I would like to know what is the default options of LinearSolve when using LinearSolve[A,b], where A is a sparse matrix. There are several methods available such as Cholesky and Krysol etc., see here.
The reason I ask this is that I have a problem involving instabilities, the matrix becomes almost singular when close to the unstable point. The LinearSolve can find the converged solution with Newton iteration. I try to solve the exact same problem in Fenics, in which I can tune the solver parameters. The available solver parameters in Fenics are listed here. I tried with various solver parameter sets but can't get the converged solution at the unstable point.
I would like to know if I can set the same solver parameters in Fenics with that in Mathematica.