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
>
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