From: wolf Date: Wed, 22 Dec 1999 22:46:52 +0000 (+0000) Subject: . X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=d858129be57bfe4b1aa6f70ec60b937a8882da12;p=dealii-svn.git . git-svn-id: https://svn.dealii.org/trunk@2114 0785d39b-7218-0410-832d-ea1e28bc413d --- diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/program2plain b/deal.II/doc/tutorial/chapter-2.step-by-step/program2plain index b55c9f922b..4fe9180d9e 100644 --- a/deal.II/doc/tutorial/chapter-2.step-by-step/program2plain +++ b/deal.II/doc/tutorial/chapter-2.step-by-step/program2plain @@ -9,7 +9,7 @@ print "

The plain program

\n"; print "(The program can be found at PROGRAMPATH.)\n

\n"; -print "

";
+print "
\n";
 
 
 while (<>) {
diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-4.results b/deal.II/doc/tutorial/chapter-2.step-by-step/step-4.results
index 4c30e00b53..5cbdf040ab 100644
--- a/deal.II/doc/tutorial/chapter-2.step-by-step/step-4.results
+++ b/deal.II/doc/tutorial/chapter-2.step-by-step/step-4.results
@@ -7,17 +7,79 @@ The output of the program looks as follows:
 ...
 
 
+It is obvious that in three spatial dimensions the number of cells and +therefore also the number of degrees of freedom is +much higher. What cannot be seen here, is that besides this higher +number of rows and columns in the matrix, there are also significantly +more entries per row of the matrix in three space +dimensions. Together, this leads to a much higher numerical effort for +solving the system of equation, which you can feel when you actually +run the program. +

+ +The program produces two files: solution-2d.gmv and +solution-3d.gmv, which can be viewed using the program +GMV (in case you do not have that program, you can easily change the +output format in the program to something which you can view more +easily). From the two-dimensional output, we have produced the +following two pictures:

-solution-3d +solution-3d -grid-3d +grid-3d

+ +The left one shows the solution of the problem under consideration as +a 3D plot. As can be seen, the solution is almost flat in the interior +of the domain and has a higher curvature near the boundary. This, of +course, is due to the fact that for Laplace's equation the curvature +of the solution is equal to the right hand side and that was chosen as +a quartic polynomial which is nearly zero in the interior and is only +rising sharply when approaching the boundaries of the domain; the +maximal values of the right hand side function are at the corners of +the domain, where also the solution is moving most rapidly. + +It is also nice to see that the solution follows the desired quadratic +boundary values along the boundaries of the domain. + +

+ +The right picture shows the two dimensional grid, colorized by the +values of the solution function. This is not very exciting, but the +colors are nice. + +

+ + +In three spatial dimensions, visualization is a bit more difficult. To +the left, you can see the solution at three of the six outer faces of +the cube in which we solved the equation, and on a plane through the +origin. On some of the planes, the cut through the grid is also shown. + +

+ + + + + +
+solution-3d + +grid-3d +
+

+ +The right picture shows the three dimensional grid, colorized by the +solutions values. 3D grids are difficult to visualize, which can be +seen here already, even though the grid is not locally refined. + +