template <class VectorType, class MatrixType, class FunctionType, int dim>
EulerPair<VectorType, MatrixType, FunctionType, dim>::EulerPair(
    MatrixType const &_A, MatrixType const &_B, VectorType const &_u_initial,
    VectorType const &_v_initial,
    Dune::BitSetVector<dim> const &_dirichletNodes,
    FunctionType const &_dirichletFunction)
    : A(_A),
      B(_B),
      u(_u_initial),
      v(_v_initial),
      dirichletNodes(_dirichletNodes),
      dirichletFunction(_dirichletFunction) {}

template <class VectorType, class MatrixType, class FunctionType, int dim>
void EulerPair<VectorType, MatrixType, FunctionType, dim>::nextTimeStep() {
  v_o = v;
  u_o = u;
}

template <class VectorType, class MatrixType, class FunctionType, int dim>
void EulerPair<VectorType, MatrixType, FunctionType, dim>::setup(
    VectorType const &ell, double _tau, double time, VectorType &problem_rhs,
    VectorType &problem_iterate, MatrixType &problem_AB) {
  postProcessCalled = false;

  tau = _tau;

  problem_rhs = ell;
  Arithmetic::addProduct(problem_rhs, 1.0 / tau, B, v_o);
  Arithmetic::subtractProduct(problem_rhs, A, u_o);

  // For fixed tau, we'd only really have to do this once
  Dune::MatrixIndexSet indices(A.N(), A.M());
  indices.import(A);
  indices.import(B);
  indices.exportIdx(problem_AB);
  problem_AB = 0.0;
  Arithmetic::addProduct(problem_AB, tau, A);
  Arithmetic::addProduct(problem_AB, 1.0 / tau, B);

  // v_o makes a good initial iterate; we could use anything, though
  problem_iterate = v_o;

  for (size_t i = 0; i < dirichletNodes.size(); ++i)
    switch (dirichletNodes[i].count()) {
      case 0:
        continue;
      case dim:
        problem_iterate[i] = 0;
        dirichletFunction.evaluate(time, problem_iterate[i][0]);
        break;
      case 1:
        if (dirichletNodes[i][0]) {
          dirichletFunction.evaluate(time, problem_iterate[i][0]);
          break;
        }
        if (dirichletNodes[i][1]) {
          problem_iterate[i][1] = 0;
          break;
        }
        assert(false);
      default:
        assert(false);
    }
}

template <class VectorType, class MatrixType, class FunctionType, int dim>
void EulerPair<VectorType, MatrixType, FunctionType, dim>::postProcess(
    VectorType const &problem_iterate) {
  postProcessCalled = true;

  v = problem_iterate;

  u = u_o;
  Arithmetic::addProduct(u, tau, v);
}

template <class VectorType, class MatrixType, class FunctionType, int dim>
void EulerPair<VectorType, MatrixType, FunctionType, dim>::extractDisplacement(
    VectorType &displacement) const {
  if (!postProcessCalled)
    DUNE_THROW(Dune::Exception, "It seems you forgot to call postProcess!");

  displacement = u;
}

template <class VectorType, class MatrixType, class FunctionType, int dim>
void EulerPair<VectorType, MatrixType, FunctionType, dim>::extractVelocity(
    VectorType &velocity) const {
  if (!postProcessCalled)
    DUNE_THROW(Dune::Exception, "It seems you forgot to call postProcess!");

  velocity = v;
}