[petsc-users] 2-norm of solution update suddenly becomes zero after a few iterations

[baikadi pranay]

Hello,

I am trying to solve the Poisson equation in 2D for heterostructure
devices. I have linearized the equation and discretized it using FDM. I am
using BiCGStab to iteratively solve for the solution as follows:

Step 1: Solve A^(i-1) x^(i) = b^(i-1)     {i = 1 to N where convergence is
reached}
Step 2: Use x^{i} to update the central coefficients of A^{i-1} to get
A^{i} and                          similarly  update b^{i-1} to get b^{i}
Step3: If ( ||x^{i}-x^{i-1}||_2 , the 2-norm of the solution update, is
greater than a                     tolerance, then go back to Step 1  to
solve the new system of equations                     using BiCGStab. Else,
exit the loop.
*1) I am facing the following problem with this procedure*:
The 2-norm of the solution update is suddenly becoming zero after a few
iterations in some cases. I print out the getconvergedreason and there are
not red flags there, so I am kind of confused whey this behaviour is being
observed. This behaviour is leading to "false convergences", in the sense
that the solutions obtained are not physical.

A similar behaviour was observed when I used SOR instead of BiCGStab. At
this point I am starting to suspect if it is wrong to use linear solvers on
the poisson equation which is a nonlinear equation (although linearized).
If you could please comment on this, that would be very helpful.

Any help with this problem is greatly appreciated. Please let me know if
you need any further information.

Thank you,

Sincerely,
Pranay.

ᐧ
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