From 96c68319a9ed6b6cfd22bf9266d7d9f494efb3ca Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Robert=20Kl=C3=B6fkorn?= <robertk@dune-project.org>
Date: Thu, 16 Feb 2006 15:28:16 +0000
Subject: [PATCH] implemented missing global and local method for Geometries
with dim=0;
[[Imported from SVN: r4102]]
---
grid/sgrid.hh | 31 +++++++++++++++++++++++++++++--
1 file changed, 29 insertions(+), 2 deletions(-)
diff --git a/grid/sgrid.hh b/grid/sgrid.hh
index de06d3617..d72f8b3e5 100644
--- a/grid/sgrid.hh
+++ b/grid/sgrid.hh
@@ -167,6 +167,33 @@ namespace Dune {
//! constructor, makes element from position and direction vectors
void make (FieldMatrix<sgrid_ctype,1,cdim>& __As);
+ //! maps a local coordinate within reference element to global coordinate in element
+ FieldVector<sgrid_ctype, 1> global (const FieldVector<sgrid_ctype, 0>& local) const { return this->operator[] (0); }
+
+ //! maps a global coordinate within the element to a local coordinate in its reference element
+ FieldVector<sgrid_ctype, 0> local (const FieldVector<sgrid_ctype, 1>& global) const { return FieldVector<sgrid_ctype,0> (0.0); }
+
+ /*! Integration over a general element is done by integrating over the reference element
+ and using the transformation from the reference element to the global element as follows:
+ \f[\int\limits_{\Omega_e} f(x) dx = \int\limits_{\Omega_{ref}} f(g(l)) A(l) dl \f] where
+ \f$g\f$ is the local to global mapping and \f$A(l)\f$ is the integration element.
+
+ For a general map \f$g(l)\f$ involves partial derivatives of the map (surface element of
+ the first kind if \f$d=2,w=3\f$, determinant of the Jacobian of the transformation for
+ \f$d=w\f$, \f$\|dg/dl\|\f$ for \f$d=1\f$).
+
+ For linear elements, the derivatives of the map with respect to local coordinates
+ do not depend on the local coordinates and are the same over the whole element.
+
+ For a structured mesh where all edges are parallel to the coordinate axes, the
+ computation is the length, area or volume of the element is very simple to compute.
+
+ Each grid module implements the integration element with optimal efficieny. This
+ will directly translate in substantial savings in the computation of finite element
+ stiffness matrices.
+ For this specialisation the integrationElement is always 1.
+ */
+
//! constructor with bool argument makes reference element if true, uninitialized else
SGeometry () {};
@@ -175,8 +202,8 @@ namespace Dune {
* This routine exists so that algorithms that integrate over grid
* boundaries can also be compiled for 1d-grids.
*/
- sgrid_ctype integration_element(const FieldVector<sgrid_ctype, 0>& local) const {
- return 1;
+ sgrid_ctype integrationElement(const FieldVector<sgrid_ctype, 0>& local) const {
+ return 1.;
}
protected:
--
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