Software for Finite Element Simulations and Scientific Computing

The use of advanced numerical techniques such as adaptive finite element meshes, multigrid, hp-adaptivity, or distributed computing requires complex software. The resulting programs are often large and utilize complicated data structures. Advances in these areas are therefore only possible if one re-uses and extends existing software, rather than write it anew for each project.

Under the leadership of two Texas A&M professors, Wolfgang Bangerth and Guido Kanschat, the Numerical Analysis group continues to develop the deal.II library that provides a large set of standard components for adaptive finite element computations and scientific computing in general. In particular, it offers h-, p-, and hp-adaptive meshes in one, two, and three space dimensions, a variety of finite elements, multigrid, support for parallel computing, and many other components. In order to allow other researchers to use the library, it comes with extensive documentation of all interfaces (more than 5000 pages) and a collection of example programs that demonstrate the use of the library. Since its inception, deal.II has grown to more than 370,000 lines of code, and has become one of the best known and most widely used finite element libraries in the field of computational mathematics research and applied sciences (see, for example, the list of publications obtained with the help of deal.II).

With several hundred installations world-wide, more than 100 downloads per month, and several thousand hits per month on its homepage http://www.dealii.org, it has received positive response from researchers and students in a wide range of scientific fields, including computational fluid dynamics, glacier flow, fuel cell design, cancer imaging, and computational biology. The deal.II project has been successful beyond expectations. It is part of the SPEC CPU2006 industry standard testsuite for computer systems and compilers. Its authors have also been awarded the 2007 J. H. Wilkinson Prize for Numerical Software.

To give an impression of the breadth of applications and the scope of capabilities here are a few images from the deal.II Wiki (see there for more details and attribution to the authors of the respective programs):

Porous media flow in a random media	Magnetic field lines in a rotating electrically conducting medium such as the earth's core	Simulation of crystal growth	Flowlines of fluid flow around an obstacle in 3d	Isosurfaces of displacement of a cylinder vertically stressed between two plates	Optimization of the topology of an electrically conductive medium

Current research and work on the library is focused on practical aspects of hp-adaptivity, parallelization of algorithms using multicore processors, and in particular further pushing the limits of parallel computing into the range of hundreds of millions to billions of unknowns on fully adapted 3D meshes. The goal is to make deal.II a standard tool for adaptive finite element simulations in applied mathematics and related fields.