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I was trying to use FiPy to solve a set of PDEs when I realized the command sweep was not working the way I thought it would. Here goes a sample with part of my code:

from pylab import *
import sys
from fipy import *

viscosity = 5.55555555556e-06 

Pe =5.


Nx =200
mesh = PeriodicGrid2DTopBottom(nx=Nx, ny=Ny, dx=dL, dy=dL)

x, y = mesh.cellCenters

xVelocity = CellVariable(mesh=mesh, hasOld=True,  name='X velocity')

xVelocity.constrain(Pe, mesh.facesLeft)
xVelocity.constrain(Pe, mesh.facesRight)


var1 = DistanceVariable(name='distance to center', mesh=mesh, value=numerix.sqrt((x-Nx*dL/2.)**2+(y-Ny*dL/2.)**2))

pi_fi= CellVariable(mesh=mesh, value=0.,name='Fluid-interface energy map')
pi_fi.setValue(pfi*exp(-1.*(var1-rad)/lfi), where=(var1 > rad) )
pi_fi.setValue(pfi, where=(var1 <= rad))

xVelocityEq = DiffusionTerm(coeff=viscosity) - ImplicitSourceTerm(pi_fi)

while (xres > 1.e-6) :
        mySolver = LinearGMRESSolver(iterations=1000,tolerance=1.e-6)
        xres = xVelocityEq.sweep(var=xVelocity,solver=mySolver)
        print 'Result = ', xres
#Thats it

In short, I am declaring a function called xVelocityEq and solving it using sweep. Here is my output:

Result =  0.0007856742013190237
Result =  6.414470433257661e-07

As you can see, the while loop ends after two iterations. My first question is: why is my first residual error (=0.0007856742013190237) higher than the solver's tolerance? I thought that, since xVelocityEq corresponds to a linear system, solver tolerance and residual error would mean the same thing.

If I increase the no. of iterations in mySolver from 1000 to 10000, I get the following output:

Result =  0.0007856742013190237
Result =  2.4619110931978988e-09

Why did the second residual change, given that the first remained the same?

If I increase the tolerance in mySolver from 1.e-6 to 7.e-4, I get the following output:

Result =  0.0007856742013190237
Result =  6.414470433257661e-07

Note that these residuals are the same as in the first output. Now if I try to further increase the tolerance to 8.e-4, here's what I get as output:

Result =  0.0007856742013190237
Result =  0.0007856742013190237
Result =  0.0007856742013190237
Result =  0.0007856742013190237
Result =  0.0007856742013190237

At this point I was completely lost. Why the residuals have the same values for all solver tolerances smaller than 7.e-4? And why these residuals are constant and equal to 0.0007856742013190237 for solver tolerances higher than 7.e-4?

If I change the mySolver to LinearLUSolver (iterations=1000, tolerance=1.e-6), here's what I get:

Result =  0.0007856742013190237
Result =  1.6772757200988522e-18

Why in the world is my first residual the same as before, even though I have changed the solver?

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