On 09/18/2017 11:39 AM, Yiyang Zhang wrote:
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.
That may be true for the *exact* solution of the PDE. But is it also
true for the *discrete* solution?
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.
Yes, you can do that. You just have to loop over the elements of your
solution vector and reset values that are too large or too small.
But you may lose the quadratic convergence of the Newton method this way
(because the solution at the end of this step no longer satisfies the
Newton update condition du=-J(u)^-1 F(u) ).
Best
W.
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Wolfgang Bangerth email: bange...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/
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