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 41.75: Parallelization on a cluster of distributed memory machines — Part 4: Parallel solvers and preconditioners
Solving PDEs in parallel ultimately requires solving linear systems in parallel. There are two historical approaches to this: Domain Decomposition and Global Solvers, though only the latter is in widespread use these days. This lecture gives an introduction to Domain Decomposition and its limitations. It then discusses how solvers and preconditioners are constructed for parallel computing, and what algorithms are needed to implement them.
Slides: click here