Ok, I ran again the tests with different max_h_levels with the perflog enabled.
Let me know if you see anything here.
Thanks,
Simone

NO AMR
 
-----------------------------------------------------------------------------------------------------------------
| libMesh Performance: Alive time=77.5482, Active time=40.2976                  
                                  |
 
-----------------------------------------------------------------------------------------------------------------
| Event                              nCalls     Total Time  Avg Time    Total 
Time  Avg Time    % of Active Time  |
|                                               w/o Sub     w/o Sub     With 
Sub    With Sub    w/o S    With S   |
|-----------------------------------------------------------------------------------------------------------------|
|                                                                               
                                  |
|                                                                               
                                  |
| DefaultCoupling                                                               
                                  |
|   operator()                       98306      0.1609      0.000002    0.1609  
    0.000002    0.40     0.40     |
|                                                                               
                                  |
| DofMap                                                                        
                                  |
|   add_neighbors_to_send_list()     1          0.0959      0.095930    0.3744  
    0.374369    0.24     0.93     |
|   build_sparsity()                 1          0.4701      0.470055    1.1433  
    1.143297    1.17     2.84     |
|   create_dof_constraints()         1          0.0137      0.013673    0.0137  
    0.013673    0.03     0.03     |
|   distribute_dofs()                1          0.0126      0.012578    0.4376  
    0.437647    0.03     1.09     |
|   dof_indices()                    11010048   9.9728      0.000001    9.9728  
    0.000001    24.75    24.75    |
|   prepare_send_list()              2          0.0000      0.000002    0.0000  
    0.000002    0.00     0.00     |
|   reinit()                         1          0.0507      0.050692    0.0507  
    0.050692    0.13     0.13     |
|                                                                               
                                  |
| EquationSystems                                                               
                                  |
|   build_parallel_solution_vector() 5          1.4241      0.284811    2.4934  
    0.498673    3.53     6.19     |
|   build_solution_vector()          5          0.0002      0.000050    2.4936  
    0.498724    0.00     6.19     |
|                                                                               
                                  |
| ExodusII_IO                                                                   
                                  |
|   write_nodal_data()               3          0.0774      0.025816    0.0774  
    0.025816    0.19     0.19     |
|                                                                               
                                  |
| FE                                                                            
                                  |
|   compute_shape_functions()        10027008   11.7027     0.000001    11.7027 
    0.000001    29.04    29.04    |
|   init_shape_functions()           102        0.0007      0.000007    0.0007  
    0.000007    0.00     0.00     |
|                                                                               
                                  |
| FEMap                                                                         
                                  |
|   compute_affine_map()             10027008   9.9328      0.000001    9.9328  
    0.000001    24.65    24.65    |
|   init_reference_to_physical_map() 102        0.0008      0.000008    0.0008  
    0.000008    0.00     0.00     |
|                                                                               
                                  |
| GMVIO                                                                         
                                  |
|   write_nodal_data()               2          0.2260      0.113020    0.2260  
    0.113020    0.56     0.56     |
|                                                                               
                                  |
| GenericProjector                                                              
                                  |
|   operator()                       1          0.8425      0.842529    2.0842  
    2.084232    2.09     5.17     |
|   project_edges                    98304      0.0765      0.000001    0.0765  
    0.000001    0.19     0.19     |
|   project_interior                 98304      0.0765      0.000001    0.0765  
    0.000001    0.19     0.19     |
|   project_nodes                    98304      0.0865      0.000001    0.0865  
    0.000001    0.21     0.21     |
|   project_sides                    98304      0.0763      0.000001    0.0763  
    0.000001    0.19     0.19     |
|                                                                               
                                  |
| Mesh                                                                          
                                  |
|   find_neighbors()                 1          0.1105      0.110532    0.1105  
    0.110532    0.27     0.27     |
|   renumber_nodes_and_elem()        2          0.0063      0.003125    0.0063  
    0.003125    0.02     0.02     |
|                                                                               
                                  |
| MeshOutput                                                                    
                                  |
|   write_equation_systems()         5          0.0001      0.000021    2.7972  
    0.559445    0.00     6.94     |
|                                                                               
                                  |
| MeshTools::Generation                                                         
                                  |
|   build_cube()                     1          0.0280      0.027995    0.0280  
    0.027995    0.07     0.07     |
|                                                                               
                                  |
| Parallel                                                                      
                                  |
|   allgather()                      1          0.0000      0.000003    0.0000  
    0.000003    0.00     0.00     |
|                                                                               
                                  |
| Partitioner                                                                   
                                  |
|   single_partition()               1          0.0028      0.002767    0.0028  
    0.002767    0.01     0.01     |
|                                                                               
                                  |
| PetscLinearSolver                                                             
                                  |
|   solve()                          101        4.8469      0.047989    4.8469  
    0.047989    12.03    12.03    |
|                                                                               
                                  |
| System                                                                        
                                  |
|   project_fem_vector()             1          0.0034      0.003364    2.0876  
    2.087598    0.01     5.18     |
|   project_vector(FunctionBase)     1          0.0000      0.000011    2.0876  
    2.087610    0.00     5.18     |
 
-----------------------------------------------------------------------------------------------------------------
| Totals:                            3.156e+07  40.2976                         
                100.00            |
 
-----------------------------------------------------------------------------------------------------------------






AMR: 1 refinement
 
-----------------------------------------------------------------------------------------------------------------
| libMesh Performance: Alive time=395.981, Active time=261.811                  
                                  |
 
-----------------------------------------------------------------------------------------------------------------
| Event                              nCalls     Total Time  Avg Time    Total 
Time  Avg Time    % of Active Time  |
|                                               w/o Sub     w/o Sub     With 
Sub    With Sub    w/o S    With S   |
|-----------------------------------------------------------------------------------------------------------------|
|                                                                               
                                  |
|                                                                               
                                  |
| DefaultCoupling                                                               
                                  |
|   operator()                       1336320    2.0806      0.000002    2.0806  
    0.000002    0.79     0.79     |
|                                                                               
                                  |
| DofMap                                                                        
                                  |
|   add_neighbors_to_send_list()     102        1.2626      0.012378    4.8311  
    0.047363    0.48     1.85     |
|   build_sparsity()                 102        6.5962      0.064669    15.1863 
    0.148885    2.52     5.80     |
|   create_dof_constraints()         102        0.1384      0.001356    0.2351  
    0.002305    0.05     0.09     |
|   distribute_dofs()                102        0.1489      0.001459    5.6797  
    0.055684    0.06     2.17     |
|   dof_indices()                    22510266   19.3897     0.000001    19.3897 
    0.000001    7.41     7.41     |
|   enforce_constraints_exactly()    303        0.1463      0.000483    0.1463  
    0.000483    0.06     0.06     |
|   old_dof_indices()                11914452   11.0468     0.000001    11.0468 
    0.000001    4.22     4.22     |
|   prepare_send_list()              103        0.0001      0.000001    0.0001  
    0.000001    0.00     0.00     |
|   reinit()                         102        0.6993      0.006856    0.6993  
    0.006856    0.27     0.27     |
|                                                                               
                                  |
| EquationSystems                                                               
                                  |
|   build_parallel_solution_vector() 5          0.1832      0.036644    0.3127  
    0.062538    0.07     0.12     |
|   build_solution_vector()          5          0.0001      0.000018    0.3128  
    0.062557    0.00     0.12     |
|                                                                               
                                  |
| ExodusII_IO                                                                   
                                  |
|   write_nodal_data()               3          0.0094      0.003131    0.0094  
    0.003131    0.00     0.00     |
|                                                                               
                                  |
| FE                                                                            
                                  |
|   compute_shape_functions()        12975978   16.6602     0.000001    16.6602 
    0.000001    6.36     6.36     |
|   init_shape_functions()           10329700   16.6365     0.000002    16.6365 
    0.000002    6.35     6.35     |
|   inverse_map()                    10386411   11.3644     0.000001    11.3644 
    0.000001    4.34     4.34     |
|                                                                               
                                  |
| FEMap                                                                         
                                  |
|   compute_affine_map()             12975978   13.4041     0.000001    13.4041 
    0.000001    5.12     5.12     |
|   compute_face_map()               7691859    8.9240      0.000001    8.9240  
    0.000001    3.41     3.41     |
|   init_face_shape_functions()      101        0.0004      0.000004    0.0004  
    0.000004    0.00     0.00     |
|   init_reference_to_physical_map() 10329700   11.4379     0.000001    11.4379 
    0.000001    4.37     4.37     |
|                                                                               
                                  |
| GMVIO                                                                         
                                  |
|   write_nodal_data()               2          0.0979      0.048947    0.0979  
    0.048947    0.04     0.04     |
|                                                                               
                                  |
| GenericProjector                                                              
                                  |
|   copy_dofs                        3917556    15.7713     0.000004    59.2081 
    0.000015    6.02     22.61    |
|   operator()                       304        11.6914     0.038458    95.5809 
    0.314411    4.47     36.51    |
|   project_edges                    66216      0.0489      0.000001    0.0489  
    0.000001    0.02     0.02     |
|   project_interior                 66216      0.0493      0.000001    0.0493  
    0.000001    0.02     0.02     |
|   project_nodes                    66216      0.2561      0.000004    3.4858  
    0.000053    0.10     1.33     |
|   project_sides                    66216      0.0498      0.000001    0.0498  
    0.000001    0.02     0.02     |
|                                                                               
                                  |
| JumpErrorEstimator                                                            
                                  |
|   estimate_error()                 101        73.8216     0.730907    
231.1510    2.288624    28.20    88.29    |
|                                                                               
                                  |
| Mesh                                                                          
                                  |
|   contract()                       101        0.0296      0.000293    0.0581  
    0.000575    0.01     0.02     |
|   find_neighbors()                 101        1.4534      0.014391    1.4534  
    0.014391    0.56     0.56     |
|   renumber_nodes_and_elem()        303        0.0847      0.000280    0.0847  
    0.000280    0.03     0.03     |
|                                                                               
                                  |
| MeshOutput                                                                    
                                  |
|   write_equation_systems()         5          0.0001      0.000017    0.4202  
    0.084033    0.00     0.16     |
|                                                                               
                                  |
| MeshRefinement                                                                
                                  |
|   _coarsen_elements()              202        0.0812      0.000402    0.0812  
    0.000402    0.03     0.03     |
|   _refine_elements()               202        0.1485      0.000735    0.2795  
    0.001383    0.06     0.11     |
|   add_node()                       64512      0.0546      0.000001    0.0546  
    0.000001    0.02     0.02     |
|   make_coarsening_compatible()     204        0.3018      0.001479    0.3018  
    0.001479    0.12     0.12     |
|   make_flags_parallel_consistent() 303        0.2300      0.000759    0.2300  
    0.000759    0.09     0.09     |
|   make_refinement_compatible()     204        0.0242      0.000119    0.0242  
    0.000119    0.01     0.01     |
|                                                                               
                                  |
| MeshTools::Generation                                                         
                                  |
|   build_cube()                     1          0.0039      0.003937    0.0039  
    0.003937    0.00     0.00     |
|                                                                               
                                  |
| OldSolutionValue                                                              
                                  |
|   Number eval_at_node()            215712     0.2301      0.000001    2.9735  
    0.000014    0.09     1.14     |
|   check_old_context(c)             3917556    10.9141     0.000003    27.5061 
    0.000007    4.17     10.51    |
|   check_old_context(c,p)           68724      0.1726      0.000003    0.4012  
    0.000006    0.07     0.15     |
|   eval_at_point()                  68724      0.8513      0.000012    2.6627  
    0.000039    0.33     1.02     |
|   eval_old_dofs()                  3917556    6.6409      0.000002    38.7818 
    0.000010    2.54     14.81    |
|                                                                               
                                  |
| Parallel                                                                      
                                  |
|   allgather()                      102        0.0001      0.000001    0.0001  
    0.000001    0.00     0.00     |
|                                                                               
                                  |
| Partitioner                                                                   
                                  |
|   single_partition()               101        0.0341      0.000338    0.0341  
    0.000338    0.01     0.01     |
|                                                                               
                                  |
| PetscLinearSolver                                                             
                                  |
|   solve()                          202        1.6660      0.008248    1.6660  
    0.008248    0.64     0.64     |
|                                                                               
                                  |
| StatisticsVector                                                              
                                  |
|   maximum()                        101        0.0018      0.000017    0.0018  
    0.000017    0.00     0.00     |
|                                                                               
                                  |
| System                                                                        
                                  |
|   assemble()                       202        11.5849     0.057351    28.7372 
    0.142263    4.42     10.98    |
|   project_fem_vector()             1          0.0004      0.000417    0.2583  
    0.258341    0.00     0.10     |
|   project_vector(FunctionBase)     1          0.0000      0.000008    0.2584  
    0.258351    0.00     0.10     |
|   project_vector(old,new)          303        5.2799      0.017425    
109.1696    0.360296    2.02     41.70    |
|                                                                               
                                  |
| TopologyMap                                                                   
                                  |
|   init()                           202        0.1071      0.000530    0.1071  
    0.000530    0.04     0.04     |
 
-----------------------------------------------------------------------------------------------------------------
| Totals:                            1.129e+08  261.8108                        
                100.00            |
 
-----------------------------------------------------------------------------------------------------------------





AMR 2 refinements
 
-----------------------------------------------------------------------------------------------------------------
| libMesh Performance: Alive time=156.79, Active time=103.985                   
                                  |
 
-----------------------------------------------------------------------------------------------------------------
| Event                              nCalls     Total Time  Avg Time    Total 
Time  Avg Time    % of Active Time  |
|                                               w/o Sub     w/o Sub     With 
Sub    With Sub    w/o S    With S   |
|-----------------------------------------------------------------------------------------------------------------|
|                                                                               
                                  |
|                                                                               
                                  |
| DefaultCoupling                                                               
                                  |
|   operator()                       487585     0.7671      0.000002    0.7671  
    0.000002    0.74     0.74     |
|                                                                               
                                  |
| DofMap                                                                        
                                  |
|   add_neighbors_to_send_list()     203        0.4861      0.002394    1.8338  
    0.009034    0.47     1.76     |
|   build_sparsity()                 203        2.8815      0.014194    6.2119  
    0.030601    2.77     5.97     |
|   create_dof_constraints()         203        0.2105      0.001037    0.4801  
    0.002365    0.20     0.46     |
|   distribute_dofs()                203        0.0596      0.000294    2.1454  
    0.010569    0.06     2.06     |
|   dof_indices()                    8055927    7.4875      0.000001    7.4875  
    0.000001    7.20     7.20     |
|   enforce_constraints_exactly()    606        0.3674      0.000606    0.3674  
    0.000606    0.35     0.35     |
|   old_dof_indices()                4358601    4.2132      0.000001    4.2132  
    0.000001    4.05     4.05     |
|   prepare_send_list()              204        0.0002      0.000001    0.0002  
    0.000001    0.00     0.00     |
|   reinit()                         203        0.2510      0.001237    0.2510  
    0.001237    0.24     0.24     |
|                                                                               
                                  |
| EquationSystems                                                               
                                  |
|   build_parallel_solution_vector() 5          0.0316      0.006312    0.0543  
    0.010852    0.03     0.05     |
|   build_solution_vector()          5          0.0001      0.000014    0.0543  
    0.010868    0.00     0.05     |
|                                                                               
                                  |
| ExodusII_IO                                                                   
                                  |
|   write_nodal_data()               3          0.0024      0.000816    0.0024  
    0.000816    0.00     0.00     |
|                                                                               
                                  |
| FE                                                                            
                                  |
|   compute_shape_functions()        4507581    6.1953      0.000001    6.1953  
    0.000001    5.96     5.96     |
|   init_shape_functions()           3783756    6.6310      0.000002    6.6310  
    0.000002    6.38     6.38     |
|   inverse_map()                    3875385    4.5491      0.000001    4.5491  
    0.000001    4.37     4.37     |
|                                                                               
                                  |
| FEMap                                                                         
                                  |
|   compute_affine_map()             4507581    5.2201      0.000001    5.2201  
    0.000001    5.02     5.02     |
|   compute_face_map()               2763882    3.5520      0.000001    3.5520  
    0.000001    3.42     3.42     |
|   init_face_shape_functions()      202        0.0007      0.000004    0.0007  
    0.000004    0.00     0.00     |
|   init_reference_to_physical_map() 3783756    4.6286      0.000001    4.6286  
    0.000001    4.45     4.45     |
|                                                                               
                                  |
| GMVIO                                                                         
                                  |
|   write_nodal_data()               2          0.1665      0.083237    0.1665  
    0.083237    0.16     0.16     |
|                                                                               
                                  |
| GenericProjector                                                              
                                  |
|   copy_dofs                        1361385    5.6580      0.000004    21.6490 
    0.000016    5.44     20.82    |
|   operator()                       607        5.0012      0.008239    40.4516 
    0.066642    4.81     38.90    |
|   project_edges                    97080      0.0766      0.000001    0.0766  
    0.000001    0.07     0.07     |
|   project_interior                 97080      0.0751      0.000001    0.0751  
    0.000001    0.07     0.07     |
|   project_nodes                    97080      0.4693      0.000005    5.0553  
    0.000052    0.45     4.86     |
|   project_sides                    97080      0.0770      0.000001    0.0770  
    0.000001    0.07     0.07     |
|                                                                               
                                  |
| JumpErrorEstimator                                                            
                                  |
|   estimate_error()                 202        28.7106     0.142132    89.7093 
    0.444106    27.61    86.27    |
|                                                                               
                                  |
| Mesh                                                                          
                                  |
|   contract()                       202        0.0160      0.000079    0.0280  
    0.000139    0.02     0.03     |
|   find_neighbors()                 203        0.5978      0.002945    0.5978  
    0.002945    0.57     0.57     |
|   renumber_nodes_and_elem()        608        0.0350      0.000058    0.0350  
    0.000058    0.03     0.03     |
|                                                                               
                                  |
| MeshOutput                                                                    
                                  |
|   write_equation_systems()         5          0.0001      0.000013    0.2233  
    0.044669    0.00     0.21     |
|                                                                               
                                  |
| MeshRefinement                                                                
                                  |
|   _coarsen_elements()              404        0.0378      0.000094    0.0378  
    0.000094    0.04     0.04     |
|   _refine_elements()               404        0.1563      0.000387    0.4010  
    0.000993    0.15     0.39     |
|   add_node()                       113664     0.1007      0.000001    0.1007  
    0.000001    0.10     0.10     |
|   make_coarsening_compatible()     407        0.1988      0.000489    0.1988  
    0.000489    0.19     0.19     |
|   make_flags_parallel_consistent() 606        0.0937      0.000155    0.0937  
    0.000155    0.09     0.09     |
|   make_refinement_compatible()     407        0.0102      0.000025    0.0102  
    0.000025    0.01     0.01     |
|                                                                               
                                  |
| MeshTools::Generation                                                         
                                  |
|   build_cube()                     1          0.0007      0.000677    0.0007  
    0.000677    0.00     0.00     |
|                                                                               
                                  |
| OldSolutionValue                                                              
                                  |
|   Number eval_at_node()            382176     0.3948      0.000001    4.1027  
    0.000011    0.38     3.95     |
|   check_old_context(c)             1361385    4.0214      0.000003    10.1149 
    0.000007    3.87     9.73     |
|   check_old_context(c,p)           85266      0.2420      0.000003    0.5679  
    0.000007    0.23     0.55     |
|   eval_at_point()                  85266      1.1648      0.000014    3.5999  
    0.000042    1.12     3.46     |
|   eval_old_dofs()                  1361385    2.4347      0.000002    14.2695 
    0.000010    2.34     13.72    |
|                                                                               
                                  |
| Parallel                                                                      
                                  |
|   allgather()                      203        0.0002      0.000001    0.0002  
    0.000001    0.00     0.00     |
|                                                                               
                                  |
| Partitioner                                                                   
                                  |
|   single_partition()               203        0.0140      0.000069    0.0140  
    0.000069    0.01     0.01     |
|                                                                               
                                  |
| PetscLinearSolver                                                             
                                  |
|   solve()                          303        0.7612      0.002512    0.7612  
    0.002512    0.73     0.73     |
|                                                                               
                                  |
| StatisticsVector                                                              
                                  |
|   maximum()                        202        0.0008      0.000004    0.0008  
    0.000004    0.00     0.00     |
|                                                                               
                                  |
| System                                                                        
                                  |
|   assemble()                       303        3.4738      0.011465    8.5615  
    0.028256    3.34     8.23     |
|   project_fem_vector()             1          0.0001      0.000142    0.0331  
    0.033134    0.00     0.03     |
|   project_vector(FunctionBase)     1          0.0000      0.000009    0.0331  
    0.033144    0.00     0.03     |
|   project_vector(old,new)          606        2.3051      0.003804    46.4861 
    0.076710    2.22     44.70    |
|                                                                               
                                  |
| TopologyMap                                                                   
                                  |
|   init()                           404        0.1561      0.000386    0.1561  
    0.000386    0.15     0.15     |
 
-----------------------------------------------------------------------------------------------------------------
| Totals:                            4.127e+07  103.9851                        
                100.00            |
 
-----------------------------------------------------------------------------------------------------------------





AMR 3 refinements
 
-----------------------------------------------------------------------------------------------------------------
| libMesh Performance: Alive time=455.466, Active time=308.123                  
                                  |
 
-----------------------------------------------------------------------------------------------------------------
| Event                              nCalls     Total Time  Avg Time    Total 
Time  Avg Time    % of Active Time  |
|                                               w/o Sub     w/o Sub     With 
Sub    With Sub    w/o S    With S   |
|-----------------------------------------------------------------------------------------------------------------|
|                                                                               
                                  |
|                                                                               
                                  |
| DefaultCoupling                                                               
                                  |
|   operator()                       1153034    1.9001      0.000002    1.9001  
    0.000002    0.62     0.62     |
|                                                                               
                                  |
| DofMap                                                                        
                                  |
|   add_neighbors_to_send_list()     304        1.1509      0.003786    4.4251  
    0.014556    0.37     1.44     |
|   build_sparsity()                 304        8.8682      0.029172    16.6976 
    0.054926    2.88     5.42     |
|   create_dof_constraints()         304        1.6469      0.005417    3.9951  
    0.013142    0.53     1.30     |
|   distribute_dofs()                304        0.2173      0.000715    5.4146  
    0.017811    0.07     1.76     |
|   dof_indices()                    19916934   18.6126     0.000001    18.6126 
    0.000001    6.04     6.04     |
|   enforce_constraints_exactly()    909        2.8034      0.003084    2.8034  
    0.003084    0.91     0.91     |
|   old_dof_indices()                10268793   10.0124     0.000001    10.0124 
    0.000001    3.25     3.25     |
|   prepare_send_list()              305        0.0003      0.000001    0.0003  
    0.000001    0.00     0.00     |
|   reinit()                         304        0.7707      0.002535    0.7707  
    0.002535    0.25     0.25     |
|                                                                               
                                  |
| EquationSystems                                                               
                                  |
|   build_parallel_solution_vector() 5          0.0498      0.009954    0.0849  
    0.016974    0.02     0.03     |
|   build_solution_vector()          5          0.0001      0.000015    0.0850  
    0.016991    0.00     0.03     |
|                                                                               
                                  |
| ExodusII_IO                                                                   
                                  |
|   write_nodal_data()               3          0.0016      0.000526    0.0016  
    0.000526    0.00     0.00     |
|                                                                               
                                  |
| FE                                                                            
                                  |
|   compute_shape_functions()        12087258   16.7562     0.000001    16.7562 
    0.000001    5.44     5.44     |
|   init_shape_functions()           10555340   23.3502     0.000002    23.3502 
    0.000002    7.58     7.58     |
|   inverse_map()                    11670851   13.6081     0.000001    13.6081 
    0.000001    4.42     4.42     |
|                                                                               
                                  |
| FEMap                                                                         
                                  |
|   compute_affine_map()             12087258   15.1613     0.000001    15.1613 
    0.000001    4.92     4.92     |
|   compute_face_map()               6822171    8.8288      0.000001    8.8288  
    0.000001    2.87     2.87     |
|   init_face_shape_functions()      303        0.0011      0.000004    0.0011  
    0.000004    0.00     0.00     |
|   init_reference_to_physical_map() 10555340   14.9343     0.000001    14.9343 
    0.000001    4.85     4.85     |
|                                                                               
                                  |
| GMVIO                                                                         
                                  |
|   write_nodal_data()               2          0.0676      0.033816    0.0676  
    0.033816    0.02     0.02     |
|                                                                               
                                  |
| GenericProjector                                                              
                                  |
|   copy_dofs                        2157561    8.8513      0.000004    33.9505 
    0.000016    2.87     11.02    |
|   operator()                       910        18.4194     0.020241    
155.7304    0.171132    5.98     50.54    |
|   project_edges                    1299333    1.0235      0.000001    1.0235  
    0.000001    0.33     0.33     |
|   project_interior                 1299333    1.0026      0.000001    1.0026  
    0.000001    0.33     0.33     |
|   project_nodes                    1299333    6.3258      0.000005    76.0383 
    0.000059    2.05     24.68    |
|   project_sides                    1299333    1.0258      0.000001    1.0258  
    0.000001    0.33     0.33     |
|                                                                               
                                  |
| JumpErrorEstimator                                                            
                                  |
|   estimate_error()                 303        71.4588     0.235838    
222.8668    0.735534    23.19    72.33    |
|                                                                               
                                  |
| Mesh                                                                          
                                  |
|   contract()                       303        0.0998      0.000329    0.1462  
    0.000483    0.03     0.05     |
|   find_neighbors()                 304        2.2488      0.007397    2.2488  
    0.007397    0.73     0.73     |
|   renumber_nodes_and_elem()        911        0.1348      0.000148    0.1348  
    0.000148    0.04     0.04     |
|                                                                               
                                  |
| MeshOutput                                                                    
                                  |
|   write_equation_systems()         5          0.0001      0.000013    0.1542  
    0.030848    0.00     0.05     |
|                                                                               
                                  |
| MeshRefinement                                                                
                                  |
|   _coarsen_elements()              606        0.1621      0.000268    0.1621  
    0.000268    0.05     0.05     |
|   _refine_elements()               606        1.6498      0.002722    4.9647  
    0.008193    0.54     1.61     |
|   add_node()                       1542432    1.3647      0.000001    1.3647  
    0.000001    0.44     0.44     |
|   make_coarsening_compatible()     809        1.4420      0.001782    1.4420  
    0.001782    0.47     0.47     |
|   make_flags_parallel_consistent() 909        0.2881      0.000317    0.2881  
    0.000317    0.09     0.09     |
|   make_refinement_compatible()     809        0.0552      0.000068    0.0552  
    0.000068    0.02     0.02     |
|                                                                               
                                  |
| MeshTools::Generation                                                         
                                  |
|   build_cube()                     1          0.0002      0.000230    0.0002  
    0.000230    0.00     0.00     |
|                                                                               
                                  |
| OldSolutionValue                                                              
                                  |
|   Number eval_at_node()            5196564    5.4931      0.000001    63.1554 
    0.000012    1.78     20.50    |
|   check_old_context(c)             2157561    6.2716      0.000003    15.8724 
    0.000007    2.04     5.15     |
|   check_old_context(c,p)           1343484    3.6784      0.000003    8.6255  
    0.000006    1.19     2.80     |
|   eval_at_point()                  1343484    18.1202     0.000013    55.9662 
    0.000042    5.88     18.16    |
|   eval_old_dofs()                  2157561    3.8284      0.000002    22.3994 
    0.000010    1.24     7.27     |
|                                                                               
                                  |
| Parallel                                                                      
                                  |
|   allgather()                      304        0.0003      0.000001    0.0003  
    0.000001    0.00     0.00     |
|                                                                               
                                  |
| Partitioner                                                                   
                                  |
|   single_partition()               304        0.0450      0.000148    0.0450  
    0.000148    0.01     0.01     |
|                                                                               
                                  |
| PetscLinearSolver                                                             
                                  |
|   solve()                          404        1.5022      0.003718    1.5022  
    0.003718    0.49     0.49     |
|                                                                               
                                  |
| StatisticsVector                                                              
                                  |
|   maximum()                        303        0.0019      0.000006    0.0019  
    0.000006    0.00     0.00     |
|                                                                               
                                  |
| System                                                                        
                                  |
|   assemble()                       404        7.4765      0.018506    18.1484 
    0.044922    2.43     5.89     |
|   project_fem_vector()             1          0.0001      0.000109    0.0045  
    0.004474    0.00     0.00     |
|   project_vector(FunctionBase)     1          0.0000      0.000010    0.0045  
    0.004485    0.00     0.00     |
|   project_vector(old,new)          909        6.4352      0.007079    
174.8106    0.192311    2.09     56.73    |
|                                                                               
                                  |
| TopologyMap                                                                   
                                  |
|   init()                           606        0.9755      0.001610    0.9755  
    0.001610    0.32     0.32     |
 
-----------------------------------------------------------------------------------------------------------------
| Totals:                            1.162e+08  308.1230                        
                100.00            |
 
-----------------------------------------------------------------------------------------------------------------


On Apr 27, 2017, at 12:14, Vikram Garg 
<[email protected]<mailto:[email protected]>> wrote:

Rossi, yes compiling with perflog should give you all the details as in the 
example.





On Thu, Apr 27, 2017 at 10:54 AM, Rossi, Simone 
<[email protected]<mailto:[email protected]>> wrote:
Dear Vikram,
as in the examples, I am using the libmesh::KellyErrorEstimator.

I’m  compiling libmesh with the  --enable-perflog option. Does it automatically 
give all the details you have listed in the example?

For the time being, I am attaching two perfLogs I had saved with only “coarse 
scale” data for 2 levels of refinements.
It looks like that most of the time is spent in the AMR step, probably in the 
call to reinit().

Thanks,
Simone

NO AMR:

 
------------------------------------------------------------------------------------------------------------
| perf_log Performance: Alive time=18.0494, Active time=18.0426                 
                             |
 
------------------------------------------------------------------------------------------------------------
| Event                         nCalls     Total Time  Avg Time    Total Time  
Avg Time    % of Active Time  |
|                                          w/o Sub     w/o Sub     With Sub    
With Sub    w/o S    With S   |
|------------------------------------------------------------------------------------------------------------|
| no amr matrix assembly               1          0.1545      0.154465    
0.1545      0.154465    0.86     0.86     |
| no amr linear solve                     101        4.8069      0.047593    
4.8069      0.047593    26.64    26.64    |
| no amr rhs  assembly                 101        12.0348     0.119156    
12.0348     0.119156    66.70    66.70    |
| time loop                                         1          1.0464      
1.046422    17.8884     17.888405   5.80     99.15    |
 
------------------------------------------------------------------------------------------------------------
| Totals:                                            204        18.0426         
                                100.00            |
 
------------------------------------------------------------------------------------------------------------


AMR:

------------------------------------------------------------------------------------------------------------
| perf_log Performance: Alive time=209.305, Active time=209.298                 
                             |
 
------------------------------------------------------------------------------------------------------------
| Event                         nCalls     Total Time  Avg Time    Total Time  
Avg Time    % of Active Time  |
|                                          w/o Sub     w/o Sub     With Sub    
With Sub    w/o S    With S   |
|------------------------------------------------------------------------------------------------------------|
|                                                                               
                             |
| amr                               303        195.1102    0.643928    195.1102 
   0.643928    93.22    93.22    |
| amr solve                     303        13.9907      0.046174    13.9907     
 0.046174    6.68     6.68     |
| time loop                         1          0.1974       0.197370    
209.2990    209.299042  0.09     100.00   |
 
------------------------------------------------------------------------------------------------------------
| Totals:                       607        209.2983                             
           100.00            |
 
------------------------------------------------------------------------------------------------------------​


On Apr 27, 2017, at 11:02, Vikram Garg 
<[email protected]<mailto:[email protected]>> wrote:

Hello Rossi,
                   Two questions:

1) Which error estimator/indicator are you using to mark elements for 
refinement ?

2) Can you send the perfLog output from libMesh ? You might need to recompile 
libMesh with the option --enable-perflog.

Looks something like this:

 
-----------------------------------------------------------------------------------------------------------------
| libMesh Performance: Alive time=0.013423, Active time=0.007095                
                                  |
 
-----------------------------------------------------------------------------------------------------------------
| Event                              nCalls     Total Time  Avg Time    Total 
Time  Avg Time    % of Active Time  |
|                                               w/o Sub     w/o Sub     With 
Sub    With Sub    w/o S    With S   |
|-----------------------------------------------------------------------------------------------------------------|
|                                                                               
                                  |
|                                                                               
                                  |
| DofMap                                                                        
                                  |
|   add_neighbors_to_send_list()     6          0.0001      0.000012    0.0001  
    0.000012    1.01     1.01     |
|   build_sparsity()                 6          0.0002      0.000033    0.0011  
    0.000187    2.78     15.84    |
|   create_dof_constraints()         6          0.0000      0.000001    0.0000  
    0.000001    0.07     0.07     |
|   distribute_dofs()                6          0.0001      0.000025    0.0004  
    0.000066    2.09     5.57     |
|   dof_indices()                    688        0.0010      0.000001    0.0010  
    0.000001    14.36    14.36    |
|   old_dof_indices()                300        0.0001      0.000000    0.0001  
    0.000000    0.96     0.96     |
|   prepare_send_list()              7          0.0000      0.000000    0.0000  
    0.000000    0.01     0.01     |
|   reinit()                         6          0.0002      0.000041    0.0002  
    0.000041    3.48     3.48     |
|                                                                               
                                  |
| EquationSystems                                                               
                                  |
|   build_solution_vector()          1          0.0001      0.000056    0.0001  
    0.000064    0.79     0.90     |


Thanks.

On Wed, Apr 26, 2017 at 10:09 PM, Rossi, Simone 
<[email protected]<mailto:[email protected]>> wrote:
Dear Roy, dear Paul, dear all,
I am testing AMR in libmesh using simple linear elements.
My test case is a propagating front described by a reaction-diffusion equation 
with a cubic bistable reaction term.
I followed the adaptivity examples to create this test case.

The run times for 100 timesteps using AMR can be more than 10 times slower than 
when using a fine uniform grid.
For example, with a 16 x 16 x 16 uniform grid, 100 iterations take about 18 
seconds with a single processor.
With AMR, using a 2 x 2 x 2 grid and 3 levels of refinement, 100 iterations 
take about 800 seconds.

I’m attaching the code I’m using.
Without AMR, I build the matrix ( mass + dt * stiffness ) once and I update the 
rhs at every timestep.
Conversely, with AMR I am building the matrix and the rhs at every timestep for 
all the refinement levels.
Do you have any suggestions?

Thanks a lot for your help,
All the best,
Simone


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--
Vikram Garg
Postdoctoral Associate
The University of Texas at Austin

http://vikramvgarg.wordpress.com/
http://www.runforindia.org/runners/vikramg




--
Vikram Garg
Postdoctoral Associate
The University of Texas at Austin

http://vikramvgarg.wordpress.com/
http://www.runforindia.org/runners/vikramg

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