From 4a3b98b77f43cb6d00be233537c63455637295d4 Mon Sep 17 00:00:00 2001
From: Oliver Sander <sander@igpm.rwth-aachen.de>
Date: Fri, 15 Jul 2011 09:53:10 +0000
Subject: [PATCH] remove a useless intermediate variable and add some more
documentation
[[Imported from SVN: r7566]]
---
dune/gfe/cosseratenergystiffness.hh | 17 +++++++----------
1 file changed, 7 insertions(+), 10 deletions(-)
diff --git a/dune/gfe/cosseratenergystiffness.hh b/dune/gfe/cosseratenergystiffness.hh
index 793256f3..a5a23f1f 100644
--- a/dune/gfe/cosseratenergystiffness.hh
+++ b/dune/gfe/cosseratenergystiffness.hh
@@ -75,25 +75,22 @@ public: // for testing
const Dune::FieldMatrix<double,7,gridDim>& derivative,
Tensor3<double,3,3,3>& DR)
{
- // derivative of the rotation part in quaternion coordinates
- Dune::FieldMatrix<double,4,gridDim> DR_quat;
- for (int i=0; i<4; i++)
- for (int j=0; j<gridDim; j++)
- DR_quat[i][j] = derivative[i+3][j];
-
- // first get the derivative of the embedding of H_1 into R^{3\times3}
- // Since the directors of a given unit quaternion are the _columns_ of the
+ // The LocalGFEFunction class gives us the derivatives of the orientation variable,
+ // but as a map into quaternion space. To obtain matrix coordinates we use the
+ // chain rule, which means that we have to multiply the given derivative with
+ // the derivative of the embedding of the unit quaternion into the space of 3x3 matrices.
+ // This second derivative is almost given by the method getFirstDerivativesOfDirectors.
+ // However, since the directors of a given unit quaternion are the _columns_ of the
// corresponding orthogonal matrix, we need to invert the i and j indices
Tensor3<double,3 , 3, 4> dd_dq;
value.q.getFirstDerivativesOfDirectors(dd_dq);
- //
DR = 0;
for (int i=0; i<3; i++)
for (int j=0; j<3; j++)
for (int k=0; k<gridDim; k++)
for (int l=0; l<4; l++)
- DR[i][j][k] += dd_dq[j][i][l] * DR_quat[l][k];
+ DR[i][j][k] += dd_dq[j][i][l] * derivative[l+3][k];
}
--
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