Reference documentation for deal.II version GIT relicensing-1054-gedd46abbd6 2024-07-12 01:20:01+00:00
\(\newcommand{\dealvcentcolon}{\mathrel{\mathop{:}}}\) \(\newcommand{\dealcoloneq}{\dealvcentcolon\mathrel{\mkern-1.2mu}=}\) \(\newcommand{\jump}[1]{\left[\!\left[ #1 \right]\!\right]}\) \(\newcommand{\average}[1]{\left\{\!\left\{ #1 \right\}\!\right\}}\)
No Matches
The geodynamics demonstration suite

deal.II's tutorial contains a set of programs that together form the geodynamics demonstration suite. The idea of these programs is to demonstrate techniques for advanced finite element software using applications from geodynamics, i.e. the investigation of processes in the solid earth. By doing so, these programs are supposed to provide a basis for more specialized, dedicated programs that can solve actual geodynamics problems, for example as part of the work of graduate students or postdocs. A more thorough discussion of the motivation for these programs follows below.

Currently, the geodynamics testsuite contains the following programs:

Some of these programs were developed under contract from the California Institute of Technology with support by the National Science Foundation under Award No. EAR-0426271, the first of the grants that funded the Computational Infrastructure in Geodynamics initiative. The recipient, Wolfgang Bangerth, gratefully acknowledges this source of support.


Adaptive mesh refinement (AMR) has long been identified as a key technology that would aid in the accurate and efficient numerical solution of a number of geodynamics applications. It has been discussed in the geodynamics community for several years and has been a continuous topic on the task list of CIG since its inception. Yet, relatively little has happened in this direction so far. Only recently have there been attempts to use AMR in geodynamics: CIG sponsored a workshop on AMR technique in Boulder in October 2007; a collaboration between George Biros, Omar Ghattas, Mike Gurnis, and Shijie Zhong's groups is currently developing a parallel adaptive mantle convection solver; and some of the principal developers of deal.II eventually developed the ASPECT code for the simulation of mantle convection that is by now a rather established and widely used code.

One of the reasons for the slow adoption of AMR techniques in geodynamics is the relatively steep initial hurdle: codes have to provide the data structures and algorithms to deal with adaptive meshes, finite elements have to be able to deal with hanging nodes, etc. To do so efficiently and in sufficient generality adds several 10,000 lines of code to finite element programs, too much for the average student to do within the time frame of a dissertation. On the other hand, there are libraries that provide the infrastructure code on which applications supporting AMR can rapidly be built. deal.II of course provides exactly this infrastructure.

The goal of the geodynamics testsuite is to write programs for a variety of topics relevant to geodynamics. Continuing in the style of the existing tutorial programs – an extensive introduction explaining the background and formulation of an application as well as the concepts of the numerical scheme used in its solution; detailed comments throughout the code explaining implementation details; and a section showing numerical results – we intend to provide the resulting programs as well-documented applications solving model problems. In particular, they are aimed at the following goals: