<h1>Results</h1>
-When you run the program, the screen output should look like the following:
+When you run the program using the following command
+@code
+mpirun -np 16 ./step-50 gmg_mf_2d.prm
+@endcode
+the screen output should look like the following:
@code
Cycle 0:
- Number of active cells: 56 (2 global levels)
- Workload imbalance: 1.14286
- Number of degrees of freedom: 665 (by level: 117, 665)
+ Number of active cells: 12 (2 global levels)
+ Partition efficiency: 0.1875
+ Number of degrees of freedom: 65 (by level: 21, 65)
Number of CG iterations: 10
+ Global error estimate: 0.355373
Wrote solution_00.pvtu
+---------------------------------------------+------------+------------+
-| Total wallclock time elapsed since start | 0.0457s | |
+| Total wallclock time elapsed since start | 0.0163s | |
| | | |
| Section | no. calls | wall time | % of total |
+---------------------------------+-----------+------------+------------+
-| Assemble right hand side | 1 | 0.000241s | 0.53% |
-| Estimate | 1 | 0.0288s | 63% |
-| Output results | 1 | 0.00219s | 4.8% |
-| Setup | 1 | 0.00264s | 5.8% |
-| Setup multigrid | 1 | 0.00261s | 5.7% |
-| Solve | 1 | 0.00355s | 7.8% |
-| Solve: 1 multigrid V-cycle | 1 | 0.000315s | 0.69% |
-| Solve: CG | 1 | 0.00186s | 4.1% |
-| Solve: Preconditioner setup | 1 | 0.000968s | 2.1% |
+| Assemble right-hand side | 1 | 0.000374s | 2.3% |
+| Estimate | 1 | 0.000724s | 4.4% |
+| Output results | 1 | 0.00277s | 17% |
+| Setup | 1 | 0.00225s | 14% |
+| Setup multigrid | 1 | 0.00181s | 11% |
+| Solve | 1 | 0.00364s | 22% |
+| Solve: 1 multigrid V-cycle | 1 | 0.000354s | 2.2% |
+| Solve: CG | 1 | 0.00151s | 9.3% |
+| Solve: Preconditioner setup | 1 | 0.00125s | 7.7% |
+---------------------------------+-----------+------------+------------+
Cycle 1:
- Number of active cells: 126 (3 global levels)
- Workload imbalance: 1.17483
- Number of degrees of freedom: 1672 (by level: 117, 665, 1100)
- Number of CG iterations: 11
+ Number of active cells: 24 (3 global levels)
+ Partition efficiency: 0.276786
+ Number of degrees of freedom: 139 (by level: 21, 65, 99)
+ Number of CG iterations: 10
+ Global error estimate: 0.216726
Wrote solution_01.pvtu
+---------------------------------------------+------------+------------+
-| Total wallclock time elapsed since start | 0.0433s | |
+| Total wallclock time elapsed since start | 0.0169s | |
| | | |
| Section | no. calls | wall time | % of total |
+---------------------------------+-----------+------------+------------+
-| Assemble right hand side | 1 | 0.000286s | 0.66% |
-| Estimate | 1 | 0.0272s | 63% |
-| Output results | 1 | 0.00333s | 7.7% |
-| Refine grid | 1 | 0.00196s | 4.5% |
-| Setup | 1 | 0.0023s | 5.3% |
-| Setup multigrid | 1 | 0.00262s | 6% |
-| Solve | 1 | 0.00549s | 13% |
-| Solve: 1 multigrid V-cycle | 1 | 0.000343s | 0.79% |
-| Solve: CG | 1 | 0.00293s | 6.8% |
-| Solve: Preconditioner setup | 1 | 0.00174s | 4% |
+| Assemble right-hand side | 1 | 0.000309s | 1.8% |
+| Estimate | 1 | 0.00156s | 9.2% |
+| Output results | 1 | 0.00222s | 13% |
+| Refine grid | 1 | 0.00278s | 16% |
+| Setup | 1 | 0.00196s | 12% |
+| Setup multigrid | 1 | 0.0023s | 14% |
+| Solve | 1 | 0.00565s | 33% |
+| Solve: 1 multigrid V-cycle | 1 | 0.000349s | 2.1% |
+| Solve: CG | 1 | 0.00285s | 17% |
+| Solve: Preconditioner setup | 1 | 0.00195s | 12% |
+---------------------------------+-----------+------------+------------+
Cycle 2:
-.
-.
-.
+ Number of active cells: 51 (4 global levels)
+ Partition efficiency: 0.41875
+ Number of degrees of freedom: 245 (by level: 21, 65, 225, 25)
+ Number of CG iterations: 11
+ Global error estimate: 0.112098
+ Wrote solution_02.pvtu
+
+
++---------------------------------------------+------------+------------+
+| Total wallclock time elapsed since start | 0.0183s | |
+| | | |
+| Section | no. calls | wall time | % of total |
++---------------------------------+-----------+------------+------------+
+| Assemble right-hand side | 1 | 0.000274s | 1.5% |
+| Estimate | 1 | 0.00127s | 6.9% |
+| Output results | 1 | 0.00227s | 12% |
+| Refine grid | 1 | 0.0024s | 13% |
+| Setup | 1 | 0.00191s | 10% |
+| Setup multigrid | 1 | 0.00295s | 16% |
+| Solve | 1 | 0.00702s | 38% |
+| Solve: 1 multigrid V-cycle | 1 | 0.000398s | 2.2% |
+| Solve: CG | 1 | 0.00376s | 21% |
+| Solve: Preconditioner setup | 1 | 0.00238s | 13% |
++---------------------------------+-----------+------------+------------+
+
+Cycle 3:
+ Number of active cells: 105 (5 global levels)
+ Partition efficiency: 0.434375
+ Number of degrees of freedom: 531 (by level: 21, 65, 225, 379, 25)
+ Number of CG iterations: 12
+ Global error estimate: 0.0577719
+ Wrote solution_03.pvtu
+
+
++---------------------------------------------+------------+------------+
+| Total wallclock time elapsed since start | 0.0188s | |
+| | | |
+| Section | no. calls | wall time | % of total |
++---------------------------------+-----------+------------+------------+
+| Assemble right-hand side | 1 | 0.000302s | 1.6% |
+| Estimate | 1 | 0.000898s | 4.8% |
+| Output results | 1 | 0.00228s | 12% |
+| Refine grid | 1 | 0.00204s | 11% |
+| Setup | 1 | 0.00143s | 7.6% |
+| Setup multigrid | 1 | 0.00346s | 18% |
+| Solve | 1 | 0.00823s | 44% |
+| Solve: 1 multigrid V-cycle | 1 | 0.00043s | 2.3% |
+| Solve: CG | 1 | 0.00462s | 25% |
+| Solve: Preconditioner setup | 1 | 0.00268s | 14% |
++---------------------------------+-----------+------------+------------+
+
+Cycle 4:
+ Number of active cells: 207 (6 global levels)
+ Partition efficiency: 0.520833
+ Number of degrees of freedom: 1009 (by level: 21, 65, 225, 737, 289, 25)
+ Number of CG iterations: 12
+ Global error estimate: 0.0332918
+ Wrote solution_04.pvtu
+
+
++---------------------------------------------+------------+------------+
+| Total wallclock time elapsed since start | 0.0241s | |
+| | | |
+| Section | no. calls | wall time | % of total |
++---------------------------------+-----------+------------+------------+
+| Assemble right-hand side | 1 | 0.000313s | 1.3% |
+| Estimate | 1 | 0.00116s | 4.8% |
+| Output results | 1 | 0.00238s | 9.8% |
+| Refine grid | 1 | 0.00422s | 18% |
+| Setup | 1 | 0.00169s | 7% |
+| Setup multigrid | 1 | 0.00444s | 18% |
+| Solve | 1 | 0.00974s | 40% |
+| Solve: 1 multigrid V-cycle | 1 | 0.000517s | 2.1% |
+| Solve: CG | 1 | 0.00557s | 23% |
+| Solve: Preconditioner setup | 1 | 0.00314s | 13% |
++---------------------------------+-----------+------------+------------+
+
+Cycle 5:
+ Number of active cells: 414 (7 global levels)
+ Partition efficiency: 0.513993
+ Number of degrees of freedom: 1953 (by level: 21, 65, 225, 815, 1108, 311, 65)
+ Number of CG iterations: 12
+ Global error estimate: 0.0196112
+ Wrote solution_05.pvtu
+
+
++---------------------------------------------+------------+------------+
+| Total wallclock time elapsed since start | 0.0293s | |
+| | | |
+| Section | no. calls | wall time | % of total |
++---------------------------------+-----------+------------+------------+
+| Assemble right-hand side | 1 | 0.000324s | 1.1% |
+| Estimate | 1 | 0.00154s | 5.2% |
+| Output results | 1 | 0.00281s | 9.6% |
+| Refine grid | 1 | 0.00529s | 18% |
+| Setup | 1 | 0.00192s | 6.5% |
+| Setup multigrid | 1 | 0.00577s | 20% |
+| Solve | 1 | 0.0115s | 39% |
+| Solve: 1 multigrid V-cycle | 1 | 0.000583s | 2% |
+| Solve: CG | 1 | 0.00665s | 23% |
+| Solve: Preconditioner setup | 1 | 0.00366s | 12% |
++---------------------------------+-----------+------------+------------+
+
+Cycle 6:
+ Number of active cells: 837 (8 global levels)
+ Partition efficiency: 0.536058
+ Number of degrees of freedom: 3769 (by level: 21, 65, 225, 833, 2657, 913, 226, 105)
+ Number of CG iterations: 12
+ Global error estimate: 0.0112446
+ Wrote solution_06.pvtu
+
+
++---------------------------------------------+------------+------------+
+| Total wallclock time elapsed since start | 0.0313s | |
+| | | |
+| Section | no. calls | wall time | % of total |
++---------------------------------+-----------+------------+------------+
+| Assemble right-hand side | 1 | 0.000305s | 0.98% |
+| Estimate | 1 | 0.00134s | 4.3% |
+| Output results | 1 | 0.00278s | 8.9% |
+| Refine grid | 1 | 0.0087s | 28% |
+| Setup | 1 | 0.0021s | 6.7% |
+| Setup multigrid | 1 | 0.00477s | 15% |
+| Solve | 1 | 0.0111s | 35% |
+| Solve: 1 multigrid V-cycle | 1 | 0.00053s | 1.7% |
+| Solve: CG | 1 | 0.00632s | 20% |
+| Solve: Preconditioner setup | 1 | 0.00372s | 12% |
++---------------------------------+-----------+------------+------------+
+
+Cycle 7:
+ Number of active cells: 1683 (9 global levels)
+ Partition efficiency: 0.507926
+ Number of degrees of freedom: 7415 (by level: 21, 65, 225, 833, 3111, 4372, 777, 354, 121)
+ Number of CG iterations: 13
+ Global error estimate: 0.00671358
+ Wrote solution_07.pvtu
+
+
++---------------------------------------------+------------+------------+
+| Total wallclock time elapsed since start | 0.0407s | |
+| | | |
+| Section | no. calls | wall time | % of total |
++---------------------------------+-----------+------------+------------+
+| Assemble right-hand side | 1 | 0.000322s | 0.79% |
+| Estimate | 1 | 0.00259s | 6.4% |
+| Output results | 1 | 0.00384s | 9.4% |
+| Refine grid | 1 | 0.0129s | 32% |
+| Setup | 1 | 0.00216s | 5.3% |
+| Setup multigrid | 1 | 0.0064s | 16% |
+| Solve | 1 | 0.0123s | 30% |
+| Solve: 1 multigrid V-cycle | 1 | 0.000624s | 1.5% |
+| Solve: CG | 1 | 0.00701s | 17% |
+| Solve: Preconditioner setup | 1 | 0.00409s | 10% |
++---------------------------------+-----------+------------+------------+
+
+Cycle 8:
+ Number of active cells: 3378 (10 global levels)
+ Partition efficiency: 0.614492
+ Number of degrees of freedom: 14527 (by level: 21, 65, 225, 833, 3201, 10087, 3321, 969, 490, 161)
+ Number of CG iterations: 13
+ Global error estimate: 0.00404791
+ Wrote solution_08.pvtu
+
+
++---------------------------------------------+------------+------------+
+| Total wallclock time elapsed since start | 0.0608s | |
+| | | |
+| Section | no. calls | wall time | % of total |
++---------------------------------+-----------+------------+------------+
+| Assemble right-hand side | 1 | 0.000334s | 0.55% |
+| Estimate | 1 | 0.0038s | 6.3% |
+| Output results | 1 | 0.00675s | 11% |
+| Refine grid | 1 | 0.0258s | 42% |
+| Setup | 1 | 0.00259s | 4.3% |
+| Setup multigrid | 1 | 0.00773s | 13% |
+| Solve | 1 | 0.0135s | 22% |
+| Solve: 1 multigrid V-cycle | 1 | 0.000676s | 1.1% |
+| Solve: CG | 1 | 0.00787s | 13% |
+| Solve: Preconditioner setup | 1 | 0.00439s | 7.2% |
++---------------------------------+-----------+------------+------------+
+
+Cycle 9:
+ Number of active cells: 6765 (11 global levels)
+ Partition efficiency: 0.547269
+ Number of degrees of freedom: 28555 (by level: 21, 65, 225, 833, 3201, 11967, 16614, 2897, 1353, 682, 193)
+ Number of CG iterations: 12
+ Global error estimate: 0.00248866
+ Wrote solution_09.pvtu
+
+
++---------------------------------------------+------------+------------+
+| Total wallclock time elapsed since start | 0.0916s | |
+| | | |
+| Section | no. calls | wall time | % of total |
++---------------------------------+-----------+------------+------------+
+| Assemble right-hand side | 1 | 0.000391s | 0.43% |
+| Estimate | 1 | 0.00612s | 6.7% |
+| Output results | 1 | 0.016s | 18% |
+| Refine grid | 1 | 0.0356s | 39% |
+| Setup | 1 | 0.00405s | 4.4% |
+| Setup multigrid | 1 | 0.0114s | 12% |
+| Solve | 1 | 0.0178s | 19% |
+| Solve: 1 multigrid V-cycle | 1 | 0.000892s | 0.97% |
+| Solve: CG | 1 | 0.0101s | 11% |
+| Solve: Preconditioner setup | 1 | 0.00593s | 6.5% |
++---------------------------------+-----------+------------+------------+
+
+Cycle 10:
+ Number of active cells: 13542 (12 global levels)
+ Partition efficiency: 0.612615
+ Number of degrees of freedom: 56241 (by level: 21, 65, 225, 833, 3201, 12503, 39503, 12121, 3393, 1794, 1082, 241)
+ Number of CG iterations: 12
+ Global error estimate: 0.00153864
+ Wrote solution_10.pvtu
+
+
++---------------------------------------------+------------+------------+
+| Total wallclock time elapsed since start | 0.167s | |
+| | | |
+| Section | no. calls | wall time | % of total |
++---------------------------------+-----------+------------+------------+
+| Assemble right-hand side | 1 | 0.000498s | 0.3% |
+| Estimate | 1 | 0.0115s | 6.9% |
+| Output results | 1 | 0.0363s | 22% |
+| Refine grid | 1 | 0.0724s | 43% |
+| Setup | 1 | 0.00645s | 3.9% |
+| Setup multigrid | 1 | 0.0165s | 9.8% |
+| Solve | 1 | 0.0235s | 14% |
+| Solve: 1 multigrid V-cycle | 1 | 0.00114s | 0.68% |
+| Solve: CG | 1 | 0.0138s | 8.3% |
+| Solve: Preconditioner setup | 1 | 0.00727s | 4.3% |
++---------------------------------+-----------+------------+------------+
+
+Cycle 11:
+ Number of active cells: 27087 (13 global levels)
+ Partition efficiency: 0.545346
+ Number of degrees of freedom: 111333 (by level: 21, 65, 225, 833, 3201, 12545, 47125, 65080, 10457, 4321, 2466, 1626, 401)
+ Number of CG iterations: 12
+ Global error estimate: 0.000959538
+ Wrote solution_11.pvtu
+
+
++---------------------------------------------+------------+------------+
+| Total wallclock time elapsed since start | 0.288s | |
+| | | |
+| Section | no. calls | wall time | % of total |
++---------------------------------+-----------+------------+------------+
+| Assemble right-hand side | 1 | 0.000819s | 0.28% |
+| Estimate | 1 | 0.0214s | 7.4% |
+| Output results | 1 | 0.08s | 28% |
+| Refine grid | 1 | 0.115s | 40% |
+| Setup | 1 | 0.0106s | 3.7% |
+| Setup multigrid | 1 | 0.027s | 9.4% |
+| Solve | 1 | 0.0328s | 11% |
+| Solve: 1 multigrid V-cycle | 1 | 0.00158s | 0.55% |
+| Solve: CG | 1 | 0.0195s | 6.8% |
+| Solve: Preconditioner setup | 1 | 0.00974s | 3.4% |
++---------------------------------+-----------+------------+------------+
+
+Cycle 12:
+ Number of active cells: 54207 (14 global levels)
+ Partition efficiency: 0.60149
+ Number of degrees of freedom: 221207 (by level: 21, 65, 225, 833, 3201, 12545, 49167, 155671, 46497, 12763, 6745, 4018, 2522, 595)
+ Number of CG iterations: 13
+ Global error estimate: 0.000599798
+ Wrote solution_12.pvtu
+
+
++---------------------------------------------+------------+------------+
+| Total wallclock time elapsed since start | 0.599s | |
+| | | |
+| Section | no. calls | wall time | % of total |
++---------------------------------+-----------+------------+------------+
+| Assemble right-hand side | 1 | 0.00112s | 0.19% |
+| Estimate | 1 | 0.0427s | 7.1% |
+| Output results | 1 | 0.164s | 27% |
+| Refine grid | 1 | 0.273s | 46% |
+| Setup | 1 | 0.0169s | 2.8% |
+| Setup multigrid | 1 | 0.042s | 7% |
+| Solve | 1 | 0.0587s | 9.8% |
+| Solve: 1 multigrid V-cycle | 1 | 0.00252s | 0.42% |
+| Solve: CG | 1 | 0.039s | 6.5% |
+| Solve: Preconditioner setup | 1 | 0.0137s | 2.3% |
++---------------------------------+-----------+------------+------------+
+
+Cycle 13:
+ Number of active cells: 108438 (15 global levels)
+ Partition efficiency: 0.538813
+ Number of degrees of freedom: 440091 (by level: 21, 65, 225, 833, 3201, 12545, 49647, 186589, 254906, 40305, 17041, 10049, 6234, 3994, 897)
+ Number of CG iterations: 13
+ Global error estimate: 0.000376279
+ Wrote solution_13.pvtu
+
+
++---------------------------------------------+------------+------------+
+| Total wallclock time elapsed since start | 1.1s | |
+| | | |
+| Section | no. calls | wall time | % of total |
++---------------------------------+-----------+------------+------------+
+| Assemble right-hand side | 1 | 0.00325s | 0.29% |
+| Estimate | 1 | 0.0717s | 6.5% |
+| Output results | 1 | 0.349s | 32% |
+| Refine grid | 1 | 0.466s | 42% |
+| Setup | 1 | 0.0314s | 2.8% |
+| Setup multigrid | 1 | 0.0861s | 7.8% |
+| Solve | 1 | 0.0957s | 8.7% |
+| Solve: 1 multigrid V-cycle | 1 | 0.00447s | 0.4% |
+| Solve: CG | 1 | 0.0623s | 5.6% |
+| Solve: Preconditioner setup | 1 | 0.0232s | 2.1% |
++---------------------------------+-----------+------------+------------+
+
+Cycle 14:
+ Number of active cells: 216939 (16 global levels)
+ Partition efficiency: 0.595755
+ Number of degrees of freedom: 876733 (by level: 21, 65, 225, 833, 3201, 12545, 49665, 195269, 617543, 180617, 49227, 25657, 15658, 10130, 6602, 1491)
+ Number of CG iterations: 13
+ Global error estimate: 0.00023629
+ Wrote solution_14.pvtu
+
+
++---------------------------------------------+------------+------------+
+| Total wallclock time elapsed since start | 2.27s | |
+| | | |
+| Section | no. calls | wall time | % of total |
++---------------------------------+-----------+------------+------------+
+| Assemble right-hand side | 1 | 0.00391s | 0.17% |
+| Estimate | 1 | 0.149s | 6.6% |
+| Output results | 1 | 0.633s | 28% |
+| Refine grid | 1 | 1.08s | 48% |
+| Setup | 1 | 0.0624s | 2.7% |
+| Setup multigrid | 1 | 0.154s | 6.8% |
+| Solve | 1 | 0.188s | 8.3% |
+| Solve: 1 multigrid V-cycle | 1 | 0.0081s | 0.36% |
+| Solve: CG | 1 | 0.126s | 5.5% |
+| Solve: Preconditioner setup | 1 | 0.0427s | 1.9% |
++---------------------------------+-----------+------------+------------+
+
+Cycle 15:
+ Number of active cells: 433905 (17 global levels)
+ Partition efficiency: 0.535565
+ Number of degrees of freedom: 1748479 (by level: 21, 65, 225, 833, 3201, 12545, 49665, 197397, 743221, 1008010, 158369, 66283, 38249, 24362, 15746, 10218, 2345)
+ Number of CG iterations: 13
+ Global error estimate: 0.000148602
+ Wrote solution_15.pvtu
+
+
++---------------------------------------------+------------+------------+
+| Total wallclock time elapsed since start | 4.25s | |
+| | | |
+| Section | no. calls | wall time | % of total |
++---------------------------------+-----------+------------+------------+
+| Assemble right-hand side | 1 | 0.00961s | 0.23% |
+| Estimate | 1 | 0.279s | 6.6% |
+| Output results | 1 | 1.2s | 28% |
+| Refine grid | 1 | 1.86s | 44% |
+| Setup | 1 | 0.151s | 3.5% |
+| Setup multigrid | 1 | 0.352s | 8.3% |
+| Solve | 1 | 0.391s | 9.2% |
+| Solve: 1 multigrid V-cycle | 1 | 0.0176s | 0.42% |
+| Solve: CG | 1 | 0.261s | 6.1% |
+| Solve: Preconditioner setup | 1 | 0.0921s | 2.2% |
++---------------------------------+-----------+------------+------------+
@endcode
Here, the timing of the `solve()` function is split up in 3 parts: setting
up the multigrid preconditioner, execution of a single multigrid V-cycle, and
projects / dealii.git / commitdiff