Hi Wolfgang, Yes the diagonal could be negative when k rises. Will Chebyshev preconditioner smoother converge when there are negative entries?
In my case k hasn't rise so large that diagonal entries is negative. The negative entries shows up only when compute_normal_flux constraints is applied. I think AffineConstraints::distribute_local_to_global <https://www.dealii.org/current/doxygen/deal.II/classAffineConstraints.html#a373fbdacd8c486e675b8d2bff8943192:~:text=Thus,%20if%20a%20degree,in%20the%20global%20matrix.> is the cause since in matrix-based assemble, this function add a positive value on the constrained dofs while matrix-free does not. Therefore the diagonals are different between matrix-free and matrix-based. Best, Wayne 在2023年2月15日星期三 UTC+8 00:39:41<Wolfgang Bangerth> 写道： > On 2/14/23 07:15, 'yy.wayne' via deal.II User Group wrote: > > The weak problem I'm solving is <curl u, curl u> + <div u, div u> - > > k^2<u, u> = RHS, which is vector Maxwell wave equation (for nodal basis). > > [...] > > 1) Is it reasonable the diagonal computed by MatrixFree operator with > > compute_normal_flux() has negative entries? > > The diagonal entries of the matrix, for this bilinear form, are > integrals of the form > > A_ii = \int (curl phi_i)*(curl phi_i) + (div phi_i)*(div phi_i) > - k^2 phi_i * phi_i > > In other words, A_ii is a sum of squares, but one of the squares is > negative. If k is small, the sum may still be positive, but for sure if > k is large, the diagonal entries of A will be negative. > > Best > W. > > -- > ------------------------------------------------------------------------ > Wolfgang Bangerth email: bang...@colostate.edu > www: http://www.math.colostate.edu/~bangerth/ > -- The deal.II project is located at http://www.dealii.org/ For mailing list/forum options, see https://groups.google.com/d/forum/dealii?hl=en --- You received this message because you are subscribed to the Google Groups "deal.II User Group" group. To unsubscribe from this group and stop receiving emails from it, send an email to dealii+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/dealii/0067be90-8710-4184-a33d-48c7c5fbdc3an%40googlegroups.com.
