From fd74cc1a26103dc5b5240089539e1f5c240b5eb2 Mon Sep 17 00:00:00 2001 From: bangerth Date: Mon, 7 Oct 2013 03:42:41 +0000 Subject: [PATCH] Rewrite in parts. git-svn-id: https://svn.dealii.org/trunk@31161 0785d39b-7218-0410-832d-ea1e28bc413d --- deal.II/examples/step-42/doc/results.dox | 458 +++++++---------------- 1 file changed, 129 insertions(+), 329 deletions(-) diff --git a/deal.II/examples/step-42/doc/results.dox b/deal.II/examples/step-42/doc/results.dox index 8ed6a6087c..bcf94f5aca 100644 --- a/deal.II/examples/step-42/doc/results.dox +++ b/deal.II/examples/step-42/doc/results.dox @@ -1,10 +1,17 @@

Results

-Running the program (with a ball as obstacle) on 12 cores produces output like this: +The directory that contains this program contains a number of input +parameter files that can be used to create various different +simulations. For example, running the program with the +p1_adaptive.prm parameter file (using a ball as obstacle and the +box as domain) on 16 cores produces output like this: @code + Using output directory 'p1adaptive/' + FE degree 1 + transfer solution false + Cycle 0: - Number of active cells: 218 - Total number of cells: 249 + Number of active cells: 512 Number of degrees of freedom: 2187 Newton iteration 1 @@ -12,371 +19,149 @@ Cycle 0: Size of active set: 1 Assembling system... Solving system... - Error: 173.076 -> 0.157131 in 8 FGMRES iterations. - Number of elastic quadrature points: 4096 and plastic quadrature points: 0 - Residual of the non-contact part of the system: 0.157131 - with a damping parameter alpha = 1 + Error: 173.076 -> 3.06875e-07 in 8 Bicgstab iterations. + Accepting Newton solution with residual: 3.06875e-07 + Active set did not change! Newton iteration 2 Updating active set... Size of active set: 1 Assembling system... Solving system... - Error: 57.3852 -> 0.0426777 in 9 FGMRES iterations. - Number of elastic quadrature points: 3944 and plastic quadrature points: 152 - Residual of the non-contact part of the system: 24.9209 - with a damping parameter alpha = 1 + Error: 57.3622 -> 2.46266e-07 in 8 Bicgstab iterations. + Accepting Newton solution with residual: 24.9028 + Active set did not change! Newton iteration 3 Updating active set... Size of active set: 1 Assembling system... Solving system... - Error: 24.9209 -> 0.0157852 in 8 FGMRES iterations. - Number of elastic quadrature points: 3960 and plastic quadrature points: 136 - Residual of the non-contact part of the system: 1.63601 - with a damping parameter alpha = 1 - - Newton iteration 4 - Updating active set... - Size of active set: 1 - Assembling system... - Solving system... - Error: 1.63601 -> 0.00131281 in 8 FGMRES iterations. - Number of elastic quadrature points: 3960 and plastic quadrature points: 136 - Residual of the non-contact part of the system: 0.00479668 - with a damping parameter alpha = 1 - - Newton iteration 5 - Updating active set... - Size of active set: 1 - Assembling system... - Solving system... - Error: 0.00479668 -> 2.27976e-06 in 9 FGMRES iterations. - Number of elastic quadrature points: 3960 and plastic quadrature points: 136 - Residual of the non-contact part of the system: 2.29051e-06 + Error: 24.9028 -> 1.83021e-07 in 7 Bicgstab iterations. + Residual of the non-contact part of the system: 1.63333 with a damping parameter alpha = 1 - - Newton iteration 6 - Updating active set... - Size of active set: 1 - Assembling system... - Solving system... - Error: 2.29051e-06 -> 1.31066e-09 in 9 FGMRES iterations. - Number of elastic quadrature points: 3960 and plastic quadrature points: 136 - Residual of the non-contact part of the system: 1.31067e-09 - with a damping parameter alpha = 1 - - Number of assembled systems = 6 - Number of Solver-Iterations = 51 - Writing graphical output... - - -+---------------------------------------------+------------+------------+ -| Total wallclock time elapsed since start | 6.23s | | -| | | | -| Section | no. calls | wall time | % of total | -+---------------------------------+-----------+------------+------------+ -| Assembling | 6 | 0.859s | 14% | -| Graphical output | 1 | 0.22s | 3.5% | -| Residual and lambda | 6 | 0.189s | 3% | -| Setup | 1 | 0.265s | 4.3% | -| Setup: distribute DoFs | 1 | 0.0549s | 0.88% | -| Setup: matrix | 1 | 0.0142s | 0.23% | -| Solve | 6 | 4.51s | 72% | -| Solve: iterate | 6 | 1.79s | 29% | -| Solve: setup preconditioner | 6 | 2.7s | 43% | -| Update solution and constraints | 6 | 0.0246s | 0.4% | -+---------------------------------+-----------+------------+------------+ - + Active set did not change! -Cycle 1: - Number of active cells: 463 - Total number of cells: 529 - Number of degrees of freedom: 6294 +... - Newton iteration 1 - Updating active set... - Size of active set: 8 - Assembling system... - Solving system... - Error: 69.7055 -> 0.0512854 in 11 FGMRES iterations. - Number of elastic quadrature points: 11400 and plastic quadrature points: 984 - Residual of the non-contact part of the system: 16.4859 - with a damping parameter alpha = 1 - - Newton iteration 2 - Updating active set... - Size of active set: 9 - Assembling system... - Solving system... - Error: 142.778 -> 0.0754216 in 8 FGMRES iterations. - Number of elastic quadrature points: 11252 and plastic quadrature points: 1132 - Residual of the non-contact part of the system: 17.2965 - with a damping parameter alpha = 1 - - Newton iteration 3 - Updating active set... - Size of active set: 9 - Assembling system... - Solving system... - Error: 17.2965 -> 0.0126474 in 10 FGMRES iterations. - Number of elastic quadrature points: 11032 and plastic quadrature points: 1352 - Residual of the non-contact part of the system: 14.2312 - with a damping parameter alpha = 1 - - Newton iteration 4 - Updating active set... - Size of active set: 9 - Assembling system... - Solving system... - Error: 14.2312 -> 0.0130557 in 10 FGMRES iterations. - Number of elastic quadrature points: 11189 and plastic quadrature points: 1195 - Residual of the non-contact part of the system: 12.6684 - with a damping parameter alpha = 1 - - Newton iteration 5 + Newton iteration 6 Updating active set... - Size of active set: 9 - Assembling system... - Solving system... - Error: 12.6684 -> 0.00951713 in 10 FGMRES iterations. - Number of elastic quadrature points: 10987 and plastic quadrature points: 1397 - Residual of the non-contact part of the system: 13.9042 - with a damping parameter alpha = 1 - Number of elastic quadrature points: 11161 and plastic quadrature points: 1223 - Residual of the non-contact part of the system: 8.7982 - with a damping parameter alpha = 0.5 - - Newton iteration 6 - Updating active set... - Size of active set: 9 - Assembling system... - Solving system... - Error: 8.7982 -> 0.0057014 in 10 FGMRES iterations. - Number of elastic quadrature points: 11068 and plastic quadrature points: 1316 - Residual of the non-contact part of the system: 9.05367 - with a damping parameter alpha = 1 - Number of elastic quadrature points: 11160 and plastic quadrature points: 1224 - Residual of the non-contact part of the system: 4.7814 - with a damping parameter alpha = 0.5 - - Newton iteration 7 - Updating active set... - Size of active set: 9 - Assembling system... - Solving system... - Error: 4.7814 -> 0.00316863 in 10 FGMRES iterations. - Number of elastic quadrature points: 11152 and plastic quadrature points: 1232 - Residual of the non-contact part of the system: 1.71796 - with a damping parameter alpha = 1 - - Newton iteration 8 - Updating active set... - Size of active set: 9 - Assembling system... - Solving system... - Error: 1.71796 -> 0.00104906 in 7 FGMRES iterations. - Number of elastic quadrature points: 11144 and plastic quadrature points: 1240 - Residual of the non-contact part of the system: 0.013944 - with a damping parameter alpha = 1 - - Newton iteration 9 - Updating active set... - Size of active set: 9 - Assembling system... - Solving system... - Error: 0.013944 -> 1.26708e-05 in 11 FGMRES iterations. - Number of elastic quadrature points: 11144 and plastic quadrature points: 1240 - Residual of the non-contact part of the system: 1.38354e-05 - with a damping parameter alpha = 1 - - Newton iteration 10 - Updating active set... - Size of active set: 9 + Size of active set: 1 Assembling system... Solving system... - Error: 1.38354e-05 -> 7.16927e-09 in 14 FGMRES iterations. - Number of elastic quadrature points: 11144 and plastic quadrature points: 1240 - Residual of the non-contact part of the system: 7.16925e-09 + Error: 1.43188e-07 -> 4.61326e-16 in 8 Bicgstab iterations. + Residual of the non-contact part of the system: 5.67016e-14 with a damping parameter alpha = 1 - - Number of assembled systems = 10 - Number of Solver-Iterations = 101 - Writing graphical output... + Active set did not change! + Writing graphical output... p1adaptive/solution-00.pvtu +---------------------------------------------+------------+------------+ -| Total wallclock time elapsed since start | 12.1s | | +| Total wallclock time elapsed since start | 1.13s | | | | | | | Section | no. calls | wall time | % of total | +---------------------------------+-----------+------------+------------+ -| Assembling | 10 | 4.07s | 34% | -| Graphical output | 1 | 0.282s | 2.3% | -| Residual and lambda | 12 | 0.819s | 6.8% | -| Setup | 1 | 0.895s | 7.4% | -| Setup: distribute DoFs | 1 | 0.139s | 1.1% | -| Setup: matrix | 1 | 0.0272s | 0.22% | -| Setup: refine mesh | 1 | 0.579s | 4.8% | -| Solve | 10 | 5.68s | 47% | -| Solve: iterate | 10 | 3.44s | 28% | -| Solve: setup preconditioner | 10 | 2.18s | 18% | -| Update solution and constraints | 10 | 0.0952s | 0.79% | +| Assembling | 6 | 0.463s | 41% | +| Graphical output | 1 | 0.0257s | 2.3% | +| Residual and lambda | 4 | 0.0754s | 6.7% | +| Setup | 1 | 0.227s | 20% | +| Setup: constraints | 1 | 0.0347s | 3.1% | +| Setup: distribute DoFs | 1 | 0.0441s | 3.9% | +| Setup: matrix | 1 | 0.0119s | 1.1% | +| Setup: vectors | 1 | 0.00155s | 0.14% | +| Solve | 6 | 0.246s | 22% | +| Solve: iterate | 6 | 0.0631s | 5.6% | +| Solve: setup preconditioner | 6 | 0.167s | 15% | +| update active set | 6 | 0.0401s | 3.6% | +---------------------------------+-----------+------------+------------+ +Peak virtual memory used, resident in kB: 541884 77464 +Contact force = 37.3058 -Cycle 2: - Number of active cells: 1170 - Total number of cells: 1337 - Number of degrees of freedom: 18207 - - . - . - . - +... Cycle 3: - Number of active cells: 2955 - Total number of cells: 3377 + Number of active cells: 14652 Number of degrees of freedom: 52497 - - . - . - . - - -Cycle 4: - Number of active cells: 7400 - Total number of cells: 8457 - Number of degrees of freedom: 154647 - - . - . - . - - -Cycle 5: - Number of active cells: 19279 - Total number of cells: 22033 - Number of degrees of freedom: 461106 - - Newton iteration 1 - Updating active set... - Size of active set: 1672 - Assembling system... - Solving system... - Error: 3.36904 -> 0.00314153 in 28 FGMRES iterations. - Number of elastic quadrature points: 57144 and plastic quadrature points: 1065608 - Residual of the non-contact part of the system: 0.174753 - with a damping parameter alpha = 1 - Newton iteration 2 - Updating active set... - Size of active set: 2335 - Assembling system... - Solving system... - Error: 2.84616 -> 0.00266184 in 25 FGMRES iterations. - Number of elastic quadrature points: 56415 and plastic quadrature points: 1066337 - Residual of the non-contact part of the system: 0.0845109 - with a damping parameter alpha = 1 - - Newton iteration 3 - Updating active set... - Size of active set: 2313 - Assembling system... - Solving system... - Error: 0.0870898 -> 8.60248e-05 in 97 FGMRES iterations. - Number of elastic quadrature points: 56802 and plastic quadrature points: 1065950 - Residual of the non-contact part of the system: 0.0148214 - with a damping parameter alpha = 1 - - Newton iteration 4 + Newton iteration 1 Updating active set... - Size of active set: 2313 + Size of active set: 145 Assembling system... Solving system... - Error: 0.0148214 -> 1.46054e-05 in 72 FGMRES iterations. - Number of elastic quadrature points: 56828 and plastic quadrature points: 1065924 - Residual of the non-contact part of the system: 0.00125281 - with a damping parameter alpha = 1 + Error: 296.309 -> 2.45532e-06 in 9 Bicgstab iterations. + Accepting Newton solution with residual: 2.45532e-06 + Active set did not change! - Newton iteration 5 - Updating active set... - Size of active set: 2313 - Assembling system... - Solving system... - Error: 0.00125281 -> 1.22184e-06 in 68 FGMRES iterations. - Number of elastic quadrature points: 56828 and plastic quadrature points: 1065924 - Residual of the non-contact part of the system: 4.38909e-06 - with a damping parameter alpha = 1 - - Newton iteration 6 +... + + Newton iteration 10 Updating active set... - Size of active set: 2313 + Size of active set: 145 Assembling system... Solving system... - Error: 4.38909e-06 -> 4.30005e-09 in 189 FGMRES iterations. - Number of elastic quadrature points: 56828 and plastic quadrature points: 1065924 - Residual of the non-contact part of the system: 4.30364e-09 + Error: 2.71542e-07 -> 2.69366e-15 in 21 Bicgstab iterations. + Residual of the non-contact part of the system: 1.73713e-13 with a damping parameter alpha = 1 - - Number of assembled systems = 6 - Number of Solver-Iterations = 479 - Writing graphical output... + Active set did not change! + Writing graphical output... p1adaptive/solution-03.pvtu +---------------------------------------------+------------+------------+ -| Total wallclock time elapsed since start | 445s | | +| Total wallclock time elapsed since start | 38.4s | | | | | | | Section | no. calls | wall time | % of total | +---------------------------------+-----------+------------+------------+ -| Assembling | 6 | 218s | 49% | -| Graphical output | 1 | 4.47s | 1% | -| Residual and lambda | 6 | 31.9s | 7.2% | -| Setup | 1 | 33s | 7.4% | -| Setup: distribute DoFs | 1 | 4.69s | 1.1% | -| Setup: matrix | 1 | 1.29s | 0.29% | -| Setup: refine mesh | 1 | 22.4s | 5% | -| Solve | 6 | 154s | 35% | -| Solve: iterate | 6 | 145s | 33% | -| Solve: setup preconditioner | 6 | 9.12s | 2.1% | -| Update solution and constraints | 6 | 1.24s | 0.28% | +| Assembling | 10 | 22.5s | 58% | +| Graphical output | 1 | 0.327s | 0.85% | +| Residual and lambda | 9 | 3.75s | 9.8% | +| Setup | 1 | 4.83s | 13% | +| Setup: constraints | 1 | 0.578s | 1.5% | +| Setup: distribute DoFs | 1 | 0.71s | 1.8% | +| Setup: matrix | 1 | 0.111s | 0.29% | +| Setup: refine mesh | 1 | 4.83s | 13% | +| Setup: vectors | 1 | 0.00548s | 0.014% | +| Solve | 10 | 5.49s | 14% | +| Solve: iterate | 10 | 3.5s | 9.1% | +| Solve: setup preconditioner | 10 | 1.84s | 4.8% | +| update active set | 10 | 0.662s | 1.7% | +---------------------------------+-----------+------------+------------+ +Peak virtual memory used, resident in kB: 566052 105788 +Contact force = 56.794 + +... @endcode -For each adaptive refinement cycle the iterations end if the active set doesn't -change anymore and if the residual is accurate enough. In the tables -at the end of each cycle you find information about computing time and the -number of calls of different parts of the program like Assembling or calculating -the residual. In the second cycle there are 12 calls for the residual function -and only 10 calls for Solving or Assembling what means that two damping steps were -necessary in this cycle. +The tables at the end of each cycle show information about computing time +and the number of calls of different parts of the program like assembly or +calculating the residual, for the most recent mesh refinement cycle. Some of +the numbers above can be improved by transfering the solution from one mesh to +the next, an option we have not exercised here. -For this simulation we used the SolutionTranfer class to interpolate the solution -of the previous cycle to new mesh of the current cycle (for the start solution of cycle 0 -we used a pure elastic solution). That worked out well for the ball but for the -Chinese symbol as obstacle it turns out that an elastic start solution for each -cycle results in fewer Newton iterations. +In a typical run, you can observe that for every refinement step, the active +set - the contact points - are iterated out at first. After that the Newton +method has only to resolve the plasticity. For the finer meshes, +quadratic convergence can be observed for the last 4 or 5 Newton iterations. -In every refinement step you can observe that the active set - the contact points - -are iterated out at first. After that the Newton method has only to struggle with the -plasticity. For the finer meshes there is quadratic convergence not until the -last 4 or 5 Newton iterations. +We will not discuss here in all detail what happens with each of the input +files. Rather, let us just show pictures of the solution (the left half of the +domain is omitted if cells have zero quadrature points at which the plastic +inequality is active):
- + - +   - +
@@ -384,35 +169,50 @@ last 4 or 5 Newton iterations. The picture shows the adaptive refinement and as well how much a cell is plastified during the contact with the ball. Remember that we consider the norm of the deviator part of the stress in each quadrature point to -see if there is elastic or plastic behavior. In the middle of the top - -where the mesh is finest - you can see the hollow caused by the ball. The blue +see if there is elastic or plastic behavior. +The blue color means that this cell contains only elastic quadrature points in contrast to the red cells in which all quadrature points are plastified. -Since we used trilinear ansatz functions each cell contains eight -of these points which may or may not be elastic or plastic. -For further details see Frohne, Heister, Bangerth: Efficient -Numerical Methods For The Large-Scale, Parallel Solution Of Elastoplastic Contact -Problems, preprint. +In the middle of the top surface - +where the mesh is finest - a very close look shows the dimple caused by the +obstacle. This is the result of the move_mesh() +function. However, because the indentation of the obstacles we consider here +is so small, it is hard to discern this effect; one could play with displacing +vertices of the mesh by a multiple of the computed displacement. + +Further discussion of results that can be obtained using this program is +provided in the publication mentioned at the very top of this page.

Possibilities for extensions

-Extend the program from a static to a quasi-static problem, perhaps by choosing a -backward-Euler-scheme for the time discretization (for theoretical results see Frohne: FEM-Simulation -der Umformtechnik metallischer Oberflächen im Mikrokosmos, Ph.D. thesis, -University of Siegen, Germany, 2011). - -Like mentioned in step-41 it would be an interesting advance to consider a contact -problem with friction. In almost every mechanical process friction has a big influence. -For the modelling we have to take into account tangential stresses at the contact -surface. Also we have to observe that friction adds another nonlinearity to -our problem. - -If we simulate a frictional contact the next step to consider heat development -over the contact zone is not too far away. The heat that is caused by friction -between two bodies rises up the temperature in the deformable body and entails an -change of some material parameters. - -It might be of interest to implement more accurate, problem-adapted error +There are, as always, multiple possibilities for extending this program. From +an algorithmic perspective, this program goes about as far as one can at the +time of writing, using the best available algorithms for the contact +inequality, the plastic nonlinearity, and the linear solvers. However, there +are things one would like to do with this program as far as more realistic +situations are concerned: + -- 2.39.5