dealII

deal.II is an open-source C++ library designed for solving partial differential equations using the finite element method. It provides a comprehensive framework for generating and refining meshes, assembling system matrices and vectors, and solving large sparse linear and nonlinear systems, with facilities for post-processing and visualization. The library emphasizes high-order elements, hp-adaptivity, support for curved geometries, and robust parallel execution.

The project originated in academic research groups and has evolved into a community-driven project with developers and users worldwide. It is distributed under the BSD 3-Clause license and is free to use, modify, and redistribute. The source code is hosted on GitHub, with documentation and tutorials available on the project website.

Key features include a modular object-oriented design based on C++ templates, extensive finite element collections, and support for distributed memory parallelism via MPI. It integrates with external linear-algebra backends such as PETSc and Trilinos and provides interfaces to common mesh tooling and visualization formats (for example VTK). The p4est library is used for scalable parallel adaptive mesh refinement, enabling hp- or h-adaptivity on large meshes. The framework includes a large set of tutorials (Step-01 onward) that cover basic to advanced topics and serve both teaching and benchmarking purposes.

Areas of application span computational mechanics, fluid dynamics, electromagnetics, geophysics, and many other PDE-based simulations. deal.II is actively maintained with regular releases and an active user and developer community that convenes in workshops and online forums.