Dear Prof. Bangerth, Thanks very much for your quick answer!
> Constraints are funny and sometimes require deep thought about what exactly > they mean. What happens if you don't apply constraints to the > cell_volume_matrix and cell_gradient_matrix -- i.e., you copy the elements 1:1 > into the matrix, without the 'constraints' object? (Like in step-4.) I rewrite my code as you say, and the results are: Cycle 0: Number of active cells: 20 Number of degrees of freedom: 89 u square 0: 0.0305621 grad u square 0: 0.256542 Cycle 1: Number of active cells: 44 Number of degrees of freedom: 209 u square 1: 0.144303 grad u square 1: 0.49794 Cycle 2: Number of active cells: 92 Number of degrees of freedom: 449 u square 2: 0.101366 grad u square 2: 0.477137 Cycle 3: Number of active cells: 188 Number of degrees of freedom: 881 u square 3: 0.13305 grad u square 3: 0.529805 Cycle 4: Number of active cells: 368 Number of degrees of freedom: 1737 u square 4: 0.145489 grad u square 4: 0.565953 Cycle 5: Number of active cells: 737 Number of degrees of freedom: 3409 u square 5: 0.141771 grad u square 5: 0.574863 Cycle 6: Number of active cells: 1436 Number of degrees of freedom: 6705 u square 6: 0.171807 grad u square 6: 0.642486 Cycle 7: Number of active cells: 2729 Number of degrees of freedom: 12521 u square 7: 0.160819 grad u square 7: 0.625337 The attached is the code ,which doesn't use "constraints.distribute_local_to_global(...)" and "DoFTools::make_hanging_node_constraints (dof_handler, constraints);" if "DoFTools::make_hanging_node_constraints (dof_handler, constraints);" remain, the results: Cycle 0: Number of active cells: 20 Number of degrees of freedom: 89 u square 0: 0.0305621 grad u square 0: 0.256542 Cycle 1: Number of active cells: 44 Number of degrees of freedom: 209 u square 1: 0.0822159 grad u square 1: 2.97512 Cycle 2: Number of active cells: 92 Number of degrees of freedom: 449 u square 2: 0.000404454 grad u square 2: 0.0534184 Cycle 3: Number of active cells: 188 Number of degrees of freedom: 937 u square 3: 9.40228e-05 grad u square 3: 0.0378517 Cycle 4: Number of active cells: 368 Number of degrees of freedom: 1793 u square 4: 7.66868e-05 grad u square 4: 0.0403114 Cycle 5: Number of active cells: 704 Number of degrees of freedom: 3321 u square 5: 5.9193e-05 grad u square 5: 0.0366146 Cycle 6: Number of active cells: 1412 Number of degrees of freedom: 6657 u square 6: 6.47763e-05 grad u square 6: 0.0455655 Cycle 7: Number of active cells: 2696 Number of degrees of freedom: 12477 u square 7: 2.50787e-05 grad u square 7: 0.0320763 So I wander if it approximate the "grad u_exact square" and "u_exact square" correctly? Because in my numerical experiments, the "grad u_h square" and "u_h square" of numerical solution u_h are what we take care of. So if the computions of "grad u_h square" and "u_h square" are divided from other work like visualization, error estimation, are these results correct if change the using of constraints? And without "constraints..distribute_local_to_global(...)", the information of boundary may not use correctly (for example, My boundary condition is periodic boundary condition). Thank you very much! Best, Chucui 在 2019年2月12日星期二 UTC+8下午1:49:15，Wolfgang Bangerth写道： > > On 2/11/19 12:20 AM, chucu...@gmail.com <javascript:> wrote: > > Dear Prof. Bangerth: > > > > Thank you very much for your quick reply! > > > > When I apply hanging node constraints to my matrix, as the step-6 > > says: https://www.dealii.org/developer/doxygen/deal.II/step_6.html > > I make 4 steps: > > 1.Create a Constraints Class: > > | > > ConstraintMatrix constraints; > > | > > > > 2.Fill this object using the function > > DoFTools::make_hanging_node_constraints() to ensure continuity of the > elements > > of the finite element space. > > | > > DoFTools::make_hanging_node_constraints (dof_handler, > > constraints); > > | > > > > 3.Copy the local contributions to the matrix and right hand side > into the > > global objects: > > | > > constraints.distribute_local_to_global (cell_matrix, > > cell_rhs, > > local_dof_indices, > > system_matrix, > > system_rhs); > > constraints.distribute_local_to_global (cell_volume_matrix, > > local_dof_indices, > > volume_matrix); > > constraints.distribute_local_to_global (cell_gradient_matrix, > > local_dof_indices, > > gradient_matrix); > > | > > > > > > 4.Make sure that the degrees of "freedom" located on hanging nodes > get > > their correct (constrained) value: > > | > > constraints.distribute (solution); > > | > > Constraints are funny and sometimes require deep thought about what > exactly > they mean. What happens if you don't apply constraints to the > cell_volume_matrix and cell_gradient_matrix -- i.e., you copy the elements > 1:1 > into the matrix, without the 'constraints' object? (Like in step-4.) > > Alternatively, you could do as you show above and after calling > 'constraint.distribute(solution)' you manually set all constrained degrees > of > freedom in the solution vector to zero. That's not what you want to use > for > visualization, error estimation, ... but it might work for the operation > you're trying here. > > I'm pretty sure that both of these solutions should work individually (but > not > in combination). But explaining why this is so would take a page or two, > I'm > afraid. > > Best > W. > > > -- > ------------------------------------------------------------------------ > Wolfgang Bangerth email: bang...@colostate.edu > <javascript:> > www: http://www.math.colostate.edu/~bangerth/ > > -- The deal.II project is located at http://www.dealii.org/ For mailing list/forum options, see https://groups.google.com/d/forum/dealii?hl=en --- You received this message because you are subscribed to the Google Groups "deal.II User Group" group. To unsubscribe from this group and stop receiving emails from it, send an email to dealii+unsubscr...@googlegroups.com. For more options, visit https://groups.google.com/d/optout.
