diff --git a/src/harmonicenergystiffness.hh b/src/harmonicenergystiffness.hh
new file mode 100644
index 0000000000000000000000000000000000000000..10b1ecfb6b355572ddb041d8a89d754bfa4cf941
--- /dev/null
+++ b/src/harmonicenergystiffness.hh
@@ -0,0 +1,662 @@
+#ifndef HARMONIC_ENERGY_LOCAL_STIFFNESS_HH
+#define HARMONIC_ENERGY_LOCAL_STIFFNESS_HH
+
+#include <dune/istl/bcrsmatrix.hh>
+#include <dune/common/fmatrix.hh>
+#include <dune/istl/matrixindexset.hh>
+#include <dune/istl/matrix.hh>
+#include <dune/disc/operators/localstiffness.hh>
+
+template<class GridView, class TargetSpace>
+class HarmonicEnergyLocalStiffness
+ : public Dune::LocalStiffness<GridView,
+ TargetSpace::TangentVector::field_type,
+ TargetSpace::TangentVector::size>
+{
+ // grid types
+ typedef typename GridView::Grid::ctype DT;
+ typedef typename GridView::template Codim<0>::Entity Entity;
+ typedef typename GridView::template Codim<0>::EntityPointer EntityPointer;
+
+ // some other sizes
+ enum {dim=GridView::dimension};
+
+ // Quadrature order used for the extension and shear energy
+ enum {shearQuadOrder = 2};
+
+ // Quadrature order used for the bending and torsion energy
+ enum {bendingQuadOrder = 2};
+
+public:
+
+ //! Each block is x, y, theta in 2d, T (R^3 \times SO(3)) in 3d
+ enum { blocksize = 6 };
+
+ // define the number of components of your system, this is used outside
+ // to allocate the correct size of (dense) blocks with a FieldMatrix
+ enum {m=blocksize};
+
+ // types for matrics, vectors and boundary conditions
+ typedef Dune::FieldMatrix<RT,m,m> MBlockType; // one entry in the stiffness matrix
+ typedef Dune::FieldVector<RT,m> VBlockType; // one entry in the global vectors
+ typedef Dune::array<Dune::BoundaryConditions::Flags,m> BCBlockType; // componentwise boundary conditions
+
+ //! Default Constructor
+ RodLocalStiffness ()
+ {}
+
+ //! Default Constructor
+ RodLocalStiffness (const Dune::array<double,3>& K, const Dune::array<double,3>& A)
+ {
+ for (int i=0; i<3; i++) {
+ K_[i] = K[i];
+ A_[i] = A[i];
+ }
+ }
+
+ //! assemble local stiffness matrix for given element and order
+ /*! On exit the following things have been done:
+ - The stiffness matrix for the given entity and polynomial degree has been assembled and is
+ accessible with the mat() method.
+ - The boundary conditions have been evaluated and are accessible with the bc() method
+ - The right hand side has been assembled. It contains either the value of the essential boundary
+ condition or the assembled source term and neumann boundary condition. It is accessible via the rhs() method.
+ @param[in] e a codim 0 entity reference
+ \param[in] localSolution Current local solution, because this is a nonlinear assembler
+ @param[in] k order of Lagrange basis
+ */
+ void assemble (const Entity& e,
+ const Dune::BlockVector<Dune::FieldVector<double, 6> >& localSolution,
+ int k=1)
+ {
+ DUNE_THROW(Dune::NotImplemented, "!");
+ }
+
+ /** \todo Remove this once this methods is not in base class LocalStiffness anymore */
+ void assemble (const Entity& e, int k=1)
+ {
+ DUNE_THROW(Dune::NotImplemented, "!");
+ }
+
+ void assembleBoundaryCondition (const Entity& e, int k=1)
+ {
+ DUNE_THROW(Dune::NotImplemented, "!");
+ }
+
+
+ RT energy (const Entity& e,
+ const Dune::array<RigidBodyMotion<3>,2>& localSolution,
+ const Dune::array<RigidBodyMotion<3>,2>& localReferenceConfiguration,
+ int k=1);
+
+ static void interpolationDerivative(const Rotation<3,RT>& q0, const Rotation<3,RT>& q1, double s,
+ Dune::array<Quaternion<double>,6>& grad);
+
+ static void interpolationVelocityDerivative(const Rotation<3,RT>& q0, const Rotation<3,RT>& q1, double s,
+ double intervalLength, Dune::array<Quaternion<double>,6>& grad);
+
+ Dune::FieldVector<double, 6> getStrain(const Dune::array<RigidBodyMotion<3>,2>& localSolution,
+ const Entity& element,
+ const Dune::FieldVector<double,1>& pos) const;
+
+ /** \brief Assemble the element gradient of the energy functional */
+ void assembleGradient(const Entity& element,
+ const Dune::array<RigidBodyMotion<3>,2>& solution,
+ const Dune::array<RigidBodyMotion<3>,2>& referenceConfiguration,
+ Dune::array<Dune::FieldVector<double,6>, 2>& gradient) const;
+
+ template <class T>
+ static Dune::FieldVector<T,3> darboux(const Rotation<3,T>& q, const Dune::FieldVector<T,4>& q_s)
+ {
+ Dune::FieldVector<double,3> u; // The Darboux vector
+
+ u[0] = 2 * (q.B(0) * q_s);
+ u[1] = 2 * (q.B(1) * q_s);
+ u[2] = 2 * (q.B(2) * q_s);
+
+ return u;
+ }
+
+};
+
+template <class GridType, class RT>
+RT RodLocalStiffness<GridType, RT>::
+energy(const Entity& element,
+ const Dune::array<RigidBodyMotion<3>,2>& localSolution,
+ const Dune::array<RigidBodyMotion<3>,2>& localReferenceConfiguration,
+ int k)
+{
+ RT energy = 0;
+
+ // ///////////////////////////////////////////////////////////////////////////////
+ // The following two loops are a reduced integration scheme. We integrate
+ // the transverse shear and extensional energy with a first-order quadrature
+ // formula, even though it should be second order. This prevents shear-locking.
+ // ///////////////////////////////////////////////////////////////////////////////
+
+ const Dune::QuadratureRule<double, 1>& shearingQuad
+ = Dune::QuadratureRules<double, 1>::rule(element.type(), shearQuadOrder);
+
+ for (size_t pt=0; pt<shearingQuad.size(); pt++) {
+
+ // Local position of the quadrature point
+ const Dune::FieldVector<double,1>& quadPos = shearingQuad[pt].position();
+
+ const double integrationElement = element.geometry().integrationElement(quadPos);
+
+ double weight = shearingQuad[pt].weight() * integrationElement;
+
+ Dune::FieldVector<double,6> strain = getStrain(localSolution, element, quadPos);
+
+ // The reference strain
+ Dune::FieldVector<double,6> referenceStrain = getStrain(localReferenceConfiguration, element, quadPos);
+
+ for (int i=0; i<3; i++)
+ energy += weight * 0.5 * A_[i] * (strain[i] - referenceStrain[i]) * (strain[i] - referenceStrain[i]);
+
+ }
+
+ // Get quadrature rule
+ const Dune::QuadratureRule<double, 1>& bendingQuad
+ = Dune::QuadratureRules<double, 1>::rule(element.type(), bendingQuadOrder);
+
+ for (size_t pt=0; pt<bendingQuad.size(); pt++) {
+
+ // Local position of the quadrature point
+ const Dune::FieldVector<double,1>& quadPos = bendingQuad[pt].position();
+
+ double weight = bendingQuad[pt].weight() * element.geometry().integrationElement(quadPos);
+
+ Dune::FieldVector<double,6> strain = getStrain(localSolution, element, quadPos);
+
+ // The reference strain
+ Dune::FieldVector<double,6> referenceStrain = getStrain(localReferenceConfiguration, element, quadPos);
+
+ // Part II: the bending and twisting energy
+ for (int i=0; i<3; i++)
+ energy += weight * 0.5 * K_[i] * (strain[i+3] - referenceStrain[i+3]) * (strain[i+3] - referenceStrain[i+3]);
+
+ }
+
+ return energy;
+}
+
+
+template <class GridType, class RT>
+void RodLocalStiffness<GridType, RT>::
+interpolationDerivative(const Rotation<3,RT>& q0, const Rotation<3,RT>& q1, double s,
+ Dune::array<Quaternion<double>,6>& grad)
+{
+ // Clear output array
+ for (int i=0; i<6; i++)
+ grad[i] = 0;
+
+ // The derivatives with respect to w^1
+
+ // Compute q_1^{-1}q_0
+ Rotation<3,RT> q1InvQ0 = q1;
+ q1InvQ0.invert();
+ q1InvQ0 = q1InvQ0.mult(q0);
+
+ {
+ // Compute v = (1-s) \exp^{-1} ( q_1^{-1} q_0)
+ Dune::FieldVector<RT,3> v = Rotation<3,RT>::expInv(q1InvQ0);
+ v *= (1-s);
+
+ Dune::FieldMatrix<RT,4,3> dExp_v = Rotation<3,RT>::Dexp(v);
+
+ Dune::FieldMatrix<RT,3,4> dExpInv = Rotation<3,RT>::DexpInv(q1InvQ0);
+
+ Dune::FieldMatrix<RT,4,4> mat(0);
+ for (int i=0; i<4; i++)
+ for (int j=0; j<4; j++)
+ for (int k=0; k<3; k++)
+ mat[i][j] += (1-s) * dExp_v[i][k] * dExpInv[k][j];
+
+ for (int i=0; i<3; i++) {
+
+ Quaternion<RT> dw;
+ for (int j=0; j<4; j++)
+ dw[j] = 0.5 * (i==j); // dExp[j][i] at v=0
+
+ dw = q1InvQ0.mult(dw);
+
+ mat.umv(dw,grad[i]);
+ grad[i] = q1.mult(grad[i]);
+
+ }
+ }
+
+
+ // The derivatives with respect to w^1
+
+ // Compute q_0^{-1}
+ Rotation<3,RT> q0InvQ1 = q0;
+ q0InvQ1.invert();
+ q0InvQ1 = q0InvQ1.mult(q1);
+
+ {
+ // Compute v = s \exp^{-1} ( q_0^{-1} q_1)
+ Dune::FieldVector<RT,3> v = Rotation<3,RT>::expInv(q0InvQ1);
+ v *= s;
+
+ Dune::FieldMatrix<RT,4,3> dExp_v = Rotation<3,RT>::Dexp(v);
+
+ Dune::FieldMatrix<RT,3,4> dExpInv = Rotation<3,RT>::DexpInv(q0InvQ1);
+
+ Dune::FieldMatrix<RT,4,4> mat(0);
+ for (int i=0; i<4; i++)
+ for (int j=0; j<4; j++)
+ for (int k=0; k<3; k++)
+ mat[i][j] += s * dExp_v[i][k] * dExpInv[k][j];
+
+ for (int i=3; i<6; i++) {
+
+ Quaternion<RT> dw;
+ for (int j=0; j<4; j++)
+ dw[j] = 0.5 * ((i-3)==j); // dExp[j][i-3] at v=0
+
+ dw = q0InvQ1.mult(dw);
+
+ mat.umv(dw,grad[i]);
+ grad[i] = q0.mult(grad[i]);
+
+ }
+ }
+}
+
+
+
+template <class GridType, class RT>
+void RodLocalStiffness<GridType, RT>::
+interpolationVelocityDerivative(const Rotation<3,RT>& q0, const Rotation<3,RT>& q1, double s,
+ double intervalLength, Dune::array<Quaternion<double>,6>& grad)
+{
+ // Clear output array
+ for (int i=0; i<6; i++)
+ grad[i] = 0;
+
+ // Compute q_0^{-1}
+ Rotation<3,RT> q0Inv = q0;
+ q0Inv.invert();
+
+
+ // Compute v = s \exp^{-1} ( q_0^{-1} q_1)
+ Dune::FieldVector<RT,3> v = Rotation<3,RT>::expInv(q0Inv.mult(q1));
+ v *= s/intervalLength;
+
+ Dune::FieldMatrix<RT,4,3> dExp_v = Rotation<3,RT>::Dexp(v);
+
+ Dune::array<Dune::FieldMatrix<RT,3,3>, 4> ddExp;
+ Rotation<3,RT>::DDexp(v, ddExp);
+
+ Dune::FieldMatrix<RT,3,4> dExpInv = Rotation<3,RT>::DexpInv(q0Inv.mult(q1));
+
+ Dune::FieldMatrix<RT,4,4> mat(0);
+ for (int i=0; i<4; i++)
+ for (int j=0; j<4; j++)
+ for (int k=0; k<3; k++)
+ mat[i][j] += 1/intervalLength * dExp_v[i][k] * dExpInv[k][j];
+
+
+ // /////////////////////////////////////////////////
+ // The derivatives with respect to w^0
+ // /////////////////////////////////////////////////
+ for (int i=0; i<3; i++) {
+
+ // \partial exp \partial w^1_j at 0
+ Quaternion<RT> dw;
+ for (int j=0; j<4; j++)
+ dw[j] = 0.5*(i==j); // dExp_v_0[j][i];
+
+ // \xi = \exp^{-1} q_0^{-1} q_1
+ Dune::FieldVector<RT,3> xi = Rotation<3,RT>::expInv(q0Inv.mult(q1));
+
+ Quaternion<RT> addend0;
+ addend0 = 0;
+ dExp_v.umv(xi,addend0);
+ addend0 = dw.mult(addend0);
+ addend0 /= intervalLength;
+
+ // \parder{\xi}{w^1_j} = ...
+ Quaternion<RT> dwConj = dw;
+ dwConj.conjugate();
+ //dwConj[3] -= 2 * dExp_v_0[3][i]; the last row of dExp_v_0 is zero
+ dwConj = dwConj.mult(q0Inv.mult(q1));
+
+ Dune::FieldVector<RT,3> dxi(0);
+ Rotation<3,RT>::DexpInv(q0Inv.mult(q1)).umv(dwConj, dxi);
+
+ Quaternion<RT> vHv;
+ for (int j=0; j<4; j++) {
+ vHv[j] = 0;
+ // vHv[j] = dxi * DDexp * xi
+ for (int k=0; k<3; k++)
+ for (int l=0; l<3; l++)
+ vHv[j] += ddExp[j][k][l]*dxi[k]*xi[l];
+ }
+
+ vHv *= s/intervalLength/intervalLength;
+
+ // Third addend
+ mat.umv(dwConj,grad[i]);
+
+ // add up
+ grad[i] += addend0;
+ grad[i] += vHv;
+
+ grad[i] = q0.mult(grad[i]);
+ }
+
+
+ // /////////////////////////////////////////////////
+ // The derivatives with respect to w^1
+ // /////////////////////////////////////////////////
+ for (int i=3; i<6; i++) {
+
+ // \partial exp \partial w^1_j at 0
+ Quaternion<RT> dw;
+ for (int j=0; j<4; j++)
+ dw[j] = 0.5 * ((i-3)==j); // dw[j] = dExp_v_0[j][i-3];
+
+ // \xi = \exp^{-1} q_0^{-1} q_1
+ Dune::FieldVector<RT,3> xi = Rotation<3,RT>::expInv(q0Inv.mult(q1));
+
+ // \parder{\xi}{w^1_j} = ...
+ Dune::FieldVector<RT,3> dxi(0);
+ dExpInv.umv(q0Inv.mult(q1.mult(dw)), dxi);
+
+ Quaternion<RT> vHv;
+ for (int j=0; j<4; j++) {
+ // vHv[j] = dxi * DDexp * xi
+ vHv[j] = 0;
+ for (int k=0; k<3; k++)
+ for (int l=0; l<3; l++)
+ vHv[j] += ddExp[j][k][l]*dxi[k]*xi[l];
+ }
+
+ vHv *= s/intervalLength/intervalLength;
+
+ // ///////////////////////////////////
+ // second addend
+ // ///////////////////////////////////
+
+
+ dw = q0Inv.mult(q1.mult(dw));
+
+ mat.umv(dw,grad[i]);
+ grad[i] += vHv;
+
+ grad[i] = q0.mult(grad[i]);
+
+ }
+
+}
+
+template <class GridType, class RT>
+Dune::FieldVector<double, 6> RodLocalStiffness<GridType, RT>::
+getStrain(const Dune::array<RigidBodyMotion<3>,2>& localSolution,
+ const Entity& element,
+ const Dune::FieldVector<double,1>& pos) const
+{
+ if (!element.isLeaf())
+ DUNE_THROW(Dune::NotImplemented, "Only for leaf elements");
+
+ assert(localSolution.size() == 2);
+
+ // Strain defined on each element
+ Dune::FieldVector<double, 6> strain(0);
+
+ // Extract local solution on this element
+ const Dune::LagrangeShapeFunctionSet<double, double, 1> & baseSet
+ = Dune::LagrangeShapeFunctions<double, double, 1>::general(element.type(), 1);
+ int numOfBaseFct = baseSet.size();
+
+ const Dune::FieldMatrix<double,1,1>& inv = element.geometry().jacobianInverseTransposed(pos);
+
+ // ///////////////////////////////////////
+ // Compute deformation gradient
+ // ///////////////////////////////////////
+ Dune::FieldVector<double,1> shapeGrad[numOfBaseFct];
+
+ for (int dof=0; dof<numOfBaseFct; dof++) {
+
+ for (int i=0; i<1; i++)
+ shapeGrad[dof][i] = baseSet[dof].evaluateDerivative(0,i,pos);
+
+ // multiply with jacobian inverse
+ Dune::FieldVector<double,1> tmp(0);
+ inv.umv(shapeGrad[dof], tmp);
+ shapeGrad[dof] = tmp;
+
+ }
+
+ // //////////////////////////////////
+ // Interpolate
+ // //////////////////////////////////
+
+ Dune::FieldVector<double,3> r_s;
+ for (int i=0; i<3; i++)
+ r_s[i] = localSolution[0].r[i]*shapeGrad[0][0] + localSolution[1].r[i]*shapeGrad[1][0];
+
+ // Interpolate the rotation at the quadrature point
+ Rotation<3,double> q = Rotation<3,double>::interpolate(localSolution[0].q, localSolution[1].q, pos);
+
+ // Get the derivative of the rotation at the quadrature point by interpolating in $H$
+ Quaternion<double> q_s = Rotation<3,double>::interpolateDerivative(localSolution[0].q, localSolution[1].q,
+ pos);
+ // Transformation from the reference element
+ q_s *= inv[0][0];
+
+ // /////////////////////////////////////////////
+ // Sum it all up
+ // /////////////////////////////////////////////
+
+ // Part I: the shearing and stretching strain
+ strain[0] = r_s * q.director(0); // shear strain
+ strain[1] = r_s * q.director(1); // shear strain
+ strain[2] = r_s * q.director(2); // stretching strain
+
+ // Part II: the Darboux vector
+
+ Dune::FieldVector<double,3> u = darboux(q, q_s);
+
+ strain[3] = u[0];
+ strain[4] = u[1];
+ strain[5] = u[2];
+
+ return strain;
+}
+
+template <class GridType, class RT>
+void RodLocalStiffness<GridType, RT>::
+assembleGradient(const Entity& element,
+ const Dune::array<RigidBodyMotion<3>,2>& solution,
+ const Dune::array<RigidBodyMotion<3>,2>& referenceConfiguration,
+ Dune::array<Dune::FieldVector<double,6>, 2>& gradient) const
+{
+ using namespace Dune;
+
+ // Extract local solution on this element
+ const Dune::LagrangeShapeFunctionSet<double, double, 1> & baseSet
+ = Dune::LagrangeShapeFunctions<double, double, 1>::general(element.type(), 1); // first order
+ const int numOfBaseFct = baseSet.size();
+
+ // init
+ for (size_t i=0; i<gradient.size(); i++)
+ gradient[i] = 0;
+
+ double intervalLength = element.geometry().corner(1)[0] - element.geometry().corner(0)[0];
+
+ // ///////////////////////////////////////////////////////////////////////////////////
+ // Reduced integration to avoid locking: assembly is split into a shear part
+ // and a bending part. Different quadrature rules are used for the two parts.
+ // This avoids locking.
+ // ///////////////////////////////////////////////////////////////////////////////////
+
+ // Get quadrature rule
+ const QuadratureRule<double, 1>& shearingQuad = QuadratureRules<double, 1>::rule(element.type(), shearQuadOrder);
+
+ for (int pt=0; pt<shearingQuad.size(); pt++) {
+
+ // Local position of the quadrature point
+ const FieldVector<double,1>& quadPos = shearingQuad[pt].position();
+
+ const FieldMatrix<double,1,1>& inv = element.geometry().jacobianInverseTransposed(quadPos);
+ const double integrationElement = element.geometry().integrationElement(quadPos);
+
+ double weight = shearingQuad[pt].weight() * integrationElement;
+
+ // ///////////////////////////////////////
+ // Compute deformation gradient
+ // ///////////////////////////////////////
+ double shapeGrad[numOfBaseFct];
+
+ for (int dof=0; dof<numOfBaseFct; dof++) {
+
+ shapeGrad[dof] = baseSet[dof].evaluateDerivative(0,0,quadPos);
+
+ // multiply with jacobian inverse
+ FieldVector<double,1> tmp(0);
+ inv.umv(shapeGrad[dof], tmp);
+ shapeGrad[dof] = tmp;
+
+ }
+
+ // //////////////////////////////////
+ // Interpolate
+ // //////////////////////////////////
+
+ FieldVector<double,3> r_s;
+ for (int i=0; i<3; i++)
+ r_s[i] = solution[0].r[i]*shapeGrad[0] + solution[1].r[i]*shapeGrad[1];
+
+ // Interpolate current rotation at this quadrature point
+ Rotation<3,double> q = Rotation<3,double>::interpolate(solution[0].q, solution[1].q,quadPos[0]);
+
+ // The current strain
+ FieldVector<double,blocksize> strain = getStrain(solution, element, quadPos);
+
+ // The reference strain
+ FieldVector<double,blocksize> referenceStrain = getStrain(referenceConfiguration, element, quadPos);
+
+
+ // dd_dvij[m][i][j] = \parder {(d_k)_i} {q}
+ array<FieldMatrix<double,3 , 4>, 3> dd_dq;
+ q.getFirstDerivativesOfDirectors(dd_dq);
+
+ // First derivatives of the position
+ array<Quaternion<double>,6> dq_dwij;
+ interpolationDerivative(solution[0].q, solution[1].q, quadPos, dq_dwij);
+
+ // /////////////////////////////////////////////
+ // Sum it all up
+ // /////////////////////////////////////////////
+
+ for (int i=0; i<numOfBaseFct; i++) {
+
+ // /////////////////////////////////////////////
+ // The translational part
+ // /////////////////////////////////////////////
+
+ // \partial \bar{W} / \partial r^i_j
+ for (int j=0; j<3; j++) {
+
+ for (int m=0; m<3; m++)
+ gradient[i][j] += weight
+ * ( A_[m] * (strain[m] - referenceStrain[m]) * shapeGrad[i] * q.director(m)[j]);
+
+ }
+
+ // \partial \bar{W}_v / \partial v^i_j
+ for (int j=0; j<3; j++) {
+
+ for (int m=0; m<3; m++) {
+ FieldVector<double,3> tmp(0);
+ dd_dq[m].umv(dq_dwij[3*i+j], tmp);
+ gradient[i][3+j] += weight
+ * A_[m] * (strain[m] - referenceStrain[m]) * (r_s*tmp);
+ }
+ }
+
+ }
+
+ }
+
+ // /////////////////////////////////////////////////////
+ // Now: the bending/torsion part
+ // /////////////////////////////////////////////////////
+
+ // Get quadrature rule
+ const QuadratureRule<double, 1>& bendingQuad = QuadratureRules<double, 1>::rule(element.type(), bendingQuadOrder);
+
+ for (int pt=0; pt<bendingQuad.size(); pt++) {
+
+ // Local position of the quadrature point
+ const FieldVector<double,1>& quadPos = bendingQuad[pt].position();
+
+ const FieldMatrix<double,1,1>& inv = element.geometry().jacobianInverseTransposed(quadPos);
+ const double integrationElement = element.geometry().integrationElement(quadPos);
+
+ double weight = bendingQuad[pt].weight() * integrationElement;
+
+ // Interpolate current rotation at this quadrature point
+ Rotation<3,double> q = Rotation<3,double>::interpolate(solution[0].q, solution[1].q,quadPos[0]);
+
+ // Get the derivative of the rotation at the quadrature point by interpolating in $H$
+ Quaternion<double> q_s = Rotation<3,double>::interpolateDerivative(solution[0].q, solution[1].q,
+ quadPos);
+ // Transformation from the reference element
+ q_s *= inv[0][0];
+
+
+ // The current strain
+ FieldVector<double,blocksize> strain = getStrain(solution, element, quadPos);
+
+ // The reference strain
+ FieldVector<double,blocksize> referenceStrain = getStrain(referenceConfiguration, element, quadPos);
+
+ // First derivatives of the position
+ array<Quaternion<double>,6> dq_dwij;
+ interpolationDerivative(solution[0].q, solution[1].q, quadPos, dq_dwij);
+
+ array<Quaternion<double>,6> dq_ds_dwij;
+ interpolationVelocityDerivative(solution[0].q, solution[1].q, quadPos[0]*intervalLength, intervalLength,
+ dq_ds_dwij);
+
+ // /////////////////////////////////////////////
+ // Sum it all up
+ // /////////////////////////////////////////////
+
+ for (int i=0; i<numOfBaseFct; i++) {
+
+ // /////////////////////////////////////////////
+ // The rotational part
+ // /////////////////////////////////////////////
+
+ // \partial \bar{W}_v / \partial v^i_j
+ for (int j=0; j<3; j++) {
+
+ for (int m=0; m<3; m++) {
+
+ // Compute derivative of the strain
+ /** \todo Is this formula correct? It seems strange to call
+ B(m) for a _derivative_ of a rotation */
+ double du_dvij_m = 2 * (dq_dwij[i*3+j].B(m) * q_s)
+ + 2* ( q.B(m) * dq_ds_dwij[i*3+j]);
+
+ // Sum it up
+ gradient[i][3+j] += weight * K_[m]
+ * (strain[m+3]-referenceStrain[m+3]) * du_dvij_m;
+
+ }
+
+ }
+
+ }
+
+ }
+}
+
+#endif
+