I concur with Satish, AIJ with inodes is essentially variable block size so trying to force BAIJ when it is not appropriate is unnecessary.
Barry On Apr 21, 2008, at 9:53 AM, Jed Brown wrote: > I am solving a Stokes problem with nonlinear slip boundary > conditions. I don't > think I can take advantage of block structure since the normal > component of > velocity has a Dirichlet constraint and this must be built into the > velocity > space in order to preserve conditioning. An alternative formulation > involves a > Lagrange multiplier for the constraint, but even with clever > preconditioning, > this system is still more expensive to solve according to [1]. > > In solving the (velocity-pressure) saddle point problem, many > approximate solves > with the velocity system is needed in the preconditioner, hence I > need a strong > preconditioner for the velocity system. Currently, I am using > algebraic > multigrid on a low-order discretization which works fairly well. > Since Hypre > and ML only take AIJ matrices, perhaps I shouldn't worry about > blocking after > all. Is there a way to use MATBAIJ when some nodes have fewer > degrees of > freedom? Should I bother? > > Note that my method (currently just a single element) uses a high > order > discretization on some elements and low order on others. The global > matrix for > the low order elements is assembled, but it is applied locally for > the high order > elements taking advantage of the tensor product basis. For the > preconditioner, > a low order discretization on the nodes of the high order elements > is globally > assembled and added to the global matrix from the low-order elements. > Experiments with a single element (spectral rather than spectral/hp > element) > show this to be effective, converging in a constant number of > iterations > independent of polynomial order when using a V-cycle of AMG as a > preconditioner. > > Thanks. > > Jed > > > [1] B?nsch, H?hn 2000, `Numerical treatment of the Navier-Stokes > equations with > slip boundary conditions', SIAM J. Sci. Comput. >
