Hi all, Thank you for your useful replies.
The matrix is A = [I - B_e F^-1 C_e] A_e, where F^-1 includes the inverse of a Laplace matrix and A_e, B_e and C_e are block diagonal matrices whose blocks are collected from smaller state-space equations, A_s (nxn), B_s (nxm) and C_s (mxn) so the blocks are full. The sparsity pattern of a 2 block example I have built so far is: * * * * * * * * * . . . . . . . * * * * . . . . . . * . . . . . * * * * * * * * . . . . * . . . . . . .* * * * . . . . . . * . I expect the same sort of "block diagonal + full rows" pattern to hold with more blocks, although some more advanced models would place selected off diagonal coupling terms into the sparsity pattern too. I suppose that the matrix does classify as sparse or at least structured by the definition above. I am not sure if there is a way to write it as A x = lambda B x with A and B sparse but there possibly might be. Thanks for the help and ideas. Michael On Thu, Jan 13, 2011 at 4:34 PM, Wolfgang Bangerth <[email protected]> wrote: > > Michael, > another question worth asking is why the matrix is not sparse. You say it's > because it involves the inverse of another matrix. Could you rewrite your > eigenvalue problem in the form > A x = lambda B x > where both A and B are sparse? > > W. > > ------------------------------------------------------------------------- > Wolfgang Bangerth email: [email protected] > www: http://www.math.tamu.edu/~bangerth/ > _______________________________________________ dealii mailing list http://poisson.dealii.org/mailman/listinfo/dealii
