Hi Dr. Bangerth,

Thanks so much for the suggestion! My code works after applying the 
constraint on the Newton update!

Best,
Jimmy

On Monday, September 7, 2020 at 11:01:53 PM UTC-5, Wolfgang Bangerth wrote:
>
> On 9/7/20 6:40 PM, Jimmy Ho wrote: 
> > 
> > I have a general question regarding the application of periodic boundary 
> > conditions in Newton's method when solving nonlinear equations. Should 
> the 
> > periodic constraint be applied to the incremental Newton update, or 
> directly 
> > to the total solution vector? 
>
> Periodicity constraints are not too different from the way you would deal 
> with 
> Dirichlet boundary conditions. step-15 discusses this in great length, and 
> the 
> solution is to make sure that your first iteration satisfies the 
> periodicity 
> constraints and that all updates do as well -- which ensures that all 
> iterates 
> do so, too. 
>
> Best 
>   W. 
>
>
> -- 
> ------------------------------------------------------------------------ 
> Wolfgang Bangerth          email:                 [email protected] 
> <javascript:> 
>                             www: http://www.math.colostate.edu/~bangerth/ 
>
>

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