LinearOperator from scipy sparse matrix

[kalosu]

Hi there PyLops community,

I came across your nice package and I wanted to ask you guys a couple of things.

1. I am interested in solving a Poisson equation system based on second order finite differences. For this I already use a scipy's sparse matrix to form the finite difference discrete Laplace operator. My problem also requires that I apply some Robin type boundary conditions for which I apply the required modification to the entries of my sparse matrix.
2. My system works fine for smooth and "continuous" entries in my right hand side vector but once I try to include some more complicated features (i.e, steps) then the problem becomes unstable. Based on this I decided to give it a try to including a regularization term (Tikhonov regularization) for which first I tried to define a scipy's LinearOperator to capture the action of the new modified matrix.
3. Nevertheless, once I try to run a solver (for instance, cg from scipy) the solver just takes a significantly longer time in contrast to the case in where I do not include the regularization term. In addition, the solutions that I obtain are not correct (this whole process is part of an additional external loop in where the solution obtained from the linear system is used as the input for the next iteration)

Based on this I was wondering if I could potentially have some speed and time benefits from using PyLops LinearOperators in this case.

If this is the case, can I also use the Laplace PyLops linear operator and perform a modification to it in order to account for the boundary conditions?

Also, can I apply Tikhonov regularization in this case using only PyLops LinearOperators??

I wonder if such an approach can be faster than the one based on using my scipy sparse matrix to define a LinearOperator (either scipy or PyLops linearOperator)

Thanks for your comments!