Starting in the spring 2013, I videotaped the lectures for my MATH 676: Finite element methods in scientific computing course at the KAMU TV studio at Texas A&M. These are lectures on many aspects of scientific computing, software, and the practical aspects of the finite element method, as well as their implementation in the deal.II software library. Support for creating these videos was also provided by the National Science Foundation and the Computational Infrastructure in Geodynamics.
Note 1: In some of the videos, I demonstrate code or user interfaces. If you can't read the text, change the video quality by clicking on the "gear" symbol at the bottom right of the YouTube player.
Note 2: deal.II is an actively developed library, and in the course of this development we occasionally deprecate and remove functionality. In some cases, this implies that we also change tutorial programs, but the nature of videos is that this is not reflected in something that may have been recorded years ago. If in doubt, consult the current version of the tutorial.
Lecture 21: Block structured solvers for vector-valued problems
Vector-valued problems naturally lead to block-structured matrices that allow for solvers that use this structure. I discuss how this block structure arises out of the bilinear form and how to exploit it in a Schur complement solver for the mixed Laplace equation. The class then shows how this is implemented in step-20. The lecture also finishes up some unfinished business on visualizing the solution of vector-valued problems using vector field plots left over from the previous lecture.
The lecture fails to show how to make sure the velocity degrees of freedom are
indeed sorted before the pressures. This happens by calling
DoFRenumbering::component_wise in the
make_grid_and_dofs function of this program. See the
documentation of step-20 for more information.
There were a number of typos in the formulas on the slides shown in the
lecture; these have been corrected on the slides linked to on this page. I
also got confused when trying to find the
in step-20. This class was a part of deal.II at the time when I
recorded the video. However, it has since been removed and this part
of the step-20 tutorial program now uses
LinearOperator framework of deal.II (with similar
functionality, but easier to read syntax).
Slides: click here