From 4ef6342e933c225e8d8b0c836197e1dc73257f38 Mon Sep 17 00:00:00 2001 From: wolf Date: Mon, 18 Jul 2005 19:14:01 +0000 Subject: [PATCH] Better documentation. git-svn-id: https://svn.dealii.org/trunk@11167 0785d39b-7218-0410-832d-ea1e28bc413d --- deal.II/base/include/base/symmetric_tensor.h | 13 +++++++++++++ 1 file changed, 13 insertions(+) diff --git a/deal.II/base/include/base/symmetric_tensor.h b/deal.II/base/include/base/symmetric_tensor.h index 30ba15e70a..966fab7240 100644 --- a/deal.II/base/include/base/symmetric_tensor.h +++ b/deal.II/base/include/base/symmetric_tensor.h @@ -2166,6 +2166,19 @@ deviator_tensor () * tensor t returns the deviator dev t. It is the operator * representation of the linear deviator operator. * + * Note that this tensor, even though it is the identity, has a somewhat funny + * form, and in particular does not only consist of zeros and ones. For + * example, for dim=2, the identity tensor has all zero entries + * except for id[0][0][0][0]=id[1][1][1][1]=1 and + * id[0][1][0][1]=id[0][1][1][0]=id[1][0][0][1]=id[1][0][1][0]=1/2. To + * see why this factor of 1/2 is necessary, consider computing A=Id + * . B. For the element a_01 we have a_01=id_0100 b_00 + + * id_0111 b_11 + id_0101 b_01 + id_0110 b_10. On the other hand, we need + * to have a_01=b_01, and symmetry implies b_01=b_10, + * leading to a_01=(id_0101+id_0110) b_01, or, again by symmetry, + * id_0101=id_0110=1/2. Similar considerations hold for the + * three-dimensional case. + * * @relates SymmetricTensor * @author Wolfgang Bangerth, 2005 */ -- 2.39.5