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.

The videos are part of a broader effort to develop a modern way of teaching Computational Science and Engineering (CS&E) courses. If you are interested in adapting our approach, you may be interested in this paper I wrote with a number of education researchers about the structure of such courses and how they work.

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 9: step-2: Degrees of freedom, sparsity in finite element matrices

This lecture introduces step-2, the second deal.II tutorial program. It first discusses the concept of sparsity in finite element matrices and its central role in making the finite element method work in practice. It then shows how it arises from an enumeration of all degrees of freedom on a mesh, how this is done in deal.II, and how to visualize the resulting sparsity pattern upon which finite element matrices will be based.

Note: The video shows how to visualize the sparsity pattern using Gnuplot. Newer versions of deal.II instead generate the output in SVG format, and you can view the sparsity pattern by just loading the output file into any web browser.

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Slides: click here