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Commit ed6a2909 authored by Oliver Sander's avatar Oliver Sander Committed by sander@PCPOOL.MI.FU-BERLIN.DE
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(hopefully) correct implementation of the gradient 

[[Imported from SVN: r1709]]
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src/rodassembler.cc
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...@@ -361,6 +361,12 @@ assembleGradient(const Entity& element, ...@@ -361,6 +361,12 @@ assembleGradient(const Entity& element,
= Dune::LagrangeShapeFunctions<double, double, 1>::general(element.type(), 1); // first order = Dune::LagrangeShapeFunctions<double, double, 1>::general(element.type(), 1); // first order
const int numOfBaseFct = baseSet.size(); const int numOfBaseFct = baseSet.size();
// init
for (size_t i=0; i<gradient.size(); i++)
gradient[i] = 0;
double intervalLength = element.geometry()[1][0] - element.geometry()[0][0];
// Get quadrature rule // Get quadrature rule
int polOrd = 2; int polOrd = 2;
const QuadratureRule<double, 1>& quad = QuadratureRules<double, 1>::rule(element.type(), polOrd); const QuadratureRule<double, 1>& quad = QuadratureRules<double, 1>::rule(element.type(), polOrd);
...@@ -405,10 +411,10 @@ assembleGradient(const Entity& element, ...@@ -405,10 +411,10 @@ assembleGradient(const Entity& element,
r_s[i] = solution[0].r[i]*shapeGrad[0] + solution[1].r[i]*shapeGrad[1]; r_s[i] = solution[0].r[i]*shapeGrad[0] + solution[1].r[i]*shapeGrad[1];
// Interpolate current rotation at this quadrature point // Interpolate current rotation at this quadrature point
Quaternion<double> hatq = Quaternion<double>::interpolate(solution[0].q, solution[1].q,quadPos[0]); Quaternion<double> q = Quaternion<double>::interpolate(solution[0].q, solution[1].q,quadPos[0]);
// Get the derivative of the rotation at the quadrature point by interpolating in $H$ // Get the derivative of the rotation at the quadrature point by interpolating in $H$
Quaternion<double> hatq_s = Quaternion<double>::interpolateDerivative(solution[0].q, solution[1].q, Quaternion<double> q_s = Quaternion<double>::interpolateDerivative(solution[0].q, solution[1].q,
quadPos, 1/shapeGrad[1]); quadPos, 1/shapeGrad[1]);
// The current strain // The current strain
...@@ -417,31 +423,23 @@ assembleGradient(const Entity& element, ...@@ -417,31 +423,23 @@ assembleGradient(const Entity& element,
// The reference strain // The reference strain
FieldVector<double,blocksize> referenceStrain = getStrain(referenceConfiguration, element, quadPos); FieldVector<double,blocksize> referenceStrain = getStrain(referenceConfiguration, element, quadPos);
// Contains \partial q / \partial v^i_j at v = 0
array<Quaternion<double>,3> dq_dvj;
array<Quaternion<double>,3> dq_dvj_ds;
for (int j=0; j<3; j++) {
for (int m=0; m<3; m++) {
dq_dvj[j][m] = (j==m) * 0.5;
dq_dvj_ds[j][m] = (j==m) * 0.5;
}
dq_dvj[j][3] = 0;
dq_dvj_ds[j][3] = 0;
}
// dd_dvij[k][i][j] = \parder {d_k} {v^i_j}
array<array<FieldVector<double,3>, 3>, 3> dd_dvj;
hatq.getFirstDerivativesOfDirectors(dd_dvj);
// 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);
array<Quaternion<double>,6> dq_ds_dwij;
interpolationVelocityDerivative(solution[0].q, solution[1].q, quadPos*intervalLength, intervalLength,
dq_ds_dwij);
// ///////////////////////////////////////////// // /////////////////////////////////////////////
// Sum it all up // Sum it all up
// ///////////////////////////////////////////// // /////////////////////////////////////////////
for (int i=0; i<numOfBaseFct; i++) { for (int i=0; i<numOfBaseFct; i++) {
// ///////////////////////////////////////////// // /////////////////////////////////////////////
...@@ -453,49 +451,42 @@ assembleGradient(const Entity& element, ...@@ -453,49 +451,42 @@ assembleGradient(const Entity& element,
for (int m=0; m<3; m++) for (int m=0; m<3; m++)
gradient[i][j] += weight gradient[i][j] += weight
* ( A_[m] * (strain[m] - referenceStrain[m]) * shapeGrad[i] * hatq.director(m)[j]); * ( A_[m] * (strain[m] - referenceStrain[m]) * shapeGrad[i] * q.director(m)[j]);
} }
// \partial \bar{W}_v / \partial v^i_j // \partial \bar{W}_v / \partial v^i_j
for (int j=0; j<3; j++) { for (int j=0; j<3; j++) {
for (int m=0; m<3; m++) 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 gradient[i][3+j] += weight
* (A_[m] * (strain[m] - referenceStrain[m]) * (r_s*dd_dvj[m][j]*shapeFunction[i])); * A_[m] * (strain[m] - referenceStrain[m]) * (r_s*tmp);
}
} }
// ///////////////////////////////////////////// // /////////////////////////////////////////////
// The rotational part // The rotational part
// ///////////////////////////////////////////// // /////////////////////////////////////////////
// \partial \bar{W}_v / \partial v^i_j // \partial \bar{W}_v / \partial v^i_j
for (int j=0; j<3; j++) { for (int j=0; j<3; j++) {
for (int m=0; m<3; m++) { for (int m=0; m<3; m++) {
double du_dvij_m; // Compute derivative of the strain
double du_dvij_m = 2 * (dq_dwij[i*3+j].B(m) * q_s)
du_dvij_m = (hatq.mult(dq_dvj[j])).B(m) * hatq_s; + 2* ( q.B(m) * dq_ds_dwij[i*3+j]);
du_dvij_m *= shapeFunction[i];
Quaternion<double> tmp = dq_dvj[j];
tmp *= shapeFunction[i];
Quaternion<double> tmp_ds = dq_dvj_ds[j];
tmp_ds *= shapeGrad[i];
du_dvij_m += hatq.B(m) * (hatq.mult(tmp_ds) + hatq_s.mult(tmp));
du_dvij_m *= 2;
// Sum it up
gradient[i][3+j] += weight * K_[m] gradient[i][3+j] += weight * K_[m]
* (strain[m+3]-referenceStrain[m+3]) * du_dvij_m; * (strain[m+3]-referenceStrain[m+3]) * du_dvij_m;
} }
} }
} }
} }
...@@ -590,7 +581,6 @@ assembleMatrix(const std::vector<Configuration>& sol, ...@@ -590,7 +581,6 @@ assembleMatrix(const std::vector<Configuration>& sol,
} }
template <class GridType> template <class GridType>
template <class MatrixType> template <class MatrixType>
void RodAssembler<GridType>:: void RodAssembler<GridType>::
...@@ -600,6 +590,7 @@ getLocalMatrix( EntityPointer &entity, ...@@ -600,6 +590,7 @@ getLocalMatrix( EntityPointer &entity,
const int matSize, MatrixType& localMat) const const int matSize, MatrixType& localMat) const
{ {
using namespace Dune; using namespace Dune;
#if 0
/* ndof is the number of vectors of the element */ /* ndof is the number of vectors of the element */
int ndof = matSize; int ndof = matSize;
...@@ -873,7 +864,7 @@ getLocalMatrix( EntityPointer &entity, ...@@ -873,7 +864,7 @@ getLocalMatrix( EntityPointer &entity,
} }
} }
#endif
} }
template <class GridType> template <class GridType>
...@@ -1088,6 +1079,7 @@ strainDerivative(const std::vector<Configuration>& localSolution, ...@@ -1088,6 +1079,7 @@ strainDerivative(const std::vector<Configuration>& localSolution,
Dune::FieldVector<double,1> shapeFunction[2], Dune::FieldVector<double,1> shapeFunction[2],
Dune::array<Dune::FieldMatrix<double,2,6>, 6>& derivatives) const Dune::array<Dune::FieldMatrix<double,2,6>, 6>& derivatives) const
{ {
#if 0
using namespace Dune; using namespace Dune;
assert(localSolution.size()==2); assert(localSolution.size()==2);
...@@ -1153,140 +1145,10 @@ strainDerivative(const std::vector<Configuration>& localSolution, ...@@ -1153,140 +1145,10 @@ strainDerivative(const std::vector<Configuration>& localSolution,
} }
}
template <class GridType>
void RodAssembler<GridType>::
strainHessian(const std::vector<Configuration>& localSolution,
double pos,
Dune::array<Dune::Matrix<Dune::FieldMatrix<double,6,6> >, 3>& translationDer,
Dune::array<Dune::Matrix<Dune::FieldMatrix<double,3,3> >, 3>& rotationDer) const
{
using namespace Dune;
assert(localSolution.size()==2);
FieldVector<double,1> shapeGrad[2];
shapeGrad[0] = -1;
shapeGrad[1] = 1;
FieldVector<double,1> shapeFunction[2];
shapeFunction[0] = 1-pos;
shapeFunction[1] = pos;
FieldVector<double,3> r_s;
for (int i=0; i<3; i++)
r_s[i] = localSolution[0].r[i]*shapeGrad[0] + localSolution[1].r[i]*shapeGrad[1];
// Interpolate current rotation at this quadrature point
Quaternion<double> q = Quaternion<double>::interpolate(localSolution[0].q, localSolution[1].q,pos);
// Contains \parder d \parder v^i_j
array<array<FieldVector<double,3>, 3>, 3> dd_dvj;
q.getFirstDerivativesOfDirectors(dd_dvj);
Quaternion<double> q_s = Quaternion<double>::interpolateDerivative(localSolution[0].q, localSolution[1].q,
pos, 1/shapeGrad[1]);
array<Quaternion<double>,3> dq_dvj;
Quaternion<double> dq_dvij_ds[2][3];
for (int i=0; i<2; i++)
for (int j=0; j<3; j++) {
for (int m=0; m<3; m++) {
dq_dvj[j][m] = (j==m) * 0.5;
dq_dvij_ds[i][j][m] = (j==m) * 0.5 * shapeGrad[i]/* * ((i==0) ? 1-pos[0] : pos[0])*/;
}
dq_dvj[j][3] = 0;
dq_dvij_ds[i][j][3] = 0;
}
Quaternion<double> dq_dvj_dvl[3][3];
Quaternion<double> dq_dvij_dvkl_ds[2][3][2][3];
for (int i=0; i<2; i++) {
for (int j=0; j<3; j++) {
for (int k=0; k<2; k++) {
for (int l=0; l<3; l++) {
for (int m=0; m<3; m++) {
dq_dvj_dvl[j][l][m] = 0;
dq_dvij_dvkl_ds[i][j][k][l][m] = 0;
}
dq_dvj_dvl[j][l][3] = -0.25 * (j==l);
dq_dvij_dvkl_ds[i][j][k][l][3] = -0.25 * (j==l) * shapeGrad[i] * shapeGrad[k]
/* * ((i==0) ? 1-pos[0] : pos[0]) * ((k==0) ? 1-pos[0] : pos[0]) */;
}
}
}
}
// the strain component
for (int m=0; m<3; m++) {
translationDer[m].setSize(2,2);
translationDer[m] = 0;
rotationDer[m].setSize(2,2);
rotationDer[m] = 0;
// the shape function
for (int i=0; i<2; i++) {
// the partial derivative direction
for (int j=0; j<3; j++) {
for (int k=0; k<2; k++) {
for (int l=0; l<3; l++) {
// //////////////////////////////////////////////////
// The rotation part
// //////////////////////////////////////////////////
Quaternion<double> tmp_ij = dq_dvj[j];
Quaternion<double> tmp_kl = dq_dvj[l];
tmp_ij *= shapeFunction[i];
tmp_kl *= shapeFunction[k];
Quaternion<double> tmp_ijkl = dq_dvj_dvl[j][l];
tmp_ijkl *= shapeFunction[i] * shapeFunction[k];
rotationDer[m][i][k][j][l] = 2 * ( (q.mult(tmp_ijkl)).B(m) * q_s);
rotationDer[m][i][k][j][l] += 2 * ( (q.mult(tmp_ij)).B(m) * (q.mult(dq_dvij_ds[k][l]) + q_s.mult(tmp_kl)));
#if 1
rotationDer[m][i][k][j][l] += 2 * ( (q.mult(tmp_kl)).B(m) * (q.mult(dq_dvij_ds[i][j]) + q_s.mult(tmp_ij)));
rotationDer[m][i][k][j][l] += 2 * ( q.B(m) * (q.mult(dq_dvij_dvkl_ds[i][j][k][l]) + q_s.mult(tmp_ijkl)));
#else
#warning Term omitted in strainHessian
#endif #endif
}
}
}
}
}
} }
template <class GridType> template <class GridType>
void RodAssembler<GridType>:: void RodAssembler<GridType>::
rotationStrainHessian(const std::vector<Configuration>& x, rotationStrainHessian(const std::vector<Configuration>& x,
......
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