From the website: "deal.II is a C++ program library targeted at the computational solution of partial differential equations using adaptive finite elements." Its primary authors are: Wolfgang Bangerth at Texas A&M University, Ralf Hartmann at the Deutsches Zentrum f@uuml;r Luft- und Raumfahrt (DLR), and Guido Kanschat also at Texas A&M University.
Put more simply, this is a convenient and flexible set of subroutines which one can use to write a program for finite element simulation of mechanical stress and deformation of a solid part, flow and pressure in a fluid, heat transfer, diffusion, electromagnetics, materials microstructure development, and many other physical phenomena. But it cannot be called user-friendly: the user must write a program which calls the deal.II subroutines, or adapt one of its many example programs.
In all of these ways, deal.II is very similar to libMesh. In fact, their feature sets overlap quite a bit. For example:
One of the primary differences between the two suites is in their examples, which reflect the backgrounds and goals of the teams which wrote them. deal.II is oriented toward mechanics, and its tutorial builds to elastic mechanics for computing deformation waves traveling through a solid. libMesh comes from a computational fluid dynamics group, so its most complex examples involve fluid flows which change with time.
To summarize, deal.II is a flexible suite of finite element analysis tools with exhaustive documentation. It has an active community of developers, focused around but by no means limited to the three primary authors. Its examples make it an ideal foundation for building complex simulations of mechanical deformation.
As for whether deal.II or libMesh is better for your needs, that will depend on your application and personal preference for the style of the libraries. Both are easy to install and test using the Opennovation Ubuntu backport repository.
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