   * Here e_(i,j) is the (i,j)-th Euclidean unit vector,
+   * and u_pos' is the internal position vector u_pos with the (i,j)-the entry replaced by x.
+   * Usually this will be the third derivative or a local Lipschitz constant of the second
+   * derivative. Note that if the subdifferential is set-valued at this position, this
+   * value will normally be infinity.
+   *
+   * \param i global index
+   * \param j local index
+   * \param x value of the (i,j)-th entry of position to evaluate the nonlinearity at
+   * \returns a value measuring the regularity
+   */
+  // { trescafunctional_regularity_begin }
+  virtual double regularity(int i, double x, int j) const
+  {
+    if (not frictionNodes_[i][0])
+      return 0.0;
+    // Compute current tangential displacement
+    LocalVectorType displacement = u_[i];
+    displacement[j] = x;
+    double tangentialNorm = tangentialPart(displacement).two_norm();
+    if (tangentialNorm < tolerance_)
+      return std::numeric_limits<double>::max();
+    return 0.0;
+  }
+  // { trescafunctional_regularity_end }
+  // { trescafunctional_domain_begin }
+  void domain(int i, Dune::Solvers::Interval<double>& dom, int j) const
+  {
+    // Our domain is the entire space
+    dom[0] = -std::numeric_limits<double>::max();
+    dom[1] =  std::numeric_limits<double>::max();
+  }
+  // { trescafunctional_domain_end }
+  /** \brief Set the internal position vector u_pos to v.
+   *
+   * This method is empty, because it is only needed if the nonlinearity
+   * does not decouple in the Euclidean directions.
+   */
+  // { trescafunctional_state_begin }
+  virtual void setVector(const VectorType& v)
+  {
+    u_ = v;
+  };
+  /** \brief Update the (i,j)-th entry of the internal position vector u_pos to x.
+   *
+   *
+   * \param i global index
+   * \param j local index
+   * \param x new value of the entry (u_pos)_(i,j)
+   */
+  virtual void updateEntry(int i, double x, int j)
+  {
+    u_[i][j] = x;
+  };
+  // { trescafunctional_state_end }
+private:
+  /** \brief For each block, the norm is weighted with the corresponding coefficient from this array */
+  const std::vector<double> coefficients_;
+  /** \brief We consider the norm function to be nondifferentiable a circle of this radius around 0 */
+  const double tolerance_;
+  /** \brief Is 'true' for all degrees of freedom with friction */
+  Dune::BitSetVector<1> frictionNodes_;
+  /** \brief The current state */
+  VectorType u_;
+};
+#endif
+#endif
--- a/dune/tnnmg/iterationsteps/CMakeLists.txt
+++ b/dune/tnnmg/iterationsteps/CMakeLists.txt
@@ -8,4 +8,5 @@ install(FILES
    preconfiguredtnnmgstep.hh
    tnnmgacceleration.hh
    tnnmgstep.hh
+    trescafrictiontnnmgstepimp.hh
    DESTINATION ${CMAKE_INSTALL_INCLUDEDIR}/dune/tnnmg/iterationsteps)