solve a special matrix with hypre
I have trouble using hypre to solve a linear equation with a special shape of matrix, so I come here looking for help.
The matrix has the shape like [A -B^T; B O; O C] where A is dense in general. B^T is transpose of B. B is pretty sparse and has only very few 1 or -1 in each of its column. C is another very sparse matrix which has one or two 1 or -1 in each of its row. The following is a small example: [1e-4 3e-5 0 0 -1 1; 3e-5 1e-4 -1 1 0 0; 0 1 0 0 0 0; 0 -1 0 0 0 0; 1 0 0 0 0 0; -1 0 0 0 0 0; 0 0 0 -1 1 0; 0 0 0 1 0 0]
The rhs is a vector with very few 1 or -1. Like [0 0 1 -1 0 0 0 0]
I have tried various options to solve this linear problem but cannot find a realiable solution. ILU works for the above example, but is not reliable. When I turn to another case it fails. I am not an expert user of hypre so I would like to see if there are any recommendations for the best setup to solve this kind of problem. Thanks for your help.