Total number of cells: 249
Number of degrees of freedom: 2187
- Newton iteration 0
+ Newton iteration 1
Updating active set...
Size of active set: 1
Assembling system...
Residual of the non-contact part of the system: 0.157131
with a damping parameter alpha = 1
- Newton iteration 1
+ Newton iteration 2
Updating active set...
Size of active set: 1
Assembling system...
Residual of the non-contact part of the system: 24.9209
with a damping parameter alpha = 1
- Newton iteration 2
+ Newton iteration 3
Updating active set...
Size of active set: 1
Assembling system...
Residual of the non-contact part of the system: 1.63601
with a damping parameter alpha = 1
- Newton iteration 3
+ Newton iteration 4
Updating active set...
Size of active set: 1
Assembling system...
Residual of the non-contact part of the system: 0.00479668
with a damping parameter alpha = 1
- Newton iteration 4
+ Newton iteration 5
Updating active set...
Size of active set: 1
Assembling system...
Residual of the non-contact part of the system: 2.29051e-06
with a damping parameter alpha = 1
- Newton iteration 5
+ 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: 1.31066e-09
+ Residual of the non-contact part of the system: 1.31067e-09
with a damping parameter alpha = 1
Number of assembled systems = 6
+---------------------------------------------+------------+------------+
-| Total wallclock time elapsed since start | 0.736s | |
+| Total wallclock time elapsed since start | 6.23s | |
| | | |
| Section | no. calls | wall time | % of total |
+---------------------------------+-----------+------------+------------+
-| Assembling | 6 | 0.0779s | 11% |
-| Graphical output | 1 | 0.219s | 30% |
-| Mesh refinement and setup system| 1 | 0.0274s | 3.7% |
-| Preconditioning | 6 | 0.147s | 20% |
-| Residual and lambda | 6 | 0.0167s | 2.3% |
-| Solving | 6 | 0.0365s | 5% |
-| Solving and Preconditioning | 6 | 0.197s | 27% |
-| Update solution and constraints | 6 | 0.0154s | 2.1% |
+| 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% |
+---------------------------------+-----------+------------+------------+
Number of active cells: 463
Total number of cells: 529
Number of degrees of freedom: 6294
-
- Newton iteration 0
- Updating active set...
- Size of active set: 9
- Assembling system...
- Solving system...
- Error: 254.373 -> 0.190863 in 9 FGMRES iterations.
- Number of elastic quadrature points: 12384 and plastic quadrature points: 0
- Residual of the non-contact part of the system: 0.190863
- with a damping parameter alpha = 1
-
+
Newton iteration 1
Updating active set...
- Size of active set: 9
+ Size of active set: 8
Assembling system...
Solving system...
- Error: 43.8161 -> 0.0315499 in 12 FGMRES iterations.
- Number of elastic quadrature points: 11092 and plastic quadrature points: 1292
- Residual of the non-contact part of the system: 24.5462
+ 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
Size of active set: 9
Assembling system...
Solving system...
- Error: 24.5462 -> 0.0222984 in 11 FGMRES iterations.
- Number of elastic quadrature points: 11152 and plastic quadrature points: 1232
- Residual of the non-contact part of the system: 5.47753
+ 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
Size of active set: 9
Assembling system...
Solving system...
- Error: 5.47753 -> 0.00277991 in 11 FGMRES iterations.
- Number of elastic quadrature points: 11160 and plastic quadrature points: 1224
- Residual of the non-contact part of the system: 1.21575
+ 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
Size of active set: 9
Assembling system...
Solving system...
- Error: 1.21575 -> 0.00104015 in 9 FGMRES iterations.
- Number of elastic quadrature points: 11144 and plastic quadrature points: 1240
- Residual of the non-contact part of the system: 0.0594461
+ 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
Size of active set: 9
Assembling system...
Solving system...
- Error: 0.0594461 -> 2.73182e-05 in 10 FGMRES iterations.
- Number of elastic quadrature points: 11144 and plastic quadrature points: 1240
- Residual of the non-contact part of the system: 5.50309e-05
+ 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: 5.50309e-05 -> 2.99676e-08 in 13 FGMRES iterations.
- Number of elastic quadrature points: 11144 and plastic quadrature points: 1240
- Residual of the non-contact part of the system: 2.99656e-08
+ 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: 2.99656e-08 -> 1.70821e-11 in 14 FGMRES iterations.
- Number of elastic quadrature points: 11144 and plastic quadrature points: 1240
- Residual of the non-contact part of the system: 1.70843e-11
- with a damping parameter alpha = 1
-
- Number of assembled systems = 8
- Number of Solver-Iterations = 89
- Writing graphical output...
-
-
-+---------------------------------------------+------------+------------+
-| Total wallclock time elapsed since start | 1.89s | |
-| | | |
-| Section | no. calls | wall time | % of total |
-+---------------------------------+-----------+------------+------------+
-| Assembling | 14 | 0.354s | 19% |
-| Graphical output | 2 | 0.394s | 21% |
-| Mesh refinement and setup system| 2 | 0.109s | 5.8% |
-| Preconditioning | 14 | 0.302s | 16% |
-| Residual and lambda | 14 | 0.0587s | 3.1% |
-| Solving | 14 | 0.142s | 7.6% |
-| Solving and Preconditioning | 14 | 0.48s | 25% |
-| Update solution and constraints | 14 | 0.0452s | 2.4% |
-+---------------------------------+-----------+------------+------------+
-
-
-Cycle 2:
- Number of active cells: 1170
- Total number of cells: 1337
- Number of degrees of freedom: 18207
-
- Newton iteration 0
- Updating active set...
- Size of active set: 37
- Assembling system...
- Solving system...
- Error: 284.124 -> 0.219038 in 12 FGMRES iterations.
- Number of elastic quadrature points: 38144 and plastic quadrature points: 0
- Residual of the non-contact part of the system: 0.219038
- with a damping parameter alpha = 1
-
- Newton iteration 1
- Updating active set...
- Size of active set: 25
- Assembling system...
- Solving system...
- Error: 29.3138 -> 0.0233274 in 18 FGMRES iterations.
- Number of elastic quadrature points: 26802 and plastic quadrature points: 11342
- Residual of the non-contact part of the system: 18.6169
- with a damping parameter alpha = 1
-
- Newton iteration 2
- Updating active set...
- Size of active set: 37
- Assembling system...
- Solving system...
- Error: 40.4533 -> 0.0289656 in 17 FGMRES iterations.
- Number of elastic quadrature points: 26314 and plastic quadrature points: 11830
- Residual of the non-contact part of the system: 13.0957
- with a damping parameter alpha = 1
-
- Newton iteration 3
- Updating active set...
- Size of active set: 37
- Assembling system...
- Solving system...
- Error: 13.0957 -> 0.00985332 in 18 FGMRES iterations.
- Number of elastic quadrature points: 27074 and plastic quadrature points: 11070
- Residual of the non-contact part of the system: 13.4255
- with a damping parameter alpha = 1
- Number of elastic quadrature points: 30111 and plastic quadrature points: 8033
- Residual of the non-contact part of the system: 4.53997
- with a damping parameter alpha = 0.5
-
- Newton iteration 4
- Updating active set...
- Size of active set: 37
- Assembling system...
- Solving system...
- Error: 4.53997 -> 0.00288706 in 16 FGMRES iterations.
- Number of elastic quadrature points: 29624 and plastic quadrature points: 8520
- Residual of the non-contact part of the system: 0.376174
- with a damping parameter alpha = 1
-
- Newton iteration 5
- Updating active set...
- Size of active set: 37
- Assembling system...
- Solving system...
- Error: 0.376174 -> 0.000319472 in 15 FGMRES iterations.
- Number of elastic quadrature points: 29500 and plastic quadrature points: 8644
- Residual of the non-contact part of the system: 0.0174717
+ 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 6
+ Newton iteration 8
Updating active set...
- Size of active set: 37
+ Size of active set: 9
Assembling system...
Solving system...
- Error: 0.0174717 -> 1.41647e-05 in 17 FGMRES iterations.
- Number of elastic quadrature points: 29512 and plastic quadrature points: 8632
- Residual of the non-contact part of the system: 6.13152e-05
+ 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 7
+ Newton iteration 9
Updating active set...
- Size of active set: 37
+ Size of active set: 9
Assembling system...
Solving system...
- Error: 6.13152e-05 -> 5.43905e-08 in 20 FGMRES iterations.
- Number of elastic quadrature points: 29512 and plastic quadrature points: 8632
- Residual of the non-contact part of the system: 5.4391e-08
+ 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 8
+ Newton iteration 10
Updating active set...
- Size of active set: 37
+ Size of active set: 9
Assembling system...
Solving system...
- Error: 5.4391e-08 -> 4.00879e-11 in 22 FGMRES iterations.
- Number of elastic quadrature points: 29512 and plastic quadrature points: 8632
- Residual of the non-contact part of the system: 4.0089e-11
+ 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
with a damping parameter alpha = 1
- Number of assembled systems = 9
- Number of Solver-Iterations = 155
+ Number of assembled systems = 10
+ Number of Solver-Iterations = 101
Writing graphical output...
+---------------------------------------------+------------+------------+
-| Total wallclock time elapsed since start | 4.76s | |
+| Total wallclock time elapsed since start | 12.1s | |
| | | |
| Section | no. calls | wall time | % of total |
+---------------------------------+-----------+------------+------------+
-| Assembling | 23 | 1.24s | 26% |
-| Graphical output | 3 | 0.61s | 13% |
-| Mesh refinement and setup system| 3 | 0.215s | 4.5% |
-| Preconditioning | 23 | 0.651s | 14% |
-| Residual and lambda | 24 | 0.19s | 4% |
-| Solving | 23 | 0.513s | 11% |
-| Solving and Preconditioning | 23 | 1.24s | 26% |
-| Update solution and constraints | 23 | 0.104s | 2.2% |
+| 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% |
+---------------------------------+-----------+------------+------------+
+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 degrees of freedom: 52497
-
- Newton iteration 0
- Updating active set...
- Size of active set: 145
- Assembling system...
- Solving system...
- Error: 296.309 -> 0.274641 in 16 FGMRES iterations.
- Number of elastic quadrature points: 117216 and plastic quadrature points: 0
- Residual of the non-contact part of the system: 0.274641
- with a damping parameter alpha = 1
-
- Newton iteration 1
- Updating active set...
- Size of active set: 101
- Assembling system...
- Solving system...
- Error: 16.3381 -> 0.0141064 in 28 FGMRES iterations.
- Number of elastic quadrature points: 43467 and plastic quadrature points: 73749
- Residual of the non-contact part of the system: 16.0978
- with a damping parameter alpha = 1
-
- Newton iteration 2
- Updating active set...
- Size of active set: 169
- Assembling system...
- Solving system...
- Error: 37.9212 -> 0.0359077 in 23 FGMRES iterations.
- Number of elastic quadrature points: 49376 and plastic quadrature points: 67840
- Residual of the non-contact part of the system: 13.2713
- with a damping parameter alpha = 1
-
- Newton iteration 3
- Updating active set...
- Size of active set: 145
- Assembling system...
- Solving system...
- Error: 13.2966 -> 0.0122436 in 31 FGMRES iterations.
- Number of elastic quadrature points: 39170 and plastic quadrature points: 78046
- Residual of the non-contact part of the system: 15.8407
- with a damping parameter alpha = 1
- Number of elastic quadrature points: 57541 and plastic quadrature points: 59675
- Residual of the non-contact part of the system: 5.37003
- with a damping parameter alpha = 0.5
-
- Newton iteration 4
- Updating active set...
- Size of active set: 153
- Assembling system...
- Solving system...
- Error: 5.37242 -> 0.00503175 in 21 FGMRES iterations.
- Number of elastic quadrature points: 53138 and plastic quadrature points: 64078
- Residual of the non-contact part of the system: 1.91646
- with a damping parameter alpha = 1
-
- Newton iteration 5
- Updating active set...
- Size of active set: 145
- Assembling system...
- Solving system...
- Error: 1.9277 -> 0.00180035 in 25 FGMRES iterations.
- Number of elastic quadrature points: 52162 and plastic quadrature points: 65054
- Residual of the non-contact part of the system: 1.12614
- with a damping parameter alpha = 1
-
- Newton iteration 6
- Updating active set...
- Size of active set: 145
- Assembling system...
- Solving system...
- Error: 1.12614 -> 0.000885797 in 19 FGMRES iterations.
- Number of elastic quadrature points: 51667 and plastic quadrature points: 65549
- Residual of the non-contact part of the system: 0.817432
- with a damping parameter alpha = 1
-
- Newton iteration 7
- Updating active set...
- Size of active set: 145
- Assembling system...
- Solving system...
- Error: 0.817432 -> 0.000802786 in 20 FGMRES iterations.
- Number of elastic quadrature points: 51659 and plastic quadrature points: 65557
- Residual of the non-contact part of the system: 0.557455
- with a damping parameter alpha = 1
-
- Newton iteration 8
- Updating active set...
- Size of active set: 145
- Assembling system...
- Solving system...
- Error: 0.557455 -> 0.000527895 in 18 FGMRES iterations.
- Number of elastic quadrature points: 51572 and plastic quadrature points: 65644
- Residual of the non-contact part of the system: 0.235355
- with a damping parameter alpha = 1
-
- Newton iteration 9
- Updating active set...
- Size of active set: 145
- Assembling system...
- Solving system...
- Error: 0.235355 -> 0.000197953 in 23 FGMRES iterations.
- Number of elastic quadrature points: 51482 and plastic quadrature points: 65734
- Residual of the non-contact part of the system: 0.0275413
- with a damping parameter alpha = 1
-
- Newton iteration 10
- Updating active set...
- Size of active set: 145
- Assembling system...
- Solving system...
- Error: 0.0275413 -> 2.37996e-05 in 25 FGMRES iterations.
- Number of elastic quadrature points: 51464 and plastic quadrature points: 65752
- Residual of the non-contact part of the system: 0.000526512
- with a damping parameter alpha = 1
-
- Newton iteration 11
- Updating active set...
- Size of active set: 145
- Assembling system...
- Solving system...
- Error: 0.000526512 -> 4.98197e-07 in 27 FGMRES iterations.
- Number of elastic quadrature points: 51464 and plastic quadrature points: 65752
- Residual of the non-contact part of the system: 5.35391e-07
- with a damping parameter alpha = 1
-
- Newton iteration 12
- Updating active set...
- Size of active set: 145
- Assembling system...
- Solving system...
- Error: 5.35391e-07 -> 5.141e-10 in 45 FGMRES iterations.
- Number of elastic quadrature points: 51464 and plastic quadrature points: 65752
- Residual of the non-contact part of the system: 5.14106e-10
- with a damping parameter alpha = 1
- Number of assembled systems = 13
- Number of Solver-Iterations = 321
- Writing graphical output...
-
-
-+---------------------------------------------+------------+------------+
-| Total wallclock time elapsed since start | 18.6s | |
-| | | |
-| Section | no. calls | wall time | % of total |
-+---------------------------------+-----------+------------+------------+
-| Assembling | 36 | 5.02s | 27% |
-| Graphical output | 4 | 1.02s | 5.5% |
-| Mesh refinement and setup system| 4 | 0.453s | 2.4% |
-| Preconditioning | 36 | 1.94s | 10% |
-| Residual and lambda | 38 | 0.682s | 3.7% |
-| Solving | 36 | 3.57s | 19% |
-| Solving and Preconditioning | 36 | 5.68s | 30% |
-| Update solution and constraints | 36 | 0.254s | 1.4% |
-+---------------------------------+-----------+------------+------------+
+ .
+ .
+ .
Cycle 4:
Number of active cells: 7400
Total number of cells: 8457
Number of degrees of freedom: 154647
-
- Newton iteration 0
- Updating active set...
- Size of active set: 609
- Assembling system...
- Solving system...
- Error: 299.883 -> 0.198142 in 22 FGMRES iterations.
- Number of elastic quadrature points: 362944 and plastic quadrature points: 0
- Residual of the non-contact part of the system: 0.198142
- with a damping parameter alpha = 1
-
- Newton iteration 1
- Updating active set...
- Size of active set: 437
- Assembling system...
- Solving system...
- Error: 10.4425 -> 0.00864082 in 54 FGMRES iterations.
- Number of elastic quadrature points: 50243 and plastic quadrature points: 312701
- Residual of the non-contact part of the system: 13.0573
- with a damping parameter alpha = 1
-
- Newton iteration 2
- Updating active set...
- Size of active set: 629
- Assembling system...
- Solving system...
- Error: 25.4296 -> 0.0250775 in 32 FGMRES iterations.
- Number of elastic quadrature points: 52693 and plastic quadrature points: 310251
- Residual of the non-contact part of the system: 4.31469
- with a damping parameter alpha = 1
-
- Newton iteration 3
- Updating active set...
- Size of active set: 609
- Assembling system...
- Solving system...
- Error: 4.42111 -> 0.0042128 in 29 FGMRES iterations.
- Number of elastic quadrature points: 53842 and plastic quadrature points: 309102
- Residual of the non-contact part of the system: 3.2446
- with a damping parameter alpha = 1
-
- Newton iteration 4
- Updating active set...
- Size of active set: 593
- Assembling system...
- Solving system...
- Error: 3.2476 -> 0.00316464 in 29 FGMRES iterations.
- Number of elastic quadrature points: 53576 and plastic quadrature points: 309368
- Residual of the non-contact part of the system: 2.71394
- with a damping parameter alpha = 1
-
- Newton iteration 5
- Updating active set...
- Size of active set: 579
- Assembling system...
- Solving system...
- Error: 2.71408 -> 0.00247937 in 27 FGMRES iterations.
- Number of elastic quadrature points: 53936 and plastic quadrature points: 309008
- Residual of the non-contact part of the system: 2.42929
- with a damping parameter alpha = 1
-
- Newton iteration 6
- Updating active set...
- Size of active set: 579
- Assembling system...
- Solving system...
- Error: 2.42929 -> 0.00234882 in 29 FGMRES iterations.
- Number of elastic quadrature points: 53201 and plastic quadrature points: 309743
- Residual of the non-contact part of the system: 2.52783
- with a damping parameter alpha = 1
- Number of elastic quadrature points: 54507 and plastic quadrature points: 308437
- Residual of the non-contact part of the system: 1.22978
- with a damping parameter alpha = 0.5
-
- Newton iteration 7
- Updating active set...
- Size of active set: 585
- Assembling system...
- Solving system...
- Error: 1.23087 -> 0.00117414 in 27 FGMRES iterations.
- Number of elastic quadrature points: 53932 and plastic quadrature points: 309012
- Residual of the non-contact part of the system: 0.913556
- with a damping parameter alpha = 1
-
- Newton iteration 8
- Updating active set...
- Size of active set: 585
- Assembling system...
- Solving system...
- Error: 0.913556 -> 0.000846686 in 29 FGMRES iterations.
- Number of elastic quadrature points: 53676 and plastic quadrature points: 309268
- Residual of the non-contact part of the system: 0.608655
- with a damping parameter alpha = 1
-
- Newton iteration 9
- Updating active set...
- Size of active set: 585
- Assembling system...
- Solving system...
- Error: 0.608915 -> 0.000590468 in 36 FGMRES iterations.
- Number of elastic quadrature points: 53769 and plastic quadrature points: 309175
- Residual of the non-contact part of the system: 0.572935
- with a damping parameter alpha = 1
-
- Newton iteration 10
- Updating active set...
- Size of active set: 585
- Assembling system...
- Solving system...
- Error: 0.574492 -> 0.000516963 in 41 FGMRES iterations.
- Number of elastic quadrature points: 53419 and plastic quadrature points: 309525
- Residual of the non-contact part of the system: 0.575742
- with a damping parameter alpha = 1
- Number of elastic quadrature points: 53568 and plastic quadrature points: 309376
- Residual of the non-contact part of the system: 0.351537
- with a damping parameter alpha = 0.5
-
- Newton iteration 11
- Updating active set...
- Size of active set: 585
- Assembling system...
- Solving system...
- Error: 0.351691 -> 0.000350487 in 32 FGMRES iterations.
- Number of elastic quadrature points: 53596 and plastic quadrature points: 309348
- Residual of the non-contact part of the system: 0.498347
- with a damping parameter alpha = 1
- Number of elastic quadrature points: 53574 and plastic quadrature points: 309370
- Residual of the non-contact part of the system: 0.287064
- with a damping parameter alpha = 0.5
-
- Newton iteration 12
- Updating active set...
- Size of active set: 585
- Assembling system...
- Solving system...
- Error: 0.287174 -> 0.000275609 in 32 FGMRES iterations.
- Number of elastic quadrature points: 53675 and plastic quadrature points: 309269
- Residual of the non-contact part of the system: 0.248843
- with a damping parameter alpha = 1
-
- Newton iteration 13
- Updating active set...
- Size of active set: 585
- Assembling system...
- Solving system...
- Error: 0.248843 -> 0.000232694 in 29 FGMRES iterations.
- Number of elastic quadrature points: 53682 and plastic quadrature points: 309262
- Residual of the non-contact part of the system: 0.341443
- with a damping parameter alpha = 1
- Number of elastic quadrature points: 53686 and plastic quadrature points: 309258
- Residual of the non-contact part of the system: 0.232367
- with a damping parameter alpha = 0.5
-
- Newton iteration 14
- Updating active set...
- Size of active set: 585
- Assembling system...
- Solving system...
- Error: 0.232367 -> 0.000231641 in 35 FGMRES iterations.
- Number of elastic quadrature points: 53691 and plastic quadrature points: 309253
- Residual of the non-contact part of the system: 0.263644
- with a damping parameter alpha = 1
- Number of elastic quadrature points: 53694 and plastic quadrature points: 309250
- Residual of the non-contact part of the system: 0.185686
- with a damping parameter alpha = 0.5
-
- Newton iteration 15
- Updating active set...
- Size of active set: 585
- Assembling system...
- Solving system...
- Error: 0.185686 -> 0.000171579 in 29 FGMRES iterations.
- Number of elastic quadrature points: 53721 and plastic quadrature points: 309223
- Residual of the non-contact part of the system: 0.273968
- with a damping parameter alpha = 1
- Number of elastic quadrature points: 53726 and plastic quadrature points: 309218
- Residual of the non-contact part of the system: 0.189887
- with a damping parameter alpha = 0.5
- Number of elastic quadrature points: 53713 and plastic quadrature points: 309231
- Residual of the non-contact part of the system: 0.0832966
- with a damping parameter alpha = 0.25
-
- Newton iteration 16
- Updating active set...
- Size of active set: 585
- Assembling system...
- Solving system...
- Error: 0.0832966 -> 8.32624e-05 in 38 FGMRES iterations.
- Number of elastic quadrature points: 53749 and plastic quadrature points: 309195
- Residual of the non-contact part of the system: 0.0306643
- with a damping parameter alpha = 1
-
- Newton iteration 17
- Updating active set...
- Size of active set: 585
- Assembling system...
- Solving system...
- Error: 0.0306643 -> 3.01898e-05 in 38 FGMRES iterations.
- Number of elastic quadrature points: 53766 and plastic quadrature points: 309178
- Residual of the non-contact part of the system: 0.00261731
- with a damping parameter alpha = 1
-
- Newton iteration 18
- Updating active set...
- Size of active set: 585
- Assembling system...
- Solving system...
- Error: 0.00261731 -> 2.33193e-06 in 51 FGMRES iterations.
- Number of elastic quadrature points: 53768 and plastic quadrature points: 309176
- Residual of the non-contact part of the system: 4.64159e-05
- with a damping parameter alpha = 1
-
- Newton iteration 19
- Updating active set...
- Size of active set: 585
- Assembling system...
- Solving system...
- Error: 4.64159e-05 -> 4.62653e-08 in 62 FGMRES iterations.
- Number of elastic quadrature points: 53768 and plastic quadrature points: 309176
- Residual of the non-contact part of the system: 5.07264e-08
- with a damping parameter alpha = 1
-
- Newton iteration 20
- Updating active set...
- Size of active set: 585
- Assembling system...
- Solving system...
- Error: 5.07264e-08 -> 4.59618e-11 in 111 FGMRES iterations.
- Number of elastic quadrature points: 53768 and plastic quadrature points: 309176
- Residual of the non-contact part of the system: 4.59615e-11
- with a damping parameter alpha = 1
-
- Number of assembled systems = 21
- Number of Solver-Iterations = 812
- Writing graphical output...
-
-+---------------------------------------------+------------+------------+
-| Total wallclock time elapsed since start | 131s | |
-| | | |
-| Section | no. calls | wall time | % of total |
-+---------------------------------+-----------+------------+------------+
-| Assembling | 57 | 23.5s | 18% |
-| Graphical output | 5 | 2.34s | 1.8% |
-| Mesh refinement and setup system| 5 | 1.07s | 0.82% |
-| Preconditioning | 57 | 8.46s | 6.5% |
-| Residual and lambda | 66 | 3.61s | 2.8% |
-| Solving | 57 | 41s | 31% |
-| Solving and Preconditioning | 57 | 50s | 38% |
-| Update solution and constraints | 57 | 0.736s | 0.56% |
-+---------------------------------+-----------+------------+------------+
+ .
+ .
+ .
Cycle 5:
Number of active cells: 19279
Total number of cells: 22033
Number of degrees of freedom: 461106
-
- Newton iteration 0
- Updating active set...
- Size of active set: 2449
- Assembling system...
- Solving system...
- Error: 300.845 -> 0.249318 in 28 FGMRES iterations.
- Number of elastic quadrature points: 1122752 and plastic quadrature points: 0
- Residual of the non-contact part of the system: 0.249318
- with a damping parameter alpha = 1
-
+
Newton iteration 1
Updating active set...
- Size of active set: 1863
+ Size of active set: 1672
Assembling system...
Solving system...
- Error: 6.17714 -> 0.0061549 in 82 FGMRES iterations.
- Number of elastic quadrature points: 53510 and plastic quadrature points: 1069242
- Residual of the non-contact part of the system: 10.188
+ 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: 2348
+ Size of active set: 2335
Assembling system...
Solving system...
- Error: 15.5579 -> 0.0151548 in 41 FGMRES iterations.
- Number of elastic quadrature points: 54822 and plastic quadrature points: 1067930
- Residual of the non-contact part of the system: 1.5258
+ 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: 2485
- Assembling system...
- Solving system...
- Error: 3.2747 -> 0.00308114 in 55 FGMRES iterations.
- Number of elastic quadrature points: 61107 and plastic quadrature points: 1061645
- Residual of the non-contact part of the system: 0.816662
- with a damping parameter alpha = 1
-
- Newton iteration 4
- Updating active set...
- Size of active set: 2294
- Assembling system...
- Solving system...
- Error: 0.846485 -> 0.000840713 in 105 FGMRES iterations.
- Number of elastic quadrature points: 54660 and plastic quadrature points: 1068092
- Residual of the non-contact part of the system: 0.651754
- with a damping parameter alpha = 1
-
- Newton iteration 5
- Updating active set...
- Size of active set: 2375
- Assembling system...
- Solving system...
- Error: 1.07345 -> 0.0010383 in 95 FGMRES iterations.
- Number of elastic quadrature points: 59982 and plastic quadrature points: 1062770
- Residual of the non-contact part of the system: 0.81415
- with a damping parameter alpha = 1
- Number of elastic quadrature points: 57363 and plastic quadrature points: 1065389
- Residual of the non-contact part of the system: 0.432614
- with a damping parameter alpha = 0.5
-
- Newton iteration 6
- Updating active set...
- Size of active set: 2294
- Assembling system...
- Solving system...
- Error: 0.600941 -> 0.000577431 in 51 FGMRES iterations.
- Number of elastic quadrature points: 56754 and plastic quadrature points: 1065998
- Residual of the non-contact part of the system: 0.434547
- with a damping parameter alpha = 1
- Number of elastic quadrature points: 57005 and plastic quadrature points: 1065747
- Residual of the non-contact part of the system: 0.209227
- with a damping parameter alpha = 0.5
-
- Newton iteration 7
- Updating active set...
- Size of active set: 2327
- Assembling system...
- Solving system...
- Error: 0.299306 -> 0.00029369 in 66 FGMRES iterations.
- Number of elastic quadrature points: 56775 and plastic quadrature points: 1065977
- Residual of the non-contact part of the system: 0.0890688
- with a damping parameter alpha = 1
-
- Newton iteration 8
- Updating active set...
- Size of active set: 2317
- Assembling system...
- Solving system...
- Error: 0.113493 -> 0.000112941 in 65 FGMRES iterations.
- Number of elastic quadrature points: 56792 and plastic quadrature points: 1065960
- Residual of the non-contact part of the system: 0.0846807
- with a damping parameter alpha = 1
-
- Newton iteration 9
- Updating active set...
- Size of active set: 2311
- Assembling system...
- Solving system...
- Error: 0.0847051 -> 8.37451e-05 in 38 FGMRES iterations.
- Number of elastic quadrature points: 56797 and plastic quadrature points: 1065955
- Residual of the non-contact part of the system: 0.0892047
- with a damping parameter alpha = 1
- Number of elastic quadrature points: 56793 and plastic quadrature points: 1065959
- Residual of the non-contact part of the system: 0.0226437
- with a damping parameter alpha = 0.5
-
- Newton iteration 10
Updating active set...
Size of active set: 2313
Assembling system...
Solving system...
- Error: 0.0240356 -> 2.37508e-05 in 72 FGMRES iterations.
- Number of elastic quadrature points: 56816 and plastic quadrature points: 1065936
- Residual of the non-contact part of the system: 0.00540846
+ 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 11
+ Newton iteration 4
Updating active set...
Size of active set: 2313
Assembling system...
Solving system...
- Error: 0.00540846 -> 5.39193e-06 in 62 FGMRES iterations.
+ 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: 0.000268289
+ Residual of the non-contact part of the system: 0.00125281
with a damping parameter alpha = 1
- Newton iteration 12
+ Newton iteration 5
Updating active set...
Size of active set: 2313
Assembling system...
Solving system...
- Error: 0.000268289 -> 2.64338e-07 in 83 FGMRES iterations.
+ 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: 8.91195e-07
+ Residual of the non-contact part of the system: 4.38909e-06
with a damping parameter alpha = 1
-
- Newton iteration 13
+
+ Newton iteration 6
Updating active set...
Size of active set: 2313
Assembling system...
Solving system...
- Error: 8.91195e-07 -> 8.85869e-10 in 255 FGMRES iterations.
+ 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: 8.86261e-10
+ Residual of the non-contact part of the system: 4.30364e-09
with a damping parameter alpha = 1
- Number of assembled systems = 14
- Number of Solver-Iterations = 1098
+ Number of assembled systems = 6
+ Number of Solver-Iterations = 479
Writing graphical output...
+---------------------------------------------+------------+------------+
-| Total wallclock time elapsed since start | 465s | |
+| Total wallclock time elapsed since start | 445s | |
| | | |
| Section | no. calls | wall time | % of total |
+---------------------------------+-----------+------------+------------+
-| Assembling | 71 | 61.6s | 13% |
-| Graphical output | 6 | 10.5s | 2.2% |
-| Mesh refinement and setup system| 6 | 2.71s | 0.58% |
-| Preconditioning | 71 | 19.9s | 4.3% |
-| Residual and lambda | 83 | 8.97s | 1.9% |
-| Solving | 71 | 170s | 36% |
-| Solving and Preconditioning | 71 | 191s | 41% |
-| Update solution and constraints | 71 | 1.46s | 0.31% |
+| 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% |
+---------------------------------+-----------+------------+------------+
+
@endcode
-For each adaptive refinement cycle the iterations end if the active set and
-the residual for the non-linear problem don't change anymore. In the tables
+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 informations about computing time and the
number of calls of different parts of the program like Assembling or calculating
-the residuals. After the last cycle there are 83 calls for the residual function.
-12 calls as the Solving or Assembling what means that 12 damping steps were
-necessary summed up over the cycles.
+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.
+
+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 every refinement step you can observe that the acitve 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.
+last 4 or 5 Newton iterations.
<table align="center">
<tr>
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 the work of Frohne, Heister, Bangerth: EFFICIENT
-NUMERICAL METHODS FOR THE LARGE-SCALE, PARALLEL SOLUTION OF ELASTOPLASTIC CONTACT
-PROBLEMS, preprint.
+For further details see Frohne, Heister, Bangerth: Efficient
+Numerical Methods For The Large-Scale, Parallel Solution Of Elastoplastic Contact
+Problems, preprint.
<a name="extensions"></a>
It might be of interest to implement more accurate, problem-adapted error
estimators for contact as well for the plasticity. To reduce the number of
-newton iterations a solution transfer of the coarse solution to the next
+Newton iterations a solution transfer of the coarse solution to the next
adaptive refined mesh could be beneficial.
\ No newline at end of file
projects / dealii-svn.git / commitdiff