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Ok, I should have been more explicit. I'm trying to implement the Elman et al. style preconditioner for Stokes using FEniCS and dolfin, in which the system:<div><br class="webkit-block-placeholder"></div><div>K = [A B^T; B 0]</div><div>A the vector laplacian, B the divergence operator, B^T the gradient operator, is preconditioned with an approximate inverse of</div><div><br class="webkit-block-placeholder"></div><div>P = [ A 0; 0 Q]</div><div>where A is still the vector laplacian, and Q is the pressure mass matrix.</div><div><br class="webkit-block-placeholder"></div><div>Matrix A naturally appears in the construction of matrix K, but matrix Q will be constructed separately. I can grab matrix A as a submatrix from K, but the question then becomes how to assemble them into a matrix P to hand off to:</div><div><div><br class="webkit-block-placeholder"></div><div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><font face="Helvetica" size="3" style="font: 12.0px Helvetica">KSPSetOperators(ksp, K, P, SAME_NONZERO_PATTERN);</font></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><br></div></div><div><br><div><div>On Jan 6, 2008, at 8:40 AM, Barry Smith wrote:</div><br class="Apple-interchange-newline"><blockquote type="cite"><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Gideon,</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><span class="Apple-converted-space"> </span>It really depends on what you want to use this new matrix for? If you wish to do</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">matrix vector products with it then I would suggest making a shell matrix that then</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">calls the matrix vector product on each part.<span class="Apple-converted-space"> </span>In other words, if possible you probably</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">want to avoid explicitly constructing this entire new matrix, unless you really need</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">it.</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><span class="Apple-converted-space"> </span>Barry</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">On Jan 5, 2008, at 7:54 PM, Gideon Simpson wrote:</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><br></div> <blockquote type="cite"><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Suppose I have two sparse matrices A and Q and now I want to construct a block diagonal matrix, K,</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">K = <span class="Apple-tab-span" style="white-space:pre"> </span>[A,0]</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><span class="Apple-tab-span" style="white-space:pre"> </span>[0,Q]</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">What is the "right" way to do this is?</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">-Gideon Simpson</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><span class="Apple-converted-space"> </span>Department of Applied Physics and Applied Mathematics</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><span class="Apple-converted-space"> </span>Columbia University</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><br></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><br></div> </blockquote><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><br></div> </blockquote></div><br></div></div></body></html>