# Problem with residual and their definition!

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February 9, 2013, 13:06
Problem with residual and their definition!
#1
Member

Simone
Join Date: Sep 2012
Posts: 95
Rep Power: 4
Hi guys, I was troubling a little with the definition of the residuals in OF. Following this thread "Residuals for convergence of segregated solvers", I've figured out that, at each step, the residual is calculated as follow: (focusing over an hypothetical momentum equation)

Quote:
 res = b - Ax
which is the "classical" definition of the residual, with x the unknown.
Then, the normalization factor is calculated as:

Quote:
 xRef = gAverage(x)
Then we have the definition of these two fields:

Quote:
 wA = A x; pA = A xRef;
So the normalization factor is:

Quote:
 normFactor = gSum(cmptMag(wA - pA) + cmptMag(b - pA)) + matrix.small_;
And it is a sum of the magnitude of the vector fields all over the domain.

Finally the residual (normalized, so dimensionless) is:

Quote:
 residual = gSum(cmptMag(b - wA))/normFactor;
In the momentum equation is the difference between the RHS and LHS summed allover the domain, divide by the normFactor.

My questions are:

1) Is my interpretation correct?
2) Could someone explains what the average function do? I think it makes an average of a field (vector or scalar) in the domain but I'm not really sure
3) How can residual be equal 1 at step 0?
4) At each iterative step (I'm thinking about simpleFoam) the "initial Value" of residual at each time step is the difference between the residual calculated as before at the i-th step and the (i-1)th step or the first?

Simone

 February 11, 2013, 07:00 #2 Member   Simone Join Date: Sep 2012 Posts: 95 Rep Power: 4 Any answer guys?

 February 14, 2013, 08:36 #3 Member   Simone Join Date: Sep 2012 Posts: 95 Rep Power: 4 Isn't really anyone that can help me to figure out my problem?

 March 27, 2013, 05:56 #4 Member   Simone Join Date: Sep 2012 Posts: 95 Rep Power: 4 Hi guys I return on this post! I wanted to ask again if there is someone that can explain me if my interpretation of the residuals is correct..in particular I wanted some explanation about the normalization factor that is used.. is it really variable at each iteration or am I wrong? Please someone answers me. Cheers Simone

 April 1, 2013, 11:01 #5 Senior Member     Santiago Marquez Damian Join Date: Aug 2009 Location: Santa Fe, Santa Fe, Argentina Posts: 418 Rep Power: 14 __________________ Santiago MÁRQUEZ DAMIÁN, Ph.D. Post-doctoral Fellow Research Center for Computational Mechanics (CIMEC) - CONICET/FICH-UNL T.E.: 54-342-4511594 Ext. 1005 Güemes 3450 - (3000) Santa Fe Santa Fe - Argentina http://www.cimec.org.ar

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