From 74831b5af83d231af4cd73f6f2d0d54f3a7e2f2d Mon Sep 17 00:00:00 2001 From: kronbichler Date: Wed, 20 Feb 2008 17:09:48 +0000 Subject: [PATCH] Some comments on the results, 2D output added. git-svn-id: https://svn.dealii.org/trunk@15749 0785d39b-7218-0410-832d-ea1e28bc413d --- deal.II/examples/step-31/doc/results.dox | 95 ++++++++++++++++++------ 1 file changed, 74 insertions(+), 21 deletions(-) diff --git a/deal.II/examples/step-31/doc/results.dox b/deal.II/examples/step-31/doc/results.dox index 3aa4674156..277f6705f1 100644 --- a/deal.II/examples/step-31/doc/results.dox +++ b/deal.II/examples/step-31/doc/results.dox @@ -1,12 +1,75 @@

Results

+

Output of the program and graphical visualization

+

2D calculations

+If we run the program in two dimensions, we get the following output: +@code +examples/step-31> make run +============================ Remaking Makefile.dep +==============optimized===== step-31.cc +============================ Linking step-31 +============================ Running step-31 +Refinement cycle 0 + Number of active cells: 64 + Number of degrees of freedom: 679 (594+85) + Assembling... + Computing preconditioner... + Solving... 11 outer CG Schur complement iterations for pressure +Refinement cycle 1 + Number of active cells: 160 + Number of degrees of freedom: 1683 (1482+201) + Assembling... + Computing preconditioner... + Solving... 11 outer CG Schur complement iterations for pressure + +Refinement cycle 2 + Number of active cells: 376 + Number of degrees of freedom: 3813 (3370+443) + Assembling... + Computing preconditioner... + Solving... 11 outer CG Schur complement iterations for pressure + +Refinement cycle 3 + Number of active cells: 880 + Number of degrees of freedom: 8723 (7722+1001) + Assembling... + Computing preconditioner... + Solving... 11 outer CG Schur complement iterations for pressure + +Refinement cycle 4 + Number of active cells: 2008 + Number of degrees of freedom: 19383 (17186+2197) + Assembling... + Computing preconditioner... + Solving... 11 outer CG Schur complement iterations for pressure +Refinement cycle 5 + Number of active cells: 4288 + Number of degrees of freedom: 40855 (36250+4605) + Assembling... + Computing preconditioner... + Solving... 11 outer CG Schur complement iterations for pressure +Refinement cycle 6 + Number of active cells: 8896 + Number of degrees of freedom: 83885 (74474+9411) + Assembling... + Computing preconditioner... + Solving... 11 outer CG Schur complement iterations for pressure +@endcode +Note that the number of (outer) iterations does not increase as we refine the +mesh. +In the images below, we show the grids for the first six steps in the program. +Note how the grid is refined in regions where the solution rapidly changes: On +the upper boundary, we have Dirichlet boundary conditions that are -1 in the +left half of the line and 1 in the right one, so there is an aprupt change at +x=0. Likewise, there are changes from Dirichlet to Neumann data in the two upper +corners, so the solution changes there as well. @@ -42,71 +105,61 @@ @image html step-31.2d.solution.png - - - - -Output in 3d: +

3D calculations

+The program now run in 3d: @code Refinement cycle 0 Number of active cells: 32 Number of degrees of freedom: 1356 (1275+81) Assembling... Computing preconditioner... - Solving... - 13 CG Schur complement iterations for pressure. + Solving... 13 outer CG Schur complement iterations for pressure. Refinement cycle 1 Number of active cells: 144 Number of degrees of freedom: 5088 (4827+261) Assembling... Computing preconditioner... - Solving... - 14 CG Schur complement iterations for pressure. + Solving... 14 outer CG Schur complement iterations for pressure. Refinement cycle 2 Number of active cells: 704 Number of degrees of freedom: 22406 (21351+1055) Assembling... Computing preconditioner... - Solving... - 14 CG Schur complement iterations for pressure. + Solving... 14 outer CG Schur complement iterations for pressure. Refinement cycle 3 Number of active cells: 3168 Number of degrees of freedom: 93176 (89043+4133) Assembling... Computing preconditioner... - Solving... - 15 CG Schur complement iterations for pressure. + Solving... 15 outer CG Schur complement iterations for pressure. Refinement cycle 4 Number of active cells: 11456 Number of degrees of freedom: 327808 (313659+14149) Assembling... Computing preconditioner... - Solving... - 15 CG Schur complement iterations for pressure. + Solving... 15 outer CG Schur complement iterations for pressure. Refinement cycle 5 Number of active cells: 45056 Number of degrees of freedom: 1254464 (1201371+53093) Assembling... Computing preconditioner... - Solving... - 14 CG Schur complement iterations for pressure. + Solving... 14 outer CG Schur complement iterations for pressure. Refinement cycle 6 Number of active cells: 170720 Number of degrees of freedom: 4625150 (4432407+192743) Assembling... Computing preconditioner... - Solving... - 15 CG Schur complement iterations for pressure. + Solving... 15 outer CG Schur complement iterations for pressure. @endcode -Note that the number of (outer) iterations does not increase as we refine the -mesh. +Note again that the number of iterations does not increase as we refine +the mesh. Compute times for each iteration alone: seconds, seconds, 1 minute, 5 minutes, 29 minutes, 3h12, 21h39 -- 2.39.5