Periodic boundary conditions in Newton's method

[Jimmy Ho]

Hi All,

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?

Thanks in advance for any suggestions!

Best,

Jimmy

[Wolfgang Bangerth]

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.


--
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Wolfgang Bangerth email: bang...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/

[Jimmy Ho]

Hi Dr. Bangerth,

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

Best,

Jimmy