On 09/26/2017 02:24 AM, 'Maxi Miller' via deal.II User Group wrote:
I initialize my solution using the code shown above, but still the sharp drop
remains. Why?
I don't know. But at least now you know what is happening, and that gives you
an angle to debugging the problem. Are you outputting the initial guess for
the solution, or the solution after the first Newton step?
Btw, the reason your solver fails in the presence of such sharp drops is that
the coefficient in the equation has the form
1 / sqrt( 1 + |grad u|^2 )
In the pictures you show, you have areas where grad u = 0 and other areas
where grad u is very large. So the coefficient varies greatly. The condition
number of your matrix is proportional to the ratio of the largest to the
smallest value of the coefficient, so a sharp drop in your solution means that
you end up with a problem with a large condition number. That's why your
solver fails.
Best
W.
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Wolfgang Bangerth email: [email protected]
www: http://www.math.colostate.edu/~bangerth/
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