src/one-body-problem-data/midpoint.hh

+#ifndef SRC_MIDPOINT_HH
+#define SRC_MIDPOINT_HH
+
+#include <dune/solvers/common/arithmetic.hh>
+
+template <class Vector> Vector midPoint(Vector const &x, Vector const &y) {
+  Vector ret(0);
+  Arithmetic::addProduct(ret, 0.5, x);
+  Arithmetic::addProduct(ret, 0.5, y);
+  return ret;
+}
+#endif

src/sand-wedge-data/mybody.hh → src/one-body-problem-data/mybody.hh

-#ifndef SRC_SAND_WEDGE_DATA_MYBODY_HH
-#define SRC_SAND_WEDGE_DATA_MYBODY_HH
+#ifndef SRC_ONE_BODY_PROBLEM_DATA_MYBODY_HH
+#define SRC_ONE_BODY_PROBLEM_DATA_MYBODY_HH
 
 #include <dune/common/fvector.hh>
 
@@ -8,8 +8,8 @@
 #include <dune/tectonic/body.hh>
 #include <dune/tectonic/gravity.hh>
 
-#include "twopiece.hh"
 #include "mygeometry.hh"
+#include "segmented-function.hh"
 
 template <int dimension> class MyBody : public Body<dimension> {
   using typename Body<dimension>::ScalarFunction;
@@ -47,9 +47,9 @@ template <int dimension> class MyBody : public Body<dimension> {
 private:
   double const poissonRatio_;
   double const youngModulus_;
-  TwoPieceFunction const shearViscosityField_;
-  TwoPieceFunction const bulkViscosityField_;
-  TwoPieceFunction const densityField_;
+  SegmentedFunction const shearViscosityField_;
+  SegmentedFunction const bulkViscosityField_;
+  SegmentedFunction const densityField_;
   Gravity<dimension> const gravityField_;
 };
 #endif

src/sand-wedge-data/mygeometry.cc → src/one-body-problem-data/mygeometry.cc

@@ -4,14 +4,13 @@
 
 #include <fstream>
 
-#include "mygeometry.hh"
+#ifdef HAVE_CAIROMM
+#include <cairomm/context.h>
+#include <cairomm/fontface.h>
+#include <cairomm/surface.h>
+#endif
 
-double MyGeometry::verticalProjection(LocalVector const &x) {
-  return zenith * x;
-}
-double MyGeometry::horizontalProjection(LocalVector const &x) {
-  return rotatedZenith * x;
-}
+#include "mygeometry.hh"
 
 void MyGeometry::write() {
   std::fstream writer("geometry", std::fstream::out);
@@ -48,19 +47,18 @@ void MyGeometry::render() {
                        ((colour & 0x00FF00) >> 8) / 255.0,
                        ((colour & 0x0000FF) >> 0) / 255.0);
   };
-  auto const moveTo = [&](LocalVector const &v) { cr->move_to(v[0], -v[1]); };
-  auto const lineTo = [&](LocalVector const &v) { cr->line_to(v[0], -v[1]); };
+  auto const moveTo = [&](LocalVector2D const &v) { cr->move_to(v[0], -v[1]); };
+  auto const lineTo = [&](LocalVector2D const &v) { cr->line_to(v[0], -v[1]); };
 
   cr->scale(widthScale, heightScale);
   cr->translate(0.1, 0.1);
-  cr->rotate(leftAngle);
   cr->set_line_width(0.0025);
 
   // triangle
   {
-    moveTo(A);
-    lineTo(B);
-    lineTo(C);
+    moveTo(reference::A);
+    lineTo(reference::B);
+    lineTo(reference::C);
     cr->close_path();
     cr->stroke();
   }
@@ -70,10 +68,10 @@ void MyGeometry::render() {
     cr->save();
     std::vector<double> dashPattern = { 0.005 };
     cr->set_dash(dashPattern, 0);
-    moveTo(Z);
-    lineTo(Y);
-    moveTo(U);
-    lineTo(X);
+    moveTo(reference::Z);
+    lineTo(reference::Y);
+    moveTo(reference::U);
+    lineTo(reference::X);
     cr->stroke();
     cr->restore();
   }
@@ -82,9 +80,9 @@ void MyGeometry::render() {
   {
     cr->save();
     setRGBColor(0x0097E0);
-    moveTo(B);
-    lineTo(K);
-    lineTo(M);
+    moveTo(reference::B);
+    lineTo(reference::K);
+    lineTo(reference::M);
     cr->fill();
     cr->restore();
   }
@@ -94,41 +92,40 @@ void MyGeometry::render() {
     cr->save();
     setRGBColor(0x7AD3FF);
     cr->set_line_width(0.005);
-    moveTo(X);
-    lineTo(Y);
+    moveTo(reference::X);
+    lineTo(reference::Y);
     cr->stroke();
     cr->restore();
   }
 
   // mark points
   {
-    auto const drawCircle = [&](LocalVector const &v) {
+    auto const drawCircle = [&](LocalVector2D const &v) {
       cr->arc(v[0], -v[1], 0.0075, -M_PI, M_PI); // x,y,radius,angle1,angle2
       cr->fill();
     };
 
     cr->save();
     setRGBColor(0x002F47);
-    drawCircle(A);
-    drawCircle(B);
-    drawCircle(C);
-    drawCircle(Y);
-    drawCircle(X);
-    drawCircle(Z);
-    drawCircle(U);
-    drawCircle(K);
-    drawCircle(M);
-    drawCircle(G);
-    drawCircle(H);
-    drawCircle(J);
-    drawCircle(I);
+    drawCircle(reference::A);
+    drawCircle(reference::B);
+    drawCircle(reference::C);
+    drawCircle(reference::Y);
+    drawCircle(reference::X);
+    drawCircle(reference::Z);
+    drawCircle(reference::U);
+    drawCircle(reference::K);
+    drawCircle(reference::M);
+    drawCircle(reference::G);
+    drawCircle(reference::H);
+    drawCircle(reference::J);
+    drawCircle(reference::I);
     cr->restore();
   }
 
   // labels
   {
-    auto const label = [&](LocalVector const &v,
-                           std::string l) { // TODO: implicit?
+    auto const label = [&](LocalVector2D const &v, std::string l) {
       moveTo(v);
       cr->rel_move_to(0.005, -0.02);
       cr->show_text(l);
@@ -140,19 +137,19 @@ void MyGeometry::render() {
     cr->set_font_face(font);
     cr->set_font_size(0.03);
 
-    label(A, "A");
-    label(B, "B");
-    label(C, "C");
-    label(K, "K");
-    label(M, "M");
-    label(U, "U");
-    label(X, "X");
-    label(Y, "Y");
-    label(Z, "Z");
-    label(G, "G");
-    label(H, "H");
-    label(J, "J");
-    label(I, "I");
+    label(reference::A, "A");
+    label(reference::B, "B");
+    label(reference::C, "C");
+    label(reference::K, "K");
+    label(reference::M, "M");
+    label(reference::U, "U");
+    label(reference::X, "X");
+    label(reference::Y, "Y");
+    label(reference::Z, "Z");
+    label(reference::G, "G");
+    label(reference::H, "H");
+    label(reference::J, "J");
+    label(reference::I, "I");
     cr->restore();
   }
 

src/one-body-problem-data/mygeometry.hh

+#ifndef SRC_MYGEOMETRY_HH
+#define SRC_MYGEOMETRY_HH
+
+#include <dune/common/fvector.hh>
+
+#include "midpoint.hh"
+
+namespace MyGeometry {
+namespace {
+  using LocalVector2D = Dune::FieldVector<double, 2>;
+  using LocalMatrix2D = Dune::FieldMatrix<double, 2, 2>;
+
+  using LocalVector = Dune::FieldVector<double, MY_DIM>;
+}
+
+namespace reference {
+  double const s = 1.0; // scaling factor
+
+  double const rightLeg = 0.27 * s;
+  double const leftLeg = 1.00 * s;
+  double const leftAngle = atan(rightLeg / leftLeg);
+  double const viscoHeight = 0.06 * s; // Height of the viscous bottom layer
+  double const weakLen = 0.20 * s;     // Length of the weak zone
+
+  double const zDistance = 0.35;
+
+  LocalVector2D const A = {0, 0};
+  LocalVector2D const B = {leftLeg, -rightLeg};
+  LocalVector2D const C = {leftLeg, 0};
+
+  LocalVector2D const Z = {zDistance * s, 0};
+  LocalVector2D const Y = {zDistance * s, -zDistance *s / leftLeg *rightLeg};
+  LocalVector2D const X = {Y[0] - weakLen * std::cos(leftAngle),
+                           Y[1] + weakLen *std::sin(leftAngle)};
+
+  LocalVector2D const U = {X[0], 0};
+
+  LocalVector2D const K = {B[0] - leftLeg * viscoHeight / rightLeg,
+                           B[1] + viscoHeight};
+  LocalVector2D const M = {B[0], B[1] + viscoHeight};
+
+  LocalVector2D const G = midPoint(A, X);
+  LocalVector2D const H = midPoint(X, Y);
+  LocalVector2D const J = midPoint(Y, B);
+
+  LocalVector2D const I = {Y[0] + G[0], Y[1] + G[1]};
+
+  LocalVector2D const zenith = {0, 1};
+
+  LocalMatrix2D const rotation = {{std::cos(leftAngle), -std::sin(leftAngle)},
+                                  {std::sin(leftAngle), std::cos(leftAngle)}};
+}
+
+namespace {
+  LocalVector rotate(LocalVector2D const &x) {
+    LocalVector2D ret2D;
+    reference::rotation.mv(x, ret2D);
+    LocalVector ret(0);
+    ret[0] = ret2D[0];
+    ret[1] = ret2D[1];
+    return ret;
+  }
+}
+
+double const lengthScale = reference::s;
+
+double const depth = 0.60 * lengthScale;
+
+LocalVector const A = rotate(reference::A);
+LocalVector const B = rotate(reference::B);
+LocalVector const C = rotate(reference::C);
+LocalVector const G = rotate(reference::G);
+LocalVector const H = rotate(reference::H);
+LocalVector const I = rotate(reference::I);
+LocalVector const J = rotate(reference::J);
+LocalVector const K = rotate(reference::K);
+LocalVector const M = rotate(reference::M);
+LocalVector const U = rotate(reference::U);
+LocalVector const X = rotate(reference::X);
+LocalVector const Y = rotate(reference::Y);
+LocalVector const Z = rotate(reference::Z);
+
+LocalVector const zenith = rotate(reference::zenith);
+
+void write();
+
+void render();
+}
+#endif

src/sand-wedge-data/myglobalfrictiondata.hh → src/one-body-problem-data/myglobalfrictiondata.hh

-#ifndef SRC_SAND_WEDGE_DATA_MYGLOBALFRICTIONDATA_HH
-#define SRC_SAND_WEDGE_DATA_MYGLOBALFRICTIONDATA_HH
+#ifndef SRC_ONE_BODY_PROBLEM_DATA_MYGLOBALFRICTIONDATA_HH
+#define SRC_ONE_BODY_PROBLEM_DATA_MYGLOBALFRICTIONDATA_HH
 
 #include <dune/common/function.hh>
-#include <dune/common/fvector.hh>
 
 #include <dune/tectonic/globalfrictiondata.hh>
 
-#include "mygeometry.hh"
 #include "patchfunction.hh"
 
-template <int dimension>
-class MyGlobalFrictionData : public GlobalFrictionData<dimension> {
+template <class LocalVector>
+class MyGlobalFrictionData : public GlobalFrictionData<LocalVector::dimension> {
 private:
-  using typename GlobalFrictionData<dimension>::VirtualFunction;
+  using typename GlobalFrictionData<LocalVector::dimension>::VirtualFunction;
 
 public:
-  MyGlobalFrictionData(Dune::ParameterTree const &parset)
+  MyGlobalFrictionData(Dune::ParameterTree const &parset,
+                       ConvexPolyhedron<LocalVector> const &segment)
       : C_(parset.get<double>("C")),
         L_(parset.get<double>("L")),
         V0_(parset.get<double>("V0")),
         a_(parset.get<double>("strengthening.a"),
-           parset.get<double>("weakening.a")),
+           parset.get<double>("weakening.a"), segment),
         b_(parset.get<double>("strengthening.b"),
-           parset.get<double>("weakening.b")),
+           parset.get<double>("weakening.b"), segment),
         mu0_(parset.get<double>("mu0")) {}
 
-  double virtual const &C() const override { return C_; }
-  double virtual const &L() const override { return L_; }
-  double virtual const &V0() const override { return V0_; }
-  VirtualFunction virtual const &a() const override { return a_; }
-  VirtualFunction virtual const &b() const override { return b_; }
-  double virtual const &mu0() const override { return mu0_; }
+  double const &C() const override { return C_; }
+  double const &L() const override { return L_; }
+  double const &V0() const override { return V0_; }
+  VirtualFunction const &a() const override { return a_; }
+  VirtualFunction const &b() const override { return b_; }
+  double const &mu0() const override { return mu0_; }
 
 private:
   double const C_;

src/one-body-problem-data/mygrid.cc

+#ifdef HAVE_CONFIG_H
+#include "config.h"
+#endif
+
+#include <dune/fufem/geometry/polyhedrondistance.hh>
+
+#include "mygrid.hh"
+#include "midpoint.hh"
+#include "../diameter.hh"
+
+#if MY_DIM == 3
+SimplexManager::SimplexManager(unsigned int shift) : shift_(shift) {}
+#endif
+
+// back-to-front, front-to-back, front-to-back
+void SimplexManager::addFromVerticesFBB(unsigned int U, unsigned int V,
+                                        unsigned int W) {
+#if MY_DIM == 3
+  unsigned int const U2 = U + shift_;
+  unsigned int const V2 = V + shift_;
+  unsigned int const W2 = W + shift_;
+
+  simplices_.push_back({ U, V, W, U2 });
+  simplices_.push_back({ V, V2, W2, U2 });
+  simplices_.push_back({ W, W2, U2, V });
+#else
+  simplices_.push_back({ U, V, W });
+#endif
+}
+
+// back-to-front, back-to-front, front-to-back
+void SimplexManager::addFromVerticesFFB(unsigned int U, unsigned int V,
+                                        unsigned int W) {
+#if MY_DIM == 3
+  unsigned int const U2 = U + shift_;
+  unsigned int const V2 = V + shift_;
+  unsigned int const W2 = W + shift_;
+
+  simplices_.push_back({ U, V, W, U2 });
+  simplices_.push_back({ V, V2, W, U2 });
+  simplices_.push_back({ V2, W, U2, W2 });
+#else
+  simplices_.push_back({ U, V, W });
+#endif
+}
+
+auto SimplexManager::getSimplices() -> SimplexList const & {
+  return simplices_;
+}
+
+template <class Grid> GridConstructor<Grid>::GridConstructor() {
+  auto const &A = MyGeometry::A;
+  auto const &B = MyGeometry::B;
+  auto const &C = MyGeometry::C;
+
+  unsigned int const vc = 3;
+
+#if MY_DIM == 3
+  Dune::FieldMatrix<double, 2 * vc, MY_DIM> vertices;
+#else
+  Dune::FieldMatrix<double, vc, MY_DIM> vertices;
+#endif
+  for (size_t i = 0; i < 2; ++i) {
+#if MY_DIM == 3
+    size_t numXYplanes = 2;
+#else
+    size_t numXYplanes = 1;
+#endif
+    size_t k = 0;
+    for (size_t j = 1; j <= numXYplanes; ++j) {
+      vertices[k++][i] = A[i];
+      vertices[k++][i] = B[i];
+      vertices[k++][i] = C[i];
+      assert(k == j * vc);
+    }
+  }
+
+#if MY_DIM == 3
+  for (size_t k = 0; k < vc; ++k) {
+    vertices[k][2] = -MyGeometry::depth / 2.0;
+    vertices[k + vc][2] = MyGeometry::depth / 2.0;
+  }
+#endif
+
+  for (size_t i = 0; i < vertices.N(); ++i)
+    gridFactory.insertVertex(vertices[i]);
+
+  Dune::GeometryType cell;
+#if MY_DIM == 3
+  cell.makeTetrahedron();
+#else
+  cell.makeTriangle();
+#endif
+
+#if MY_DIM == 3
+  SimplexManager sm(vc);
+#else
+  SimplexManager sm;
+#endif
+  sm.addFromVerticesFFB(1, 2, 0);
+  auto const &simplices = sm.getSimplices();
+
+  // sanity-check choices of simplices
+  for (size_t i = 0; i < simplices.size(); ++i) {
+    Dune::FieldMatrix<double, MY_DIM, MY_DIM> check;
+    for (size_t j = 0; j < MY_DIM; ++j)
+      check[j] = vertices[simplices[i][j + 1]] - vertices[simplices[i][j]];
+    assert(check.determinant() > 0);
+    gridFactory.insertElement(cell, simplices[i]);
+  }
+}
+
+template <class Grid> std::shared_ptr<Grid> GridConstructor<Grid>::getGrid() {
+  return std::shared_ptr<Grid>(gridFactory.createGrid());
+}
+
+template <class Grid>
+template <class GridView>
+MyFaces<GridView> GridConstructor<Grid>::constructFaces(
+    GridView const &gridView) {
+  return MyFaces<GridView>(gridView);
+}
+
+template <class GridView>
+template <class Vector>
+bool MyFaces<GridView>::xyCollinear(Vector const &a, Vector const &b,
+                                    Vector const &c) {
+  return isClose2((b[0] - a[0]) * (c[1] - a[1]), (b[1] - a[1]) * (c[0] - a[0]));
+}
+
+template <class GridView>
+template <class Vector>
+bool MyFaces<GridView>::xyBoxed(Vector const &v1, Vector const &v2,
+                                Vector const &x) {
+  auto const minmax0 = std::minmax(v1[0], v2[0]);
+  auto const minmax1 = std::minmax(v1[1], v2[1]);
+
+  if (minmax0.first - 1e-14 * MyGeometry::lengthScale > x[0] or
+      x[0] > minmax0.second + 1e-14 * MyGeometry::lengthScale)
+    return false;
+  if (minmax1.first - 1e-14 * MyGeometry::lengthScale > x[1] or
+      x[1] > minmax1.second + 1e-14 * MyGeometry::lengthScale)
+    return false;
+
+  return true;
+}
+
+template <class GridView>
+template <class Vector>
+bool MyFaces<GridView>::xyBetween(Vector const &v1, Vector const &v2,
+                                  Vector const &x) {
+  return xyCollinear(v1, v2, x) && xyBoxed(v1, v2, x);
+}
+
+template <class GridView>
+MyFaces<GridView>::MyFaces(GridView const &gridView)
+    :
+#if MY_DIM == 3
+      lower(gridView),
+      right(gridView),
+      upper(gridView),
+      front(gridView),
+      back(gridView)
+#else
+      lower(gridView),
+      right(gridView),
+      upper(gridView)
+#endif
+{
+  assert(isClose(MyGeometry::A[1], 0));
+  assert(isClose(MyGeometry::B[1], 0));
+  lower.insertFacesByProperty([&](typename GridView::Intersection const &in) {
+    return isClose(0, in.geometry().center()[1]);
+  });
+#if MY_DIM == 3
+  front.insertFacesByProperty([&](typename GridView::Intersection const &in) {
+    return isClose(MyGeometry::depth / 2.0, in.geometry().center()[2]);
+  });
+
+  back.insertFacesByProperty([&](typename GridView::Intersection const &in) {
+    return isClose(-MyGeometry::depth / 2.0, in.geometry().center()[2]);
+  });
+#endif
+
+  upper.insertFacesByProperty([&](typename GridView::Intersection const &in) {
+    return xyBetween(MyGeometry::A, MyGeometry::C, in.geometry().center());
+  });
+
+  right.insertFacesByProperty([&](typename GridView::Intersection const &in) {
+    return xyBetween(MyGeometry::B, MyGeometry::C, in.geometry().center());
+  });
+}
+
+double computeAdmissibleDiameter(double distance, double smallestDiameter) {
+  return (distance / 0.0125 / MyGeometry::lengthScale + 1.0) * smallestDiameter;
+}
+
+template <class Grid, class LocalVector>
+void refine(Grid &grid, ConvexPolyhedron<LocalVector> const &weakPatch,
+            double smallestDiameter) {
+  bool needRefine = true;
+  while (true) {
+    needRefine = false;
+    for (auto &&e : elements(grid.leafGridView())) {
+      auto const geometry = e.geometry();
+
+      auto const weakeningRegionDistance =
+          distance(weakPatch, geometry, 1e-6 * MyGeometry::lengthScale);
+      auto const admissibleDiameter =
+          computeAdmissibleDiameter(weakeningRegionDistance, smallestDiameter);
+
+      if (diameter(geometry) <= admissibleDiameter)
+        continue;
+
+      needRefine = true;
+      grid.mark(1, e);
+    }
+    if (!needRefine)
+      break;
+
+    grid.preAdapt();
+    grid.adapt();
+    grid.postAdapt();
+  }
+}
+
+#include "mygrid_tmpl.cc"

src/one-body-problem-data/mygrid.hh

+#ifndef SRC_ONE_BODY_PROBLEM_DATA_MYGRID_HH
+#define SRC_ONE_BODY_PROBLEM_DATA_MYGRID_HH
+
+#include <dune/common/fmatrix.hh>
+#include <dune/grid/common/gridfactory.hh>
+
+#include <dune/fufem/boundarypatch.hh>
+#include <dune/fufem/geometry/convexpolyhedron.hh>
+
+#include "mygeometry.hh"
+
+template <class GridView> struct MyFaces {
+  BoundaryPatch<GridView> lower;
+  BoundaryPatch<GridView> right;
+  BoundaryPatch<GridView> upper;
+
+#if MY_DIM == 3
+  BoundaryPatch<GridView> front;
+  BoundaryPatch<GridView> back;
+#endif
+
+  MyFaces(GridView const &gridView);
+
+private:
+  bool isClose(double a, double b) {
+    return std::abs(a - b) < 1e-14 * MyGeometry::lengthScale;
+  };
+
+  bool isClose2(double a, double b) {
+    return std::abs(a - b) <
+           1e-14 * MyGeometry::lengthScale * MyGeometry::lengthScale;
+  };
+
+  template <class Vector>
+  bool xyBoxed(Vector const &v1, Vector const &v2, Vector const &x);
+
+  template <class Vector>
+  bool xyCollinear(Vector const &a, Vector const &b, Vector const &c);
+
+  template <class Vector>
+  bool xyBetween(Vector const &v1, Vector const &v2, Vector const &x);
+};
+
+class SimplexManager {
+public:
+  using SimplexList = std::vector<std::vector<unsigned int>>;
+
+#if MY_DIM == 3
+  SimplexManager(unsigned int shift);
+#endif
+
+  void addFromVerticesFBB(unsigned int U, unsigned int V, unsigned int W);
+  void addFromVerticesFFB(unsigned int U, unsigned int V, unsigned int W);
+
+  SimplexList const &getSimplices();
+
+private:
+  SimplexList simplices_;
+
+#if MY_DIM == 3
+  unsigned int const shift_;
+#endif
+};
+
+template <class Grid> class GridConstructor {
+public:
+  GridConstructor();
+
+  std::shared_ptr<Grid> getGrid();
+
+  template <class GridView>
+  MyFaces<GridView> constructFaces(GridView const &gridView);
+
+private:
+  Dune::GridFactory<Grid> gridFactory;
+};
+
+double computeAdmissibleDiameter(double distance, double smallestDiameter);
+
+template <class Grid, class LocalVector>
+void refine(Grid &grid, ConvexPolyhedron<LocalVector> const &weakPatch,
+            double smallestDiameter);
+
+#endif

src/one-body-problem-data/mygrid_tmpl.cc

+#ifndef MY_DIM
+#error MY_DIM unset
+#endif
+
+#include "../explicitgrid.hh"
+#include "../explicitvectors.hh"
+
+template class GridConstructor<Grid>;
+
+template struct MyFaces<GridView>;
+
+template MyFaces<GridView> GridConstructor<Grid>::constructFaces(
+    GridView const &gridView);
+
+template void refine<Grid, LocalVector>(
+    Grid &grid, ConvexPolyhedron<LocalVector> const &weakPatch,
+    double smallestDiameter);

src/one-body-problem-data/patchfunction.hh

+#ifndef SRC_ONE_BODY_PROBLEM_DATA_PATCHFUNCTION_HH
+#define SRC_ONE_BODY_PROBLEM_DATA_PATCHFUNCTION_HH
+
+#include <dune/common/function.hh>
+#include <dune/common/fvector.hh>
+#include <dune/common/parametertree.hh>
+
+#include <dune/fufem/geometry/polyhedrondistance.hh>
+
+class PatchFunction
+    : public Dune::VirtualFunction<Dune::FieldVector<double, MY_DIM>,
+                                   Dune::FieldVector<double, 1>> {
+private:
+  using Polyhedron = ConvexPolyhedron<Dune::FieldVector<double, MY_DIM>>;
+
+  double const v1_;
+  double const v2_;
+  Polyhedron const &segment_;
+
+public:
+  PatchFunction(double v1, double v2, Polyhedron const &segment)
+      : v1_(v1), v2_(v2), segment_(segment) {}
+
+  void evaluate(Dune::FieldVector<double, MY_DIM> const &x,
+                Dune::FieldVector<double, 1> &y) const {
+    y = distance(x, segment_, 1e-6 * MyGeometry::lengthScale) <= 1e-5 ? v2_
+                                                                      : v1_;
+  }
+};
+
+#endif

src/sand-wedge-data/twopiece.hh → src/one-body-problem-data/segmented-function.hh

-#ifndef SRC_SAND_WEDGE_DATA_TWOPIECE_HH
-#define SRC_SAND_WEDGE_DATA_TWOPIECE_HH
+#ifndef SRC_ONE_BODY_PROBLEM_DATA_SEGMENTED_FUNCTION_HH
+#define SRC_ONE_BODY_PROBLEM_DATA_SEGMENTED_FUNCTION_HH
 
 #include <dune/common/function.hh>
 #include <dune/common/fvector.hh>
@@ -7,30 +7,26 @@
 
 #include "mygeometry.hh"
 
-class TwoPieceFunction
-    : public Dune::VirtualFunction<Dune::FieldVector<double, 2>,
+class SegmentedFunction
+    : public Dune::VirtualFunction<Dune::FieldVector<double, MY_DIM>,
                                    Dune::FieldVector<double, 1>> {
 private:
-  bool liesBelow(Dune::FieldVector<double, 2> const &x,
-                 Dune::FieldVector<double, 2> const &y,
-                 Dune::FieldVector<double, 2> const &z) const {
-    return (z[0] - x[0]) * (y[1] - x[1]) / (y[0] - x[0]) >= z[1] - x[1];
+  bool liesBelow(Dune::FieldVector<double, MY_DIM> const &x,
+                 Dune::FieldVector<double, MY_DIM> const &y,
+                 Dune::FieldVector<double, MY_DIM> const &z) const {
+    return x[1] + (z[0] - x[0]) * (y[1] - x[1]) / (y[0] - x[0]) >= z[1];
   };
-  bool insideRegion2(Dune::FieldVector<double, 2> const &z) const {
-    return liesBelow(_K, _M, z);
+  bool insideRegion2(Dune::FieldVector<double, MY_DIM> const &z) const {
+    return liesBelow(MyGeometry::K, MyGeometry::M, z);
   };
 
-  Dune::FieldVector<double, 2> const &_K;
-  Dune::FieldVector<double, 2> const &_M;
-
   double const _v1;
   double const _v2;
 
 public:
-  TwoPieceFunction(double v1, double v2)
-      : _K(MyGeometry::K), _M(MyGeometry::M), _v1(v1), _v2(v2) {}
+  SegmentedFunction(double v1, double v2) : _v1(v1), _v2(v2) {}
 
-  void evaluate(Dune::FieldVector<double, 2> const &x,
+  void evaluate(Dune::FieldVector<double, MY_DIM> const &x,
                 Dune::FieldVector<double, 1> &y) const {
     y = insideRegion2(x) ? _v2 : _v1;
   }

src/one-body-problem-data/weakpatch.hh

+#ifndef SRC_ONE_BODY_PROBLEM_DATA_WEAKPATCH_HH
+#define SRC_ONE_BODY_PROBLEM_DATA_WEAKPATCH_HH
+
+template <class LocalVector>
+ConvexPolyhedron<LocalVector> getWeakPatch(Dune::ParameterTree const &parset) {
+  ConvexPolyhedron<LocalVector> weakPatch;
+#if MY_DIM == 3
+  weakPatch.vertices.resize(4);
+  weakPatch.vertices[0] = weakPatch.vertices[2] = MyGeometry::X;
+  weakPatch.vertices[1] = weakPatch.vertices[3] = MyGeometry::Y;
+  for (size_t k = 0; k < 2; ++k) {
+    weakPatch.vertices[k][2] = -MyGeometry::depth / 2.0;
+    weakPatch.vertices[k + 2][2] = MyGeometry::depth / 2.0;
+  }
+  switch (parset.get<Config::PatchType>("patchType")) {
+    case Config::Rectangular:
+      break;
+    case Config::Trapezoidal:
+      weakPatch.vertices[1][0] += 0.05 * MyGeometry::lengthScale;
+      weakPatch.vertices[3][0] -= 0.05 * MyGeometry::lengthScale;
+      break;
+    default:
+      assert(false);
+  }
+#else
+  weakPatch.vertices.resize(2);
+  weakPatch.vertices[0] = MyGeometry::X;
+  weakPatch.vertices[1] = MyGeometry::Y;
+#endif
+  return weakPatch;
+};
+#endif

src/one-body-problem.cc

+#ifdef HAVE_CONFIG_H
+#include "config.h"
+#endif
+
+#ifdef HAVE_IPOPT
+#undef HAVE_IPOPT
+#endif
+
+#include <atomic>
+#include <cmath>
+#include <csignal>
+#include <exception>
+#include <fstream>
+#include <iostream>
+#include <iomanip>
+
+#include <dune/common/bitsetvector.hh>
+#include <dune/common/exceptions.hh>
+#include <dune/common/fmatrix.hh>
+#include <dune/common/function.hh>
+#include <dune/common/fvector.hh>
+#include <dune/common/parallel/mpihelper.hh>
+#include <dune/common/parametertree.hh>
+#include <dune/common/parametertreeparser.hh>
+
+#include <dune/grid/common/mcmgmapper.hh>
+#include <dune/istl/bcrsmatrix.hh>
+#include <dune/istl/bvector.hh>
+
+#include <dune/fufem/boundarypatch.hh>
+#include <dune/fufem/formatstring.hh>
+
+#include <dune/solvers/norms/energynorm.hh>
+#include <dune/solvers/solvers/loopsolver.hh>
+#include <dune/solvers/solvers/solver.hh>
+#include <dune/tnnmg/problem-classes/convexproblem.hh>
+
+#include <dune/tectonic/geocoordinate.hh>
+#include <dune/tectonic/myblockproblem.hh>
+#include <dune/tectonic/globalfriction.hh>
+#include <dune/fufem/hdf5/file.hh>
+
+#include "assemblers.hh"
+#include "diameter.hh"
+#include "enumparser.hh"
+#include "enums.hh"
+#include "gridselector.hh"
+#include "hdf5-writer.hh"
+#include "hdf5/restart-io.hh"
+#include "matrices.hh"
+#include "program_state.hh"
+#include "one-body-problem-data/bc.hh"
+#include "one-body-problem-data/mybody.hh"
+#include "one-body-problem-data/mygeometry.hh"
+#include "one-body-problem-data/myglobalfrictiondata.hh"
+#include "one-body-problem-data/mygrid.hh"
+#include "one-body-problem-data/weakpatch.hh"
+#include "spatial-solving/solverfactory.hh"
+#include "time-stepping/adaptivetimestepper.hh"
+#include "time-stepping/rate.hh"
+#include "time-stepping/state.hh"
+#include "time-stepping/updaters.hh"
+#include "vtk.hh"
+
+size_t const dims = MY_DIM;
+
+Dune::ParameterTree getParameters(int argc, char *argv[]) {
+  Dune::ParameterTree parset;
+  Dune::ParameterTreeParser::readINITree("one-body-problem.cfg", parset);
+  Dune::ParameterTreeParser::readINITree(
+      Dune::Fufem::formatString("one-body-problem-%dD.cfg", dims), parset);
+  Dune::ParameterTreeParser::readOptions(argc, argv, parset);
+  return parset;
+}
+
+static std::atomic<bool> terminationRequested(false);
+void handleSignal(int signum) { terminationRequested = true; }
+
+int main(int argc, char *argv[]) {
+  try {
+    Dune::MPIHelper::instance(argc, argv);
+    auto const parset = getParameters(argc, argv);
+
+    MyGeometry::render();
+    MyGeometry::write();
+
+    using GridView = Grid::LeafGridView;
+    using MyAssembler = MyAssembler<GridView, dims>;
+    using Matrix = MyAssembler::Matrix;
+    using Vector = MyAssembler::Vector;
+    using LocalVector = Vector::block_type;
+    using ScalarMatrix = MyAssembler::ScalarMatrix;
+    using ScalarVector = MyAssembler::ScalarVector;
+
+    auto const weakPatch =
+        getWeakPatch<LocalVector>(parset.sub("boundary.friction.weakening"));
+
+    // {{{ Set up grid
+    GridConstructor<Grid> gridConstructor;
+    auto grid = gridConstructor.getGrid();
+
+    refine(*grid, weakPatch,
+           parset.get<double>("boundary.friction.smallestDiameter"));
+
+    double minDiameter = std::numeric_limits<double>::infinity();
+    double maxDiameter = 0.0;
+    for (auto &&e : elements(grid->leafGridView())) {
+      auto const geometry = e.geometry();
+      auto const diam = diameter(geometry);
+      minDiameter = std::min(minDiameter, diam);
+      maxDiameter = std::max(maxDiameter, diam);
+    }
+    std::cout << "min diameter: " << minDiameter << std::endl;
+    std::cout << "max diameter: " << maxDiameter << std::endl;
+
+    auto const leafView = grid->leafGridView();
+    auto const leafVertexCount = leafView.size(dims);
+
+    std::cout << "Number of DOFs: " << leafVertexCount << std::endl;
+
+    auto myFaces = gridConstructor.constructFaces(leafView);
+
+    BoundaryPatch<GridView> const neumannBoundary(leafView);
+    BoundaryPatch<GridView> const &frictionalBoundary = myFaces.lower;
+    BoundaryPatch<GridView> const &surface = myFaces.upper;
+
+    // Dirichlet Boundary
+    Dune::BitSetVector<dims> noNodes(leafVertexCount);
+    Dune::BitSetVector<dims> dirichletNodes(leafVertexCount);
+    for (size_t i = 0; i < leafVertexCount; ++i) {
+      if (myFaces.right.containsVertex(i))
+        dirichletNodes[i][0] = true;
+
+      if (myFaces.lower.containsVertex(i))
+        dirichletNodes[i][1] = true;
+
+#if MY_DIM == 3
+      if (myFaces.front.containsVertex(i) || myFaces.back.containsVertex(i))
+        dirichletNodes[i][2] = true;
+#endif
+    }
+
+    // Set up functions for time-dependent boundary conditions
+    using Function = Dune::VirtualFunction<double, double>;
+    Function const &velocityDirichletFunction = VelocityDirichletCondition();
+    Function const &neumannFunction = NeumannCondition();
+
+    MyAssembler const myAssembler(leafView);
+
+    MyBody<dims> const body(parset);
+
+    Matrices<Matrix> matrices;
+    myAssembler.assembleElasticity(body.getYoungModulus(),
+                                   body.getPoissonRatio(), matrices.elasticity);
+    myAssembler.assembleViscosity(body.getShearViscosityField(),
+                                  body.getBulkViscosityField(),
+                                  matrices.damping);
+    myAssembler.assembleMass(body.getDensityField(), matrices.mass);
+
+    ScalarMatrix relativeFrictionalBoundaryMass;
+    myAssembler.assembleFrictionalBoundaryMass(frictionalBoundary,
+                                               relativeFrictionalBoundaryMass);
+    relativeFrictionalBoundaryMass /= frictionalBoundary.area();
+    EnergyNorm<ScalarMatrix, ScalarVector> const stateEnergyNorm(
+        relativeFrictionalBoundaryMass);
+
+    // Assemble forces
+    Vector gravityFunctional;
+    myAssembler.assembleBodyForce(body.getGravityField(), gravityFunctional);
+
+    // Problem formulation: right-hand side
+    std::function<void(double, Vector &)> computeExternalForces =
+        [&](double _relativeTime, Vector &_ell) {
+          myAssembler.assembleNeumann(neumannBoundary, _ell, neumannFunction,
+                                      _relativeTime);
+          _ell += gravityFunctional;
+        };
+
+    using MyProgramState = ProgramState<Vector, ScalarVector>;
+    MyProgramState programState(leafVertexCount);
+    auto const firstRestart = parset.get<size_t>("io.restarts.first");
+    auto const restartSpacing = parset.get<size_t>("io.restarts.spacing");
+    auto const writeRestarts = parset.get<bool>("io.restarts.write");
+    auto const writeData = parset.get<bool>("io.data.write");
+    bool const handleRestarts = writeRestarts or firstRestart > 0;
+
+    auto dataFile =
+        writeData ? std::make_unique<HDF5::File>("output.h5") : nullptr;
+    auto restartFile = handleRestarts
+                           ? std::make_unique<HDF5::File>(
+                                 "restarts.h5",
+                                 writeRestarts ? HDF5::Access::READWRITE
+                                               : HDF5::Access::READONLY)
+                           : nullptr;
+    auto restartIO = handleRestarts
+                         ? std::make_unique<RestartIO<MyProgramState>>(
+                               *restartFile, leafVertexCount)
+                         : nullptr;
+
+    if (firstRestart > 0) // automatically adjusts the time and timestep
+      restartIO->read(firstRestart, programState);
+    else
+      programState.setupInitialConditions(parset, computeExternalForces,
+                                          matrices, myAssembler, dirichletNodes,
+                                          noNodes, frictionalBoundary, body);
+
+    MyGlobalFrictionData<LocalVector> frictionInfo(
+        parset.sub("boundary.friction"), weakPatch);
+    auto myGlobalFriction = myAssembler.assembleFrictionNonlinearity(
+        parset.get<Config::FrictionModel>("boundary.friction.frictionModel"),
+        frictionalBoundary, frictionInfo, programState.weightedNormalStress);
+    myGlobalFriction->updateAlpha(programState.alpha);
+
+    Vector vertexCoordinates(leafVertexCount);
+    {
+      Dune::MultipleCodimMultipleGeomTypeMapper<
+          GridView, Dune::MCMGVertexLayout> const vertexMapper(leafView);
+      for (auto &&v : vertices(leafView))
+        vertexCoordinates[vertexMapper.index(v)] = geoToPoint(v.geometry());
+    }
+
+    using MyVertexBasis = typename MyAssembler::VertexBasis;
+    auto dataWriter =
+        writeData ? std::make_unique<
+                        HDF5Writer<MyProgramState, MyVertexBasis, GridView>>(
+                        *dataFile, vertexCoordinates, myAssembler.vertexBasis,
+                        surface, frictionalBoundary, weakPatch)
+                  : nullptr;
+    MyVTKWriter<MyVertexBasis, typename MyAssembler::CellBasis> const vtkWriter(
+        myAssembler.cellBasis, myAssembler.vertexBasis, "obs");
+
+    IterationRegister iterationCount;
+    auto const report = [&](bool initial = false) {
+      if (writeData) {
+        dataWriter->reportSolution(programState, *myGlobalFriction);
+        if (!initial)
+          dataWriter->reportIterations(programState, iterationCount);
+        dataFile->flush();
+      }
+
+      if (writeRestarts and !initial and
+          programState.timeStep % restartSpacing == 0) {
+        restartIO->write(programState);
+        restartFile->flush();
+      }
+
+      if (parset.get<bool>("io.printProgress"))
+        std::cout << "timeStep = " << std::setw(6) << programState.timeStep
+                  << ", time = " << std::setw(12) << programState.relativeTime
+                  << ", tau = " << std::setw(12) << programState.relativeTau
+                  << std::endl;
+
+      if (parset.get<bool>("io.vtk.write")) {
+        ScalarVector stress;
+        myAssembler.assembleVonMisesStress(body.getYoungModulus(),
+                                           body.getPoissonRatio(),
+                                           programState.u, stress);
+        vtkWriter.write(programState.timeStep, programState.u, programState.v,
+                        programState.alpha, stress);
+      }
+    };
+    report(true);
+
+    // Set up TNNMG solver
+    using NonlinearFactory = SolverFactory<
+        dims,
+        MyBlockProblem<ConvexProblem<GlobalFriction<Matrix, Vector>, Matrix>>,
+        Grid>;
+    NonlinearFactory factory(parset.sub("solver.tnnmg"), *grid, dirichletNodes);
+
+    using MyUpdater = Updaters<RateUpdater<Vector, Matrix, Function, dims>,
+                               StateUpdater<ScalarVector, Vector>>;
+    MyUpdater current(
+        initRateUpdater(parset.get<Config::scheme>("timeSteps.scheme"),
+                        velocityDirichletFunction, dirichletNodes, matrices,
+                        programState.u, programState.v, programState.a),
+        initStateUpdater<ScalarVector, Vector>(
+            parset.get<Config::stateModel>("boundary.friction.stateModel"),
+            programState.alpha, *frictionalBoundary.getVertices(),
+            parset.get<double>("boundary.friction.L"),
+            parset.get<double>("boundary.friction.V0")));
+
+    auto const refinementTolerance =
+        parset.get<double>("timeSteps.refinementTolerance");
+    auto const mustRefine = [&](MyUpdater &coarseUpdater,
+                                MyUpdater &fineUpdater) {
+      ScalarVector coarseAlpha;
+      coarseUpdater.state_->extractAlpha(coarseAlpha);
+
+      ScalarVector fineAlpha;
+      fineUpdater.state_->extractAlpha(fineAlpha);
+
+      return stateEnergyNorm.diff(fineAlpha, coarseAlpha) > refinementTolerance;
+    };
+
+    std::signal(SIGXCPU, handleSignal);
+    std::signal(SIGINT, handleSignal);
+    std::signal(SIGTERM, handleSignal);
+
+    AdaptiveTimeStepper<NonlinearFactory, MyUpdater,
+                        EnergyNorm<ScalarMatrix, ScalarVector>>
+        adaptiveTimeStepper(factory, parset, myGlobalFriction, current,
+                            programState.relativeTime, programState.relativeTau,
+                            computeExternalForces, stateEnergyNorm, mustRefine);
+    while (!adaptiveTimeStepper.reachedEnd()) {
+      programState.timeStep++;
+
+      iterationCount = adaptiveTimeStepper.advance();
+
+      programState.relativeTime = adaptiveTimeStepper.relativeTime_;
+      programState.relativeTau = adaptiveTimeStepper.relativeTau_;
+      current.rate_->extractDisplacement(programState.u);
+      current.rate_->extractVelocity(programState.v);
+      current.rate_->extractAcceleration(programState.a);
+      current.state_->extractAlpha(programState.alpha);
+
+      report();
+
+      if (terminationRequested) {
+        std::cerr << "Terminating prematurely" << std::endl;
+        break;
+      }
+    }
+  } catch (Dune::Exception &e) {
+    Dune::derr << "Dune reported error: " << e << std::endl;
+  } catch (std::exception &e) {
+    std::cerr << "Standard exception: " << e.what() << std::endl;
+  }
+}

src/sand-wedge-data/parset.cfg → src/one-body-problem.cfg

@@ -2,19 +2,23 @@
 gravity         = 9.81  # [m/s^2]
 
 [io]
+data.write      = true
 printProgress   = false
-writeVTK        = false
+restarts.first  = 0
+restarts.spacing= 20
+restarts.write  = true
+vtk.write       = false
 
 [problem]
-finalTime       = 1800  # [s]
+finalTime       = 1000  # [s]
 
 [body]
-bulkModulus     = 1e5   # [Pa]
-poissonRatio    = 0.3   # [1]      0.2 - 0.3
+bulkModulus     = 0.5e5 # [Pa]
+poissonRatio    = 0.3   # [1]
 [body.elastic]
 density         = 900   # [kg/m^3]
-shearViscosity  = 1e3   # [Pas]    0
-bulkViscosity   = 1e3   # [Pas]    0
+shearViscosity  = 1e3   # [Pas]
+bulkViscosity   = 1e3   # [Pas]
 [body.viscoelastic]
 density         = 1000  # [kg/m^3]
 shearViscosity  = 1e4   # [Pas]
@@ -22,49 +26,40 @@ bulkViscosity   = 1e4   # [Pas]
 
 [boundary.friction]
 C               = 10    # [Pa]
-mu0             = 0.7   # [1]
+mu0             = 0.7   # [ ]
 V0              = 5e-5  # [m/s]
-L               = 2e-5  # [m]      ?
-initialLogState = 0     # [ ]      ?
-stateModel      = Dieterich
+L               = 2.25e-5 # [m]
+initialAlpha    = 0     # [ ]
+stateModel      = AgeingLaw
+frictionModel   = Regularised
 [boundary.friction.weakening]
-a               = 0.015 # [1]      ?
-b               = 0.030 # [1]      ?
+a               = 0.002 # [ ]
+b               = 0.017 # [ ]
 [boundary.friction.strengthening]
-a               = 0.030 # [1]      ?
-b               = 0.015 # [1]      ?
+a               = 0.020 # [ ]
+b               = 0.005 # [ ]
 
 [timeSteps]
-number = 100000
 scheme = newmark
 
-[grid]
-refinements = 4
-
 [u0.solver]
-tolerance         = 1e-10
 maximumIterations = 100000
 verbosity         = quiet
 
 [a0.solver]
-tolerance         = 1e-10
 maximumIterations = 100000
 verbosity         = quiet
 
 [v.solver]
-tolerance         = 1e-10
 maximumIterations = 100000
 verbosity         = quiet
 
 [v.fpi]
-tolerance         = 1e-10
 maximumIterations = 10000
-relaxation        = 0.5
-requiredReduction = 0.5
+lambda            = 0.5
 
 [solver.tnnmg.linear]
 maxiumumIterations = 100000
-tolerance          = 1e-10
 pre                = 3
 cycle              = 1  # 1 = V, 2 = W, etc.
 post               = 3
@@ -73,6 +68,3 @@ post               = 3
 pre   = 1
 multi = 5 # number of multigrid steps
 post  = 0
-
-[localsolver]
-steps = 100

src/program_state.hh

+#ifndef SRC_PROGRAM_STATE_HH
+#define SRC_PROGRAM_STATE_HH
+
+#include <dune/common/parametertree.hh>
+
+#include <dune/fufem/boundarypatch.hh>
+#include <dune/tnnmg/nonlinearities/zerononlinearity.hh>
+#include <dune/tnnmg/problem-classes/blocknonlineartnnmgproblem.hh>
+
+#include <dune/tectonic/body.hh>
+
+#include "assemblers.hh"
+#include "matrices.hh"
+#include "spatial-solving/solverfactory.hh"
+
+template <class VectorTEMPLATE, class ScalarVectorTEMPLATE> class ProgramState {
+public:
+  using Vector = VectorTEMPLATE;
+  using ScalarVector = ScalarVectorTEMPLATE;
+
+  ProgramState(int leafVertexCount)
+      : u(leafVertexCount),
+        v(leafVertexCount),
+        a(leafVertexCount),
+        alpha(leafVertexCount),
+        weightedNormalStress(leafVertexCount) {}
+
+  // Set up initial conditions
+  template <class Matrix, class GridView>
+  void setupInitialConditions(
+      Dune::ParameterTree const &parset,
+      std::function<void(double, Vector &)> externalForces,
+      Matrices<Matrix> const matrices,
+      MyAssembler<GridView, Vector::block_type::dimension> const &myAssembler,
+      Dune::BitSetVector<Vector::block_type::dimension> const &dirichletNodes,
+      Dune::BitSetVector<Vector::block_type::dimension> const &noNodes,
+      BoundaryPatch<GridView> const &frictionalBoundary,
+      Body<Vector::block_type::dimension> const &body) {
+
+    using LocalVector = typename Vector::block_type;
+    using LocalMatrix = typename Matrix::block_type;
+    auto constexpr dims = LocalVector::dimension;
+
+    // Solving a linear problem with a multigrid solver
+    auto const solveLinearProblem = [&](
+        Dune::BitSetVector<dims> const &_dirichletNodes, Matrix const &_matrix,
+        Vector const &_rhs, Vector &_x,
+        Dune::ParameterTree const &_localParset) {
+
+      using LinearFactory = SolverFactory<
+          dims, BlockNonlinearTNNMGProblem<ConvexProblem<
+                    ZeroNonlinearity<LocalVector, LocalMatrix>, Matrix>>,
+          typename GridView::Grid>;
+      ZeroNonlinearity<LocalVector, LocalMatrix> zeroNonlinearity;
+
+      LinearFactory factory(parset.sub("solver.tnnmg"), // FIXME
+                            myAssembler.gridView.grid(), _dirichletNodes);
+
+      typename LinearFactory::ConvexProblem convexProblem(
+          1.0, _matrix, zeroNonlinearity, _rhs, _x);
+      typename LinearFactory::BlockProblem problem(parset, convexProblem);
+
+      auto multigridStep = factory.getStep();
+      multigridStep->setProblem(_x, problem);
+      EnergyNorm<Matrix, Vector> const norm(_matrix);
+      LoopSolver<Vector> solver(
+          multigridStep.get(), _localParset.get<size_t>("maximumIterations"),
+          _localParset.get<double>("tolerance"), &norm,
+          _localParset.get<Solver::VerbosityMode>("verbosity"),
+          false); // absolute error
+
+      solver.preprocess();
+      solver.solve();
+    };
+
+    timeStep = 0;
+    relativeTime = 0.0;
+    relativeTau = 1e-6;
+
+    Vector ell0(u.size());
+    externalForces(relativeTime, ell0);
+
+    // Initial velocity
+    v = 0.0;
+
+    // Initial displacement: Start from a situation of minimal stress,
+    // which is automatically attained in the case [v = 0 = a].
+    // Assuming dPhi(v = 0) = 0, we thus only have to solve Au = ell0
+    solveLinearProblem(dirichletNodes, matrices.elasticity, ell0, u,
+                       parset.sub("u0.solver"));
+
+    // Initial acceleration: Computed in agreement with Ma = ell0 - Au
+    // (without Dirichlet constraints), again assuming dPhi(v = 0) = 0
+    Vector accelerationRHS = ell0;
+    Arithmetic::subtractProduct(accelerationRHS, matrices.elasticity, u);
+    solveLinearProblem(noNodes, matrices.mass, accelerationRHS, a,
+                       parset.sub("a0.solver"));
+
+    // Initial state
+    alpha = parset.get<double>("boundary.friction.initialAlpha");
+
+    // Initial normal stress
+    myAssembler.assembleWeightedNormalStress(
+        frictionalBoundary, weightedNormalStress, body.getYoungModulus(),
+        body.getPoissonRatio(), u);
+  }
+
+public:
+  Vector u;
+  Vector v;
+  Vector a;
+  ScalarVector alpha;
+  ScalarVector weightedNormalStress;
+  double relativeTime;
+  double relativeTau;
+  size_t timeStep;
+};
+
+#endif

src/sand-wedge-data/boundaryconditions.py

-class neumannCondition:
-    def __call__(self, relativeTime):
-        return 0
-
-class velocityDirichletCondition:
-    def __call__(self, relativeTime):
-        if relativeTime <= 0.25:
-            factor = 4*relativeTime;
-        else:
-            factor = 1
-        return -5e-5 * factor
-
-Functions = {
-    'neumannCondition' : neumannCondition(),
-    'velocityDirichletCondition' : velocityDirichletCondition()
-}

src/sand-wedge-data/mygeometry.hh

-#ifndef MY_GEOMETRY_HH
-#define MY_GEOMETRY_HH
-
-#include <dune/common/fassign.hh>
-#include <dune/common/fvector.hh>
-
-#include <dune/fufem/arithmetic.hh>
-
-#ifdef HAVE_CAIROMM
-#include <cairomm/context.h>
-#include <cairomm/fontface.h>
-#include <cairomm/surface.h>
-#endif
-
-namespace MyGeometry {
-namespace {
-  using LocalVector = Dune::FieldVector<double, 2>;
-
-  // kludge because fieldvectors have no initialiser_list constructor, see
-  // https://dune-project.org/flyspray/index.php?do=details&task_id=1166
-  LocalVector generateVector(double x, double y) {
-    LocalVector tmp;
-    tmp <<= x, y;
-    return tmp;
-  }
-
-  double degreesToRadians(double degrees) {
-    return M_PI * degrees / 180;
-  };
-
-  LocalVector convexCombination(LocalVector const &x, LocalVector const &y) {
-    LocalVector ret;
-    ret = 0.0;
-    Arithmetic::addProduct(ret, 0.5, x);
-    Arithmetic::addProduct(ret, 0.5, y);
-    return ret;
-  }
-
-  double leftLeg = 1.00;
-  double rightLeg = 0.27;
-  double leftAngle = degreesToRadians(15);
-  double rightAngle = degreesToRadians(75);
-
-  double const depth = 0.10;
-}
-
-LocalVector const A = generateVector(0, 0);
-LocalVector const B = generateVector(std::hypot(leftLeg, rightLeg), 0);
-LocalVector const C = generateVector(leftLeg * std::sin(rightAngle),
-                                     leftLeg * std::sin(leftAngle));
-
-LocalVector const Y = generateVector(0.35 / std::sin(rightAngle), 0);
-LocalVector const X = generateVector(Y[0] - 0.20, 0);
-LocalVector const Z =
-    generateVector(0.35 * std::sin(rightAngle), 0.35 * std::sin(leftAngle));
-
-LocalVector const U = generateVector(Z[0] * X[0] / Y[0], Z[1] * X[0] / Y[0]);
-
-LocalVector const K = generateVector(B[0] - 0.06 / std::sin(leftAngle), 0);
-LocalVector const M = generateVector(B[0] - 0.06 * std::sin(leftAngle),
-                                     0.06 * std::sin(rightAngle));
-
-LocalVector const G = convexCombination(A, X);
-LocalVector const H = convexCombination(X, Y);
-LocalVector const J = convexCombination(Y, B);
-
-LocalVector const I = generateVector(Y[0] + G[0], 0);
-
-LocalVector const zenith =
-    generateVector(-std::sin(leftAngle), std::cos(leftAngle));
-
-LocalVector const rotatedZenith =
-    generateVector(-std::cos(leftAngle), -std::sin(leftAngle));
-
-double verticalProjection(LocalVector const &);
-double horizontalProjection(LocalVector const &);
-
-void write();
-
-void render();
-}
-#endif

src/sand-wedge-data/mygrid.cc

-#ifdef HAVE_CONFIG_H
-#include "config.h"
-#endif
-
-#include "mygrid.hh"
-
-template <class Grid> std::shared_ptr<Grid> constructGrid() {
-  Dune::GridFactory<Grid> gridFactory;
-
-  Dune::FieldMatrix<double, 3, DIM> vertices;
-  vertices[0] = MyGeometry::A;
-  vertices[1] = MyGeometry::B;
-  vertices[2] = MyGeometry::C;
-  for (size_t i = 0; i < vertices.N(); ++i)
-    gridFactory.insertVertex(vertices[i]);
-
-  Dune::GeometryType cell;
-  cell.makeTriangle();
-
-  std::vector<std::vector<unsigned int>> simplices = { { 0, 1, 2 } };
-
-  // sanity-check choices of simplices
-  for (size_t i = 0; i < simplices.size(); ++i) {
-    Dune::FieldMatrix<double, DIM, DIM> check;
-    for (size_t j = 0; j < DIM; ++j)
-      check[j] = vertices[simplices[i][j + 1]] - vertices[simplices[i][j]];
-    assert(check.determinant() > 0);
-    gridFactory.insertElement(cell, simplices[i]);
-  }
-  return std::shared_ptr<Grid>(gridFactory.createGrid());
-}
-
-template <class GridView>
-MyFaces<GridView>::MyFaces(GridView const &gridView)
-    : lower(gridView), right(gridView) {
-  using Grid = typename GridView::Grid;
-  using LevelGridView = typename Grid::LevelGridView;
-  LevelGridView const rootView = gridView.grid().levelView(0);
-
-  lower.insertFacesByProperty([&](
-      typename Grid::LeafGridView::Intersection const &in) {
-    return isClose(0, in.geometry().center()[1]);
-  });
-
-  BoundaryPatch<LevelGridView> upperRoot(rootView);
-  upperRoot.insertFacesByProperty([&](
-      typename LevelGridView::Intersection const &in) {
-    auto const geometry = in.geometry();
-    auto const range = boost::irange(0, geometry.corners());
-    return boost::algorithm::all_of(range, [&](int i) {
-      auto const &co = geometry.corner(i);
-      return (isClose(co[1], MyGeometry::A[1]) &&
-              isClose(co[0], MyGeometry::A[0])) ||
-             (isClose(co[1], MyGeometry::C[1]) &&
-              isClose(co[0], MyGeometry::C[0]));
-    });
-  });
-  BoundaryPatchProlongator<Grid>::prolong(upperRoot, upper);
-
-  BoundaryPatch<LevelGridView> rightRoot(rootView);
-  rightRoot.insertFacesByProperty([&](
-      typename LevelGridView::Intersection const &in) {
-    auto const geometry = in.geometry();
-    auto const range = boost::irange(0, geometry.corners());
-    return boost::algorithm::all_of(range, [&](int i) {
-      auto const &co = geometry.corner(i);
-      return (isClose(co[1], MyGeometry::C[1]) &&
-              isClose(co[0], MyGeometry::C[0])) ||
-             (isClose(co[1], MyGeometry::B[1]) &&
-              isClose(co[0], MyGeometry::B[0]));
-    });
-  });
-  BoundaryPatchProlongator<Grid>::prolong(rightRoot, right);
-}
-
-#include "mygrid_tmpl.cc"

src/sand-wedge-data/mygrid.hh

-#ifndef SRC_SAND_WEDGE_DATA_MYGRID_HH
-#define SRC_SAND_WEDGE_DATA_MYGRID_HH
-
-#include <boost/range/irange.hpp>
-#include <boost/algorithm/cxx11/all_of.hpp>
-
-#include <dune/common/fmatrix.hh>
-#include <dune/grid/common/gridfactory.hh>
-
-#pragma clang diagnostic push
-#pragma clang diagnostic ignored "-Wdeprecated-declarations"
-#include <dune/fufem/boundarypatch.hh>
-#pragma clang diagnostic pop
-#include <dune/fufem/boundarypatchprolongator.hh>
-
-#include "mygeometry.hh"
-
-template <class Grid> std::shared_ptr<Grid> constructGrid();
-
-template <class GridView> struct MyFaces {
-  BoundaryPatch<GridView> lower;
-  BoundaryPatch<GridView> right;
-  BoundaryPatch<GridView> upper;
-  MyFaces(GridView const &gridView);
-
-private:
-  bool isClose(double a, double b) {
-    return std::abs(a - b) < 1e-14;
-  };
-};
-#endif

src/sand-wedge-data/mygrid_tmpl.cc

-#ifndef DIM
-#error DIM unset
-#endif
-
-#include "explicitgrid.hh"
-
-template std::shared_ptr<Grid> constructGrid();
-
-template struct MyFaces<GridView>;

src/sand-wedge-data/patchfunction.hh

-#ifndef SRC_SAND_WEDGE_DATA_PATCHFUNCTION_HH
-#define SRC_SAND_WEDGE_DATA_PATCHFUNCTION_HH
-
-#include <dune/common/function.hh>
-#include <dune/common/fvector.hh>
-#include <dune/common/parametertree.hh>
-
-class PatchFunction
-    : public Dune::VirtualFunction<Dune::FieldVector<double, 2>,
-                                   Dune::FieldVector<double, 1>> {
-private:
-  bool static isBetween(double x, double lower, double upper) {
-    return lower <= x and x <= upper;
-  }
-
-  bool static isClose(double a, double b) {
-    return std::abs(a - b) < 1e-14;
-  };
-
-  bool insideRegion2(Dune::FieldVector<double, 2> const &z) const {
-    assert(isClose(0, z[1]));
-    return isBetween(z[0], _X[0], _Y[0]);
-  }
-
-  Dune::FieldVector<double, 2> const &_X;
-  Dune::FieldVector<double, 2> const &_Y;
-
-  double const _v1;
-  double const _v2;
-
-public:
-  PatchFunction(double v1, double v2)
-      : _X(MyGeometry::X), _Y(MyGeometry::Y), _v1(v1), _v2(v2) {}
-
-  void evaluate(Dune::FieldVector<double, 2> const &x,
-                Dune::FieldVector<double, 1> &y) const {
-    y = insideRegion2(x) ? _v2 : _v1;
-  }
-};
-#endif