Dear Prof Bangerth. Thank you for your reply.
I had seen that github issue/pull-request, but didn't realise that "saddle-point problems = (indefinite + symmetric)". These three words do not appear in close-proximity to each other anywhere in the slides, tutorials or video lectures. While I acknowledge the importance of mathematical terminology, perhaps it would be quite useful to de-jargonise this for the newcomers? Now, my question becomes "how to test for definiteness and symmetric nature of my DAEs?", i.e. simply by looking at the weak form of the equation which consists of only symbolic notations, can one somehow infer the definiteness/symmetry of the matrix? Regards, Krishna On Wed, 11 Mar 2020 at 17:17, Wolfgang Bangerth <bange...@colostate.edu> wrote: > On 3/11/20 7:57 AM, Krishnakumar Gopalakrishnan wrote: > > In Step-21 tutorial, we have a statement that starts with the following > > (emphasis is mine): > > > > /_"Given the saddle point structure_ of the first two equations and > > their similarity to the mixed Laplace formulation we have introduced in > > step-20 > > < > https://nam01.safelinks.protection.outlook.com/?url=https%3A%2F%2Fdealii.org%2Fdeveloper%2Fdoxygen%2Fdeal.II%2Fstep_20.html&data=02%7C01%7CWolfgang.Bangerth%40colostate.edu%7Ccd1596e29c4a427d467808d7c5c41aa8%7Cafb58802ff7a4bb1ab21367ff2ecfc8b%7C0%7C1%7C637195318357612315&sdata=1Y%2Fp8SQc%2F2YETGls%2FU5J8XPtkz5JLEZW%2FYGdLEnM9rc%3D&reserved=0 > >"/ > > / > > / > > // > > It would be helpful if someone could explain the saddle-point structure > > of the problem (and/or point to some easily readable online resources). > > [...] > > However, I'd really appreciate if there was some "simple test" or > > practical advice to determine whether our own PDEs and DAEs belong to > > the saddle-point category or not, i.e. how to detect the presence of > > saddle-point nature of the PDEs, just simulate with Qp elements and look > > for a checkerboard pattern in the results? > > I thought we had addressed this a while ago already: > https://github.com/dealii/dealii/pull/9470/files > > Is that not enough? Or is the issue that the text added there just says > "indefinite", whereas you are looking for the term "saddle point problem"? > > I think a good approximation is that > saddle point problem = indefinite + symmetric > > We could presumably add this there. > > 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. To view this discussion on the web visit https://groups.google.com/d/msgid/dealii/CABvf3kZWr2iWJOJ%2BtrxuDYrPfBCFzCe%3D4JzMmTBthEosf6Z-Tw%40mail.gmail.com.
