Good morning Ding. Sorry to not have an answer since I do not try to solve that type of problem. But, are the matrices formed and populated in a way that is appropriate to solution with PETSc? If that is the case then there does appear to be an issue with PETSc itself. I'll bet the developers would love to have your example.
My own development exercise is to compute the Kronecker tensor product where all components are distributed. Am using the Matrix and Vector level of PETSc, with some use of higher levels. It is a most interesting undertaking. Best, Peter.
