Dear Wolfgang. Thanks a ton for your input! You are completely right. Now that is you mention it, the problem is completely obvious.
I really appreciate you pulling me out of that hole. Bests, Bob On Tue, 16 Apr 2019 at 15:49, Wolfgang Bangerth <bange...@colostate.edu> wrote: > On 4/15/19 8:46 AM, Robert Spartus wrote: > > > > > It is hard to imagine situations in which the mass matrix would be > singular. > > > It is a positive definite form that gives rise to the mass matrix and > so it > > > really shouldn't be singular at all. Can you show the code again with > which > > > you build it? > > > > It seems that my mesh is neither singular nor degenerate. I wonder if > the > > problem is that I am solving a vector valued problem. To build this mass > > matrix, I adapted the function Diffusion::assemble_system from step-52. > > I don't think the function you have gives you what you want. You have this: > > cell_mass_matrix(i, j) += > fe_values.shape_value(i, q_point) * > fe_values.shape_value(j, q_point) * > fe_values.JxW(q_point); > > If you read the documentation of FEValues::shape_value(), you will see > that > for vector-valued elements, it returns the one nonzero component of the > vector > shape function. So shape_value(i)*shape_value(j) will always return > something > nonzero. But what you really mean to do in your case is to multiply the > *vector* shape function i times the vector shape function j. Both of these > vectors may have a nonzero entry, but their dot product will only be > nonzero > if these components are the same. > > You will want to write the mass matrix here with extractors (i.e., > fe_values[...]) in the same way you would build any other matrix for > vector-valued problems. > > > > You will find the code attached, as well as the output of one run. If I > > isolate the mass matrix built and calculate its determinant in Python, > the > > result is indeed zero. > > Using the determinant is an unreliable technique for large matrices. Think > about the case where you have a 1000x1000 matrix with eigenvalues all > equal to > 0.1. This is a perfectly invertible matrix, but the determinant is > 0.1^1000, > which is zero for all practical purposes. You really need to look at the > eigenvalues themselves. > > But, seeing the issue I mentioned above, if you have two components, then > you > currently are computing the matrix > [ M M ] > [ M M ] > instead of > [ M 0 ] > [ 0 M ] > The former is clearly singular, so I'm not surprised. > > Best > W. > > > -- > ------------------------------------------------------------------------ > Wolfgang Bangerth email: bange...@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. > For more options, visit https://groups.google.com/d/optout. > -- 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. For more options, visit https://groups.google.com/d/optout.
