> On Mar 6, 2018, at 4:37 PM, Ju Liu <liu...@gmail.com> wrote: > > > > 2018-03-06 14:13 GMT-08:00 Smith, Barry F. <bsm...@mcs.anl.gov>: > > > > On Mar 6, 2018, at 4:09 PM, John <johnlucassatur...@gmail.com> wrote: > > > > Hi PETSc team: > > > > I am trying to create a SIMPLE type approximation for the Schur complement. > > It is a nonlinear code, so I have to update the Schur matrix once the > > tangent jacobian is updated. I am trying to figure out the best way of > > doing that. > > > > In terms of generating an algebraic form of Schur S, I am trying to do the > > following. > > > > // S = A10 x A01, I have performed a diagonal scaling on all matrices, so > > the diag(A00) = I. > > MatMatMult(A10, A01, MAT_INITIAL_MATRIX, S); > > MatScale(S, -1.0); // S = -1 x S > > MatAXPY(S, 1.0, A11, S, DIFFERENT_NONZERO_PATTERN); // S = A11 + S > > > > My questions are: > > (1) When I update the Schur complement, do I need to call > > MatDestroy(&S); > > MatMatMult(A10, A01, MAT_INITIAL_MATRIX, S); > > or shall I just call > > MatMatMult(A10, A01, MAT_REUSE_MATRIX, S); > > The second form. No reason to delete the matrix and rebuild it each time > (delete and rebuild will be a bit slower) > > > > > Basically, I am not sure how to properly use the flag MAT_REUSE_MATRIX. > > > > (2) When I update the Schur complement, the initial call of MatAXPY already > > incorporated the contribution of A00 in terms of nonzero patterns. So in my > > second call of MatAXPY, shall I use the flag SUBSET_NONZERO_PATTERN? > > If it is a subset then you should use the subset flag, if they have same > nonzero pattern you should use SAME_NONZERO_PATTERN (same nonzero is fastest) > > Thanks Barry! I guess I still need some clarifications on the second point. > > In the first assembly of S, I called MatAXPY to incorporate the entries of > A11 into S (with differnet nonzero pattern for safety). > > Now, with new blocks of A, I update S by calling > MatMatMult(A10, A01, MAT_REUSE_MATRIX, S);

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Ahh, you cannot do this if the MatAXPY introduces new nonzeros into the structure of S (the second MatMatMult() will likely crash or generate incorrect results since MAT_REUSE_MATRIX requires that each time the routine is called S has the exact same nonzero pattern.) Now for most problems I would expect that A11 has a subset of the nonzeros of S, in that case you can use MatAXPY with subset each time and you can use MAT_REUSE_MATRIX. But you would need to verify for your problem that A11 has a subset of the nonzeros of S. This is the "ideal" case in terms of performance. If A11 does not have a subset of the nonzeros of S then you (obviously) cannot use subset and you must destroy the S each time and create a new one with each MatMatMult(). Barry > At this stage, what is the nonzero pattern of S? If S's pattern is determined > by the most recent call of MatMatMult, I guess I will still use the different > nonzero pattern. If the pattern of S is inherited from the first assembly, > the A11's nonzero pattern is a subset of S's, so subset flag should be safe. > > Thanks! > > John > > > > > Barry > > > > > Best regards, > > > > John > > > > > -- > Ju Liu, Ph.D. > Postdoctoral Research Fellow > Stanford School of Medicine > http://ju-liu.github.io/