From daec870b7654c46a6fe831d67a968915b447ad67 Mon Sep 17 00:00:00 2001 From: schrage Date: Wed, 24 Mar 1999 16:58:58 +0000 Subject: [PATCH] First checkin. git-svn-id: https://svn.dealii.org/trunk@1042 0785d39b-7218-0410-832d-ea1e28bc413d --- .../chapter-1.elements/grid_creation.html | 105 ++++++++++++++++++ 1 file changed, 105 insertions(+) create mode 100644 deal.II/doc/tutorial/chapter-1.elements/grid_creation.html diff --git a/deal.II/doc/tutorial/chapter-1.elements/grid_creation.html b/deal.II/doc/tutorial/chapter-1.elements/grid_creation.html new file mode 100644 index 0000000000..adaefac8dd --- /dev/null +++ b/deal.II/doc/tutorial/chapter-1.elements/grid_creation.html @@ -0,0 +1,105 @@ + + + +Creation of a Grid + + + + + + + +

Creation of a Grid

+ +

Grid Types

+ +

+Choosing the right type of grid can be essential for solving your problem. +A grid should be chosen to fit your problem space in the best way possible. +Otherwise you waste memory and computing time. +

+ +

+deal.II offers three fundamental grid types: +a hypercube, a hyperball +and a hyper_L. Furthermore it is possible to +read a triangulation from a ucd-file. +

+ +

Hypercube

+ +

+A hypercube can be created using the function
+void Triangulation::create_hypercube(const double left=0.,const double right=1.)
+The cube created is the tensor product of the left and right edges which +default to 0 and 1, creating the unit hypercube. The hypercube will consist of +exactly one cell. +

+ +

Hyperball

+

+A hyperball can be created using the function
+void Triangulation::create_hyper_ball(const Point<dim&rt; center=0.,const double radius=1.)
+This will create a hyperball of given centre and radius where the location of the centre defaults to the origin and the radius to unity. +

+ +

Hyper-L

+

+A hyper-L can be created using the function
+void Triangulation::create_hyper_L(const double left=-1.,const double right=1.)
+This will create a hyper-L consisting of 2dimension-1 cells. +The hyper-L is created from the hypercube [left,right]dimension by taking +away the hypercube [left+right/2,right]dimension. +

+

+Use of the hyper-L: +The hyper-L is mainly of use in testing grid refinement, error estimates etc. +Boundary conditions of the form u=g on the faces of the original +hypercube and nu=0 on the "inner" faces resulting +from the smaller hypercube taken away. +

+ +

Reading a grid from a file

+ +

In many problems taken from real life you will find those grid types +insufficient and you will need to create your own grid. Fortunately, +this is possible. deal.II offers the possibility of +reading a complete triangulation from a file in the ucd-format +used by avs. A ucd-file can be read with the function
+void DataIn::read_ucd(istream&)
+At present only lines in on dimension and lines and quads in two dimensions +are accepted. All other data is rejected. +

+ +

Vertex numbering in input files: +The vertex numbering must start at the vertex with the lowest number for lines +and be counterclockwise for quads. Also, faces between adjacent cells +must face in the same direction. This must be ensured by you, or by the +grid construction algorithm. Otherwise some of your matrix elements +may have the wrong sign (plus instead of minus or vice versa). +A more detailed description of the problems +encountered in two dimensions can be found in the + DataIn class description. +

+ +
+ + + + + + + +
+
+Jan Schrage
+

+Last modified: Wed Mar 24 1999 +

+ + -- 2.39.5