Hi,
I'm having a problem for some values of parameters in my code.
I get an error "dealii::SolverControl::NoConvergence", almost instantly
after the start of the solving process. The status at the end is this :
"Iterative method reported convergence failure in step 1959. The residual
in the last step was nan."
Here is some details about my problem.
I'm solving this equation in phi :
[image: Screenshot from 2021-04-15 10-03-35.png]
with u and v, speeds that are calculated in another part of the code.
Since it is a non linear problem in phi, i'm using a Newton method to solve
it.
I have developped my Newton Method and calculated the part that I'm
assembling.
[image: Screenshot from 2021-04-15 10-05-29.png]
As you can see, it is a non symmetric problem because of the advection term
and as such, i'm using the Bicgstab solver like this :
SolverControl
solver_control(phi_system_rhs.size()*2,1e-10);
SolverBicgstab<Vector<double>> solver(solver_control);
PreconditionJacobi<> preconditioner;
preconditioner.initialize(phi_system_matrix, 1.0);
solver.solve(phi_system_matrix, phi_update, phi_system_rhs,
preconditioner);
phi_constraints.distribute(phi_update);
Note that if I use a direct solver like this :
SparseDirectUMFPACK A_direct;
A_direct.initialize(phi_system_matrix);
A_direct.vmult(phi_update, phi_system_rhs);
phi_constraints.distribute(phi_update);
I don't get an error but it is of course much slower (and the newton method
painfully converge but I knew this was gonna be difficult).
"The other situation where this error may occur is when your matrix is not
invertible (e.g., your matrix has a null-space), or if you try to apply the
wrong solver to a matrix (e.g., using CG for a matrix that is not symmetric
or not positive definite). In these cases, the residual in the last
iteration is likely going to be large."
This message at the end of the error made me wonder if I was choosing a bad
solver for this task and tried to find the Bicgstab recquirements.
Unfortunately, I was not able to find the recquirements for the Bicgstab in
the documentation.
I found this page
<https://www.dealii.org/current/doxygen/deal.II/classSolverBicgstab.html>that
tells me to go to the solver base for requirements but I could not find the
solverBase page with this information.
So could someone point me in the right direction and/or tell me if they
have an idea of why this solver is not converging in my case ?
Thanks again for developing dealii that is very useful to my research.
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