[petsc-users] Assembling Restriction and Prolongation Operators for Parallel Calculations

[Eric Mittelstaedt]

Hello all,
    We are working on implementing restriction and prolongation 
operators for algebraic multigrid in our finite difference (staggered 
grid) code that solves the incompressible Stokes problem.  So far, the 
restriction and prolongation operators we have assembled in serial can 
successfully solve on a simple 2D grid with multiple-level v-cycles.  
However, we are running into problems when we attempt to progress to 
parallel solves.  One of the primary errors we run into is an 
incompatibility in matrix types for MatMatMatMult and similar calls:

[0]PETSC ERROR: [1]PETSC ERROR: MatMatMatMult() line 9173 in 
/opt/petsc/src/mat/interface/matrix.c MatMatMatMult requires A, seqaij, 
to be compatible with B, mpiaij, C, seqaij
MatMatMatMult() line 9173 in /opt/petsc/src/mat/interface/matrix.c 
MatMatMatMult requires A, seqaij, to be compatible with B, mpiaij, C, seqaij


The root cause of this is likely the matrix types we chose for 
restriction and prolongation. To ease calculation of our restriction (R) 
and prolongation (P) matrices, we have created them as sparse, 
sequential matrices (SEQAIJ) that are identical on all procs.  Will this 
matrix type actually work for R and P operators in parallel?

It seem that setting this matrix type correctly is the heart of our 
problem.  Originally, we chose SEQAIJ because we want to let Petsc deal 
with partitioning of the grid on multiple processors.  If we do this, 
however, we don't know a priori whether Petsc will place a processor 
boundary on an even or odd nodal point.  This makes determining the 
processor bounds on the subsequent coarse levels difficult.  One method 
for resolving this may be to handle the partitioning ourselves, but it 
would be nice to avoid this if possible. Is there a better way to set up 
these operators?

Thank you,
Eric and Arthur