[petsc-users] MatSetNullSpace

[Bikash Kanungo]

Hi,

I'm trying to solve a linear system of equations  Ax=b, where A has a null
space (say Q) and x is known to be orthogonal to Q. In order to avoid
ill-conditioning, I was trying to do the following:


   1.  Create A as a shell matrix
   2.  Overload the MATOP_MULT operation for with my own function which
   returns
   y = A*(I - QQ^T)x instead of y = Ax
   3. Upon convergence, solution = (I-QQ^T)x instead of x.

However, I realized that the linear solver can make x have any arbitrary
component along Q and still y = A*(I-QQ^T)x will remain unaffected, and
hence can cause convergence issues. Indeed, I saw such convergence
problems. What fixed the problem was using MatSetNullSpace for A with Q as
the nullspace, in addition to the above three steps.

So my question is what exactly is MatSetNullSpace doing? And since the full
A information is not present and A is only accessed through MAT_OP_MULT,
I'm confused as how MatSetNullSpace might be fixing the convergence issue.

Thanks,
Bikash

-- 
Bikash S. Kanungo
PhD Student
Computational Materials Physics Group
Mechanical Engineering
University of Michigan
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