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.
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Wolfgang Bangerth email: [email protected]
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