Dear Sebastian, Many thanks for your detailed explanation.
Best, Lixing On Monday, April 11, 2022 at 3:37:14 PM UTC+8 SebG wrote: > Dear Lixing, > > I think you are right. In Newton's method, the entries of the residual > vector which correspond to degrees of freedom that are constrained through > a Dirichlet boundary condition should vanish. In step-57, this is achieved > using the member variable AffineConstraints<double> zero_constraints and > the constraints are enforced during the assembly process by calling > AffineConstraints<double>::distribute_local_to_global. Since > inhomogeneous boundary conditions are applied in step-57, a switch between > the inhomogeneous and homogeneous constraints is necessary. The > inhomogeneous constraints are actually only used in the very first assembly > of the linear system (system matrix and right-hand side vector). In all > subsequent assemblies of the residual vector and the linear system, the > homogeneous constraints are used. This is achieved by > > const AffineConstraints<double> &constraints_used = > initial_step ? nonzero_constraints : zero_constraints; > > In step-15, Dirichlet boundary conditions and hanging node constraints are > not treated using a joint AffineConstraints<double> object. The hanging > node constraints are enforced through an explicit condensation after > assembling the system matrix and right-hand side vector by means of an > AffineConstraints<double> object. The Dirichlet boundary conditions are > then enforced by calling MatrixTools::apply_boundary_values and by > explicitly setting them to zero in the residual vector. In step-15, only > homogeneous constraints are applied because the solution automatically > satisfies them due to the call to the method set_boundary_values. > > Both approaches are equivalent, but should not be confused or mixed. I > prefer the way of step-57, but this is a personal flavor. I hope my > comments are helpful. > > Best wishes, > Sebastian > > > Lixing Zhu schrieb am Sonntag, 10. April 2022 um 20:00:14 UTC+2: > >> Hi all, >> >> I am confused with Newton's method's residual computation (i.e., L2 norm >> of the system residual vector) in Step-15 and Step-57. >> >> In Step-15, to eliminate the residual component corresponding to the >> Dirichlet boundary condition, DOFTools::extract_boundary_dofs() is used to >> explicitly make those components zero. >> >> However, in Step-57, there seems no explicit treatment to eliminate the >> residual components on the Dirichlet boundary in the computation of >> residuals in each iteration within Newton's method. Is this because of the >> zero_constraints? >> >> Regards, >> Lixing >> > -- 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 [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/dealii/a6c4d519-3c4e-414d-84a9-40ad7e0dd7bbn%40googlegroups.com.
