Custom Newton Solver NOT converging due to singularity at corners

[violetus]

You might want to have a look at Default absolute tolerance and relative tolerance.

@jt509

• I suspect ill conditioning is being introduced due to the boundary conditions and the problem. How is the Newton solver able to handle this but not the custom newton solve using the linear solver that I wrote?

I think it is rather an issue of Jacobian, kindly verify the Jacobian if it is defined correctly. Also consider reading Solution nonconvergence.

@jt509

Does the Newton solver introduce some kind of preconditioning in the system by default? If so how can I use it in my linear solve step?

Kindly see source code here.

@jt509

Is there anyway to resolve this? Any hints or ideas in this direction will help.

As I said, please verify Jacobian once if it is correctly built because when you were using the built in Newton solver, Jacobian is defined as -

@jt509

No Jacobian form specified for nonlinear variational problem.
Differentiating residual form F to obtain Jacobian J = F'.

But when the custom solver is used then you are explicitly Jacobian which might be causing issue.
I hope this helps.