[petsc-users] A question on Schur complement

[saturday luis]

Hi PETSc team:

I want to consult for a good way of doing an approximated Schur complement
matrix. So I just want to handle a matrix in the format C + B^t B, or
sometimes B^t B.

An easy way is to run with the MatCreateSchurComplement to create C + B^t
inv A B, wherein A is an identity matrix. The downside is that the matrix
free style does not allow for algebraic preconditioners.

Another way is to generate the matrix B^t B. For my case, I checked the
sparsity of the resulting matrix from MatMatMult and it is pretty sparse
still. I found a similar approach in
http://www.mcs.anl.gov/petsc/petsc-current/src/snes/examples/tutorials/ex70.c.html
where the B^t B matrix is created explicitly (line 367-388). However, there
is a line of comment saying  " in real life this matrix would be build
directly without MatMatMult". So I just want to ask the best way of
assemblying and solving the B^t B matrix.

Thanks,

Luis
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