From ea84e3ab1f4d586ed20b84dce75cdb1a8da5fc69 Mon Sep 17 00:00:00 2001 From: wolf Date: Tue, 28 Mar 2006 05:14:48 +0000 Subject: [PATCH] Generate results section out of doxygen as well. git-svn-id: https://svn.dealii.org/trunk@12703 0785d39b-7218-0410-832d-ea1e28bc413d --- .../step-1.data/grid-1.jpg | Bin 16918 -> 0 bytes .../step-1.data/grid-2.jpg | Bin 17437 -> 0 bytes .../step-1.data/results.dox | 10 +- .../step-1.data/step-1.grid-1.png | Bin 0 -> 9111 bytes .../step-1.data/step-1.grid-2.png | Bin 0 -> 29392 bytes .../step-2.data/results.dox | 10 +- .../step-2.data/sparsity_pattern_1.jpg | Bin 21662 -> 0 bytes .../step-2.data/sparsity_pattern_2.jpg | Bin 23141 -> 0 bytes .../step-2.data/step-2.sparsity-1.png | Bin 0 -> 9070 bytes .../step-2.data/step-2.sparsity-2.png | Bin 0 -> 12862 bytes .../step-3.data/results.dox | 19 ++-- .../step-3.data/solution-1.jpg | Bin 15240 -> 0 bytes .../step-3.data/solution-2.jpg | Bin 13623 -> 0 bytes .../step-3.data/step-3.solution-1.png | Bin 0 -> 24423 bytes .../step-3.data/step-3.solution-2.png | Bin 0 -> 23047 bytes .../step-4.data/grid-2d.jpg | Bin 17980 -> 0 bytes .../step-4.data/grid-3d.jpg | Bin 37140 -> 0 bytes .../step-4.data/{results.html => results.dox} | 83 ++++++++-------- .../step-4.data/solution-2d.jpg | Bin 14672 -> 0 bytes .../step-4.data/solution-3d.jpg | Bin 34352 -> 0 bytes .../step-4.data/step-4.grid-2d.png | Bin 0 -> 181192 bytes .../step-4.data/step-4.grid-3d.png | Bin 0 -> 154856 bytes .../step-4.data/step-4.solution-2d.png | Bin 0 -> 59039 bytes .../step-4.data/step-4.solution-3d.png | Bin 0 -> 152434 bytes .../step-5.data/{results.html => results.dox} | 92 +++++++++--------- .../step-5.data/solution-0.jpg | Bin 8449 -> 0 bytes .../step-5.data/solution-1.jpg | Bin 14341 -> 0 bytes .../step-5.data/solution-2.jpg | Bin 20986 -> 0 bytes .../step-5.data/solution-3.jpg | Bin 25254 -> 0 bytes .../step-5.data/solution-4.jpg | Bin 25237 -> 0 bytes .../step-5.data/solution-5.jpg | Bin 18554 -> 0 bytes .../step-5.data/step-5.solution-0.png | Bin 0 -> 45503 bytes .../step-5.data/step-5.solution-1.png | Bin 0 -> 88359 bytes .../step-5.data/step-5.solution-2.png | Bin 0 -> 122929 bytes .../step-5.data/step-5.solution-3.png | Bin 0 -> 144386 bytes .../step-5.data/step-5.solution-4.png | Bin 0 -> 154978 bytes .../step-5.data/step-5.solution-5.png | Bin 0 -> 138354 bytes .../step-6.data/final-solution.jpg | Bin 24397 -> 0 bytes .../step-6.data/grid-0.jpg | Bin 8106 -> 0 bytes .../step-6.data/grid-1.jpg | Bin 11955 -> 0 bytes .../step-6.data/grid-2.jpg | Bin 15170 -> 0 bytes .../step-6.data/grid-3.jpg | Bin 18395 -> 0 bytes .../step-6.data/grid-4.jpg | Bin 24435 -> 0 bytes .../step-6.data/grid-5.jpg | Bin 27990 -> 0 bytes .../step-6.data/grid-6.jpg | Bin 28616 -> 0 bytes .../step-6.data/grid-7.jpg | Bin 29172 -> 0 bytes .../step-6.data/step-6.grid-0.png | Bin 0 -> 13379 bytes .../step-6.data/step-6.grid-1.png | Bin 0 -> 20547 bytes .../step-6.data/step-6.grid-2.png | Bin 0 -> 27097 bytes 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-solution-1 - -solution-2 -
+ + + + +
+ @image html step-3.solution-1.png + + @image html step-3.solution-2.png +
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Results

-

+ The output of the program looks as follows (the number of iterations may vary by one or two, depending on your computer, since this is often dependent on the round-off accuracy of floating point operations, which differs between processors): -


+@code
 Solving problem in 2 space dimensions.
    Number of active cells: 256
    Total number of cells: 341
@@ -17,7 +17,7 @@ Solving problem in 3 space dimensions.
    Total number of cells: 4681
    Number of degrees of freedom: 4913
    30 CG iterations needed to obtain convergence.
-
+@endcode 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 @@ -26,31 +26,31 @@ 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-2d - -grid-2d -
+ + + + +
+ @image html step-4.solution-2d.png + + @image html step-4.grid-2d.png +
-

-

+ 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 @@ -62,49 +62,50 @@ 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 -
+ + + + +
+ @image html step-4.solution-3d.png + + @image html step-4.grid-3d.png +
-

-

+ + 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 even locally refined. -

+

Possibilities for extensions

-

+ Essentially the possibilities for playing around with the program are the same as for the previous one, except that the will now also apply to the 3d -case. For inspiration read up on possible extensions in the documentation of step-3. -

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Results

-

+ When the last block in main() is commented in, the output of the program looks as follows: -


+@code
 Cycle 0:
    Number of active cells: 20
    Total number of cells: 20
@@ -52,61 +52,61 @@ Stacktrace:
 #1  ./step-5: main
 --------------------------------------------------------
 make: *** [run] Aborted
-
-

+@endcode + + -

Let's first focus on the things before the error: In each cycle, the number of cells quadruples and the number of CG iterations roughly doubles. Also, in each cycle, the program writes one output graphic file in EPS format. They are depicted in the following: -

-

+ + - - - - - - - - - - - - - - + + + + + + + + + + + + + +
-solution-0 - -solution-1 -
-solution-2 - -solution-3 -
-solution-4 - -solution-5 -
+ @image html step-5.solution-0.png + + @image html step-5.solution-1.png +
+ @image html step-5.solution-2.png + + @image html step-5.solution-3.png +
+ @image html step-5.solution-4.png + + @image html step-5.solution-5.png +
-

-

+ + Due to the variable coefficient (the curvature there is reduced by the same factor by which the coefficient is increased), the top region of the solution is flattened. The gradient of the solution is discontinuous there, although this is not very clearly visible in the pictures above. We will look at this in more detail in the next example. -

-

+ + As for the error — let's look at it again: -


+@code
 --------------------------------------------------------
 An error occurred in line <273> of file <step-5.cc> in function
     void Coefficient<dim>::value_list(const std::vector<Point<dim>, std::allocator<Point<dim> > >&, std::vector<double, std::allocator<double> >&, unsigned int)
@@ -124,10 +124,10 @@ Stacktrace:
 #1  ./step-5: main
 --------------------------------------------------------
 make: *** [run] Aborted
-
-

+@endcode + + -

What we see is that the error was triggered in line 273 of the step-5.cc file (as we modify tutorial programs over time, these line numbers change, so you should check what line number you actually get @@ -136,18 +136,18 @@ in the code what exactly happened. But the text tells you even more. First, it prints the function this happens in, and then the plain text version of the condition that was violated. This will almost always be enough already to let you know what exactly went wrong. -

-

+ + But that's not all yet. You get to see the name of the exception (ExcDimensionMismatch) and this exception even prints the values of the two array sizes. If you go back to the code in main(), you will remember that we gave the two variables sizes 1 and 2, which of course are the ones that you find in the output again. -

-

+ + So now we know pretty exactly where the error happened and what went wrong. What we don't know yet is how exactly we got there. The stacktrace at the bottom actually tells us what happened: the problem @@ -160,4 +160,4 @@ function, in which case stack frame 1 would be LaplaceProblem<2>::assemble_system, stack frame 2 would be LaplaceProblem<2>::run, and stack frame 3 would be main() — you get the idea. -

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