From bd0953e932bf77b301e19608989f5aa8b83dc46f Mon Sep 17 00:00:00 2001 From: wolf Date: Tue, 28 Mar 2006 15:22:06 +0000 Subject: [PATCH] Doxygenize git-svn-id: https://svn.dealii.org/trunk@12723 0785d39b-7218-0410-832d-ea1e28bc413d --- .../step-17.data/{intro.html => intro.dox} | 26 +++--- .../{results.html => results.dox} | 77 ++++++++---------- .../step-17.data/solution-12-grid.png | Bin 17194 -> 0 bytes .../step-17.data/solution-12-partition.png | Bin 8913 -> 0 bytes .../step-17.data/solution-12-ux.png | Bin 82918 -> 0 bytes .../step-17.data/solution-12-uy.png | Bin 75566 -> 0 bytes .../step-17.data/solution-4-3d-partition.png | Bin 23990 -> 0 bytes .../step-17.data/solution-4-3d-ux.png | Bin 85345 -> 0 bytes .../step-17.data/step-17.12-grid.png | Bin 0 -> 53688 bytes .../step-17.data/step-17.12-partition.png | Bin 0 -> 18093 bytes .../step-17.data/step-17.12-ux.png | Bin 0 -> 43842 bytes .../step-17.data/step-17.12-uy.png | Bin 0 -> 42640 bytes .../step-17.data/step-17.4-3d-partition.png | Bin 0 -> 77778 bytes .../step-17.data/step-17.4-3d-ux.png | Bin 0 -> 79647 bytes 14 files changed, 45 insertions(+), 58 deletions(-) rename deal.II/doc/tutorial/chapter-2.step-by-step/step-17.data/{intro.html => intro.dox} (96%) rename deal.II/doc/tutorial/chapter-2.step-by-step/step-17.data/{results.html => results.dox} (89%) delete mode 100644 deal.II/doc/tutorial/chapter-2.step-by-step/step-17.data/solution-12-grid.png delete mode 100644 deal.II/doc/tutorial/chapter-2.step-by-step/step-17.data/solution-12-partition.png delete mode 100644 deal.II/doc/tutorial/chapter-2.step-by-step/step-17.data/solution-12-ux.png delete mode 100644 deal.II/doc/tutorial/chapter-2.step-by-step/step-17.data/solution-12-uy.png delete mode 100644 deal.II/doc/tutorial/chapter-2.step-by-step/step-17.data/solution-4-3d-partition.png delete mode 100644 deal.II/doc/tutorial/chapter-2.step-by-step/step-17.data/solution-4-3d-ux.png create mode 100644 deal.II/doc/tutorial/chapter-2.step-by-step/step-17.data/step-17.12-grid.png create mode 100644 deal.II/doc/tutorial/chapter-2.step-by-step/step-17.data/step-17.12-partition.png create mode 100644 deal.II/doc/tutorial/chapter-2.step-by-step/step-17.data/step-17.12-ux.png create mode 100644 deal.II/doc/tutorial/chapter-2.step-by-step/step-17.data/step-17.12-uy.png create mode 100644 deal.II/doc/tutorial/chapter-2.step-by-step/step-17.data/step-17.4-3d-partition.png create mode 100644 deal.II/doc/tutorial/chapter-2.step-by-step/step-17.data/step-17.4-3d-ux.png diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-17.data/intro.html b/deal.II/doc/tutorial/chapter-2.step-by-step/step-17.data/intro.dox similarity index 96% rename from deal.II/doc/tutorial/chapter-2.step-by-step/step-17.data/intro.html rename to deal.II/doc/tutorial/chapter-2.step-by-step/step-17.data/intro.dox index 3921f1f19b..db168de9c3 100644 --- a/deal.II/doc/tutorial/chapter-2.step-by-step/step-17.data/intro.html +++ b/deal.II/doc/tutorial/chapter-2.step-by-step/step-17.data/intro.dox @@ -1,9 +1,9 @@

Introduction

-

+ This program does not introduce any new mathematical ideas; in fact, all it -does is to do the exact same computations that step-8 +does is to do the exact same computations that @ref step_8 "step-8" already does, but it does so in a different manner: instead of using deal.II's own linear algebra classes, we build everything on top of classes deal.II provides that wrap around the linear algebra implementation of the -

+ + As a prerequisite of this program, you need to have PETSc installed, and if you want to run in parallel on a cluster, you also need METIS to partition meshes. The installation of deal.II together with these two additional libraries is described in the README file. -

-

+ + Now, for the details: as mentioned, the program does not compute anything new, so the use of finite element classes etc. is exactly the same as before. The difference to previous programs is that we have replaced almost all uses of @@ -40,18 +40,18 @@ functionality themselves, they simply pass on to their corresponding PETSc functions. The wrappers are therefore only used to give PETSc a more modern, object oriented interface, and to make the use of PETSc and deal.II objects as interchangable as possible. -

-

+ + While the sequential PETSc wrappers classes do not have any advantage over their deal.II counterparts, the main point of using PETSc is that it can run in parallel. We will make use of this by partitioning the domain into as many blocks (``subdomains'') as there are processes in the MPI network. At the same time, PETSc provides dummy MPI stubs that allow to run the same program on a single machine if so desired, without any changes. -

-

+ + Note, however, that the only data structures we parallelize are matrices and vectors. We do, in particular, not split up the Triangulation and DoFHandler classes: each process still has a complete copy of @@ -62,12 +62,12 @@ present. It also requires that many more aspects of the application program have to be changed, since for example loops over all cells can only include locally available cells. We thus went for the path of least resistance and only parallelized the linear algebra part. -

-

+ + The techniques this program demonstrates are: how to use the PETSc wrapper classes; how to parallelize operations for jobs running on an MPI network; and how to partition the domain into subdomains to parallelize up the work. Since all this can only be demonstrated using actual code, let us go straight to the code without much further ado. -

+ diff --git a/deal.II/doc/tutorial/chapter-2.step-by-step/step-17.data/results.html b/deal.II/doc/tutorial/chapter-2.step-by-step/step-17.data/results.dox similarity index 89% rename from deal.II/doc/tutorial/chapter-2.step-by-step/step-17.data/results.html rename to deal.II/doc/tutorial/chapter-2.step-by-step/step-17.data/results.dox index b101786ad2..fbcf5be57c 100644 --- a/deal.II/doc/tutorial/chapter-2.step-by-step/step-17.data/results.html +++ b/deal.II/doc/tutorial/chapter-2.step-by-step/step-17.data/results.dox @@ -1,7 +1,7 @@

Results

-

+ If the program above is compiled and run on a single processor machine, it should generate results that are very similar to those that we already got with step-8. However, it becomes more interesting if we run it on a cluster of @@ -11,7 +11,7 @@ have different calling syntaxes - on my system, I have to use the command that the exact command line syntax varies. If you have found out how to run a job on your system, you should get output like this for a job on 8 processors, and with a few more refinement cycles than in the code above: -

+@code
 Cycle 0:
    Number of active cells:       64
    Number of degrees of freedom: 162 (by partition: 22+22+20+20+18+16+20+24)
@@ -81,10 +81,10 @@ Cycle 16:
    Number of degrees of freedom: 3771884 (by partition: 468452+474204+470818+470884+469960+
 471186+470686+475694)
    Solver converged in 2251 iterations.
-
-

+@endcode + + -

As can be seen, we can easily get to almost four million unknowns. In fact, the code's runtime with 8 processes was less than 7 minutes up to (and including) cycle 14, and 14 minutes including the second to last step. I lost the timing @@ -99,37 +99,28 @@ although matrices and vectors are split up. For the 7.1M computation, the memory consumption was about 600 bytes per unknown, which is not bad, but one has to consider that this is for every unknown, whether we store the matrix and vector entries locally or not. -

-

+ + Here is some output generated in the 12th cycle of the program, i.e. with roughly 300,000 unknowns: -

-

- ux - uy -

-

+@image html step-17.12-ux.png +@image html step-17.12-uy.png + + + As one would hope for, the x- (left) and y-displacements (right) shown here closely match what we already saw in step-8. What may be more interesting, though, is to look at the mesh and partition at this step (to see the picture in its original size, simply click on it): -

-

- grid - partition -

+@image html step-17.12-grid.png +@image html step-17.12-partition.png + -

Again, the mesh (left) shows the same refinement pattern as seen previously. The right panel shows the partitioning of the domain across the 8 processes, each indicated by a different color. The picture shows that the @@ -138,9 +129,9 @@ expected given that the partitioning algorithm tries to equilibrate the number of cells in each subdomain; this equilibration is also easily identified in the output shown above, where the number of degrees per subdomain is roughly the same. -

-

+ + It is worth noting that if we ran the same program with a different number of processes, that we would likely get slightly different output: a different mesh, different number of unknowns and iterations to convergence. The reason @@ -153,22 +144,22 @@ preconditioner leads to slight changes in the computed solution, this will then lead to slightly different mesh cells tagged for refinement, and larger differences in subsequent steps. The solution will always look very similar, though. -

-

+ + Finally, here are some results for a 3d simulation. You can repeat these by first changing -

+@code
         ElasticProblem<2> elastic_problem;
-
+@endcode to -
+@code
         ElasticProblem<3> elastic_problem;
-
+@endcode in the main function, and then in the Makefile, change the reference to the 2d libraries to their 3d counterparts. If you then run the program in parallel, you get something similar to this (this is for a job with 16 processes): -
+@code
 Cycle 0:
    Number of active cells:       512
    Number of degrees of freedom: 2187 (by partition: 114+156+150+114+114+210+105+102+120+120+96+123+141+183+156+183)
@@ -197,25 +188,21 @@ Cycle 6:
    Number of active cells:       461392
    Number of degrees of freedom: 1497951 (by partition: 103587+100827+97611+93726+93429+88074+95892+88296+96882+93000+87864+90915+92232+86931+98091+90594)
    Solver converged in 261 iterations.
-
-

+@endcode + + -

The last step, going up to 1.5 million unknowns, takes about 55 minutes with 16 processes on 8 dual-processor machines. The graphical output generated by this job is rather large (cycle 5 already prints around 82 MB of GMV data), so we contend ourselves with showing output from cycle 4 (again, clicking on the picture gives a version in original size): -

-

- uy - ux -

-

+@image html step-17.4-3d-partition.png +@image html step-17.4-3d-ux.png + + The left picture shows the partitioning of the cube into 16 processes, whereas the right one shows the x-displacement along two cutplanes through the cube. -

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