I am following, e.g. Step-15, to solve a nonlinear system with Newton method.
The system is with the scalar potential V(phi)=(phi^2-1)^2. The solution satisfies the boundary condition phi=1 at infinity, such that the total energy is finite. Actually, we expect phi goes from 0 to 1 when the when the coordinate goes from center to infinity. phi should never exceeds 1. However, when I do Newton iteration, phi always exceeds 1 near the boundary (my early description is wrong, it is not a local minima...), then things blow up... Previously, I also solved such problems in 1D with finite difference. the field will also blow up at some point. In that case, after every iteration, I examine the values of the field at each discretized point. Wherever it exceed 1, I will manually replace it with 1. That will solve the problem. Thus I wonder if I can do the same thing in dealii. Thank you. Best, Yiyang On Monday, September 18, 2017 at 11:15:02 AM UTC-5, Wolfgang Bangerth wrote: > > On 09/18/2017 09:33 AM, Yiyang Zhang wrote: > > > > For some problems, we might know in advance that the solution is in some > > range, e.g. [-1,1]. > > You mean the exact solution u(x)? > > > > If we do not impose this restriction, the iteration may > > easily go to some other local minima. > > Correct. But do you also know that the solution u_h(x) of the > *discretized* > equation satisfies the restriction that -1 <= u_h(x) <= 1 ? In general, > this > is not an easy thing to prove -- in fact, it will in general not be true. > And > if that statement is not true for the discrete solution u_h(x), then it is > not > correct to also *impose* this restriction. > > > > In dealii, how do we impose such a restriction on the solution vector > after > > each iteration? > > You mean within the SolverCG, for example? Why would you want to impose it > in > each iteration, as opposed to just on the final solution of the linear > system? > Or do you mean in a nonlinear iteration? > > 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.
