Dear firedrakers, Can we have a discussion about the "R" space (function space of global constants), which if I understand correctly has not been implemented? Clearly, the R space is not good for performance, since it inserts an entire column or row into the matrix of non-zero entries, and the high performance solution is to solve the problem with a Krylov solver by projecting out the constant from the solver as Lawrence has recently implemented. However, the R space is useful for verifying other parts of Firedrake by e.g. computing eigenvalues of the Laplacian etc. I argue that we want this feature for testing, even though we don't expect to use it for big production code. --cjc
On 12/03/14 06:35, Cotter, Colin J wrote:
Dear firedrakers, Can we have a discussion about the "R" space (function space of global constants), which if I understand correctly has not been implemented?
R is useful for things other than boundary conditions, too. If you have a constrained optimisation problem with a single constraint (an integral constraint, say, like [0]), you'll need R to write down the associated KKT system. I don't see how that would be possible with passing nullspaces to Krylov solvers. (Please enlighten me if someone here does know how.) Some problems really just do have a global coupling through a single real. (I also completely understand that its implementation is a pain) Patrick [0] 10.1002/fld.426
On 12/03/14 09:17, Patrick Farrell wrote:
R is useful for things other than boundary conditions, too. If you have a constrained optimisation problem with a single constraint (an integral constraint, say, like [0]),
P.S. For working code where you need this, see https://bitbucket.org/dolfin-adjoint/da-applications/src/3907be10e58ab0f61e5... which solves the KKT equations associated with example 4 of [0] by means of a combined continuation on log barrier terms and casting the problem as a mixed complementarity problem to the PETSc VI solver. I'd be dead impressed if firedrake could do this (even more so if it could do this on GPUs). Patrick
participants (2)
-
Cotter, Colin J
-
Patrick Farrell