Is there an efficient way to perform an incomplete Cholesky factorization on a symmetric positive definite sparse matrix (CSR format), in order to use it as a preconditioner for a CG solver? Is there a FORTRAN subroutine that performs such an factorization in parallel?
There's no need to do it yourself: The good people who bring us PETSc, Trilinos, and a number of other linear algebra libraries have already done it for you. I'm not sure about Fortran interfaces, but I think that PETSc has them. If they don't, it should not be overly difficult to write some if the ILU is all you want to compute and apply.