sorry:
N_{ij} (u^l) = (cos(u^l)\varphi_i,\varphi_j)_{\Omega}
Am Mittwoch, den 12.01.2011, 17:29 +0100 schrieb Steffen Härting:
> Hello,
>
> please correct me, if I am wrong:
>
> If you take a look at step-25:
> The part
>
> double initial_rhs_norm = 0.;
> bool first_iteration = true;
> do
> {
> assemble_system ();
>
> if (first_iteration == true)
> initial_rhs_norm = system_rhs.l2_norm();
>
> const unsigned int n_iterations
> = solve ();
>
> solution += solution_update;
>
> if (first_iteration == true)
> std::cout << " " << n_iterations;
> else
> std::cout << '+' << n_iterations;
> first_iteration = false;
> }
> while (system_rhs.l2_norm() > 1e-6 * initial_rhs_norm);
>
> std::cout << " CG iterations per nonlinear step."
> << std::endl;
>
> in the void SineGordonEquation::run
> should be what you are searching for.
>
> But your assemble_system, compute_nl_term and compute_nl_matrix look
> different (actually you could use the implemented compute_nl_* with
> theta=1, but you would have a useless old_solution bothering your
> processor - but you can modify them), because the discretization now
> reads (in the case of homogeneous neumann boundary conditions):
> F_h(U^l) = A U^l + S(u^l) = -rhs for newton step
> F_h'(U^l) = A + N (u^l) = system matrix for newton step
>
> where A_{ij}=-(\nabla \varphi_i, \nabla \varphi_j)_{\Omega}
> S_j(u^l) = (sin(u^l), \varphi_j)_{\Omega}
> N_j(u^l) = (cos(u^l), \varphi_j)_{\Omega}
>
> If I may comment one more thing: If you are not interested in them,
> beware of the spatially homogeneous solutions if you have homogeneous
> neumann boundary conditions or the one spatially homogeneous solution if
> you have homogeneous dirichlet boundary conditions.
>
> Cheers,
> Steffen
>
> Am Dienstag, den 11.01.2011, 18:30 +0200 schrieb [email protected]:
> > Dear all,
> >
> > I'm trying to solve the *time-independent* 2D sine-Gordon equation (u_{xx} +
> > u_{yy} - sin(u) = 0) using deal.II. Is anybody aware of any implementation
> > existing, or perhaps any other elliptic semilinear PDE, or even a Newton
> > method
> > implementation for elliptic non-linear PDEs?
> >
> > Please note that I'm aware of tutorial 25 which solves the sine-Gordon
> > equation,
> > however, it solves the *time-dependent* one and I can't see how I can make
> > use
> > of it.
> >
> > Thanks in advance.
> > _______________________________________________
> > dealii mailing list http://poisson.dealii.org/mailman/listinfo/dealii
>
>
> _______________________________________________
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