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

[John Naliboff]

Hi Wolfgang,

Ok, yes, got it now.   I was misinterpreting the listed residual as having already been normalized relative to || b ||.  Sorry for the confusion and thanks again for the clarification.

Cheers,
John




> On Jun 6, 2016, at 1:11 PM, Wolfgang Bangerth <bangerth at tamu.edu> wrote:
> 
> 
>> 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.
> 
> -- 
> ------------------------------------------------------------------------
> Wolfgang Bangerth               email:            bangerth at math.tamu.edu
>                                www: http://www.math.tamu.edu/~bangerth/
> 
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