[aspect-devel] Problem: Iterative advection solver does not converge

[Wolfgang Bangerth]

> However, I think the definition of the residual may be a bit different than
> what I’m used to:
> r = || v_i - v_i-1  ||  / || v_i  ||
> where v_i is the current velocities and v_i-1 are the previous values.

The "residual" (literally: "what is left") in iterative solver methods is 
typically the quantity
   r_i = A x_i - b
(or the norm of this vector), where x_i is the solution vector in the i-th 
iteration. It can be "large" because it carries physical units. As a 
consequence, its numerical size is meaningless unless compared to, say, the 
norm of the right hand side itself.

For example, we typically terminate iterative solver if the condition
   || r_i ||    <=    10^-6  || b ||
is satisfied. What is relevant is not whether the numeric value on the left is 
large or small, but whether it is large or small compared to ||b||.

Does that help?
Cheers
  W.

-- 
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Wolfgang Bangerth               email:            bangerth at math.tamu.edu
                                 www: http://www.math.tamu.edu/~bangerth/