Titlebook: DUNE — The Distributed and Unified Numerics Environment; Oliver Sander Textbook 2020 Springer Nature Switzerland AG 2020 Dune.software.fin

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Getting Started with DuneThis chapter describes the first steps with DUNE. It shows how to install DUNE on a computer, and how to create a first DUNE module. Then, it presents two example applications that give a first impression of how DUNE can be used.

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Grids and the Dune Grid InterfaceThe dune-grid module and the interface to finite element grids it contains are the historical and conceptual core of the DUNE software system.

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Dune Grids on Distributed MachinesThe previous chapter has always assumed that there is a single process only, which knows the entire grid. However, a considerable portion of today’s applications needs multi-processor machines to run, either to keep the run-time acceptable or to handle the large storage requirements, frequently both.

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Linear Algebra with dune-istlBesides the grids and their data structures, it is probably the linear algebra that requires most care in a finite element code. This is so because the linear systems resulting from finite element discretizations can get enormously big.

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Quadrature RulesBoth finite element and finite volume methods are based on integral expressions, and these are usually computed using numerical quadrature. Computer codes implementing such methods need to provide quadrature rules, and Dune is no exception.

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Function Space Bases and Discrete FunctionsIn previous chapters we have described the DUNE interface for grids, linear algebra, and finite element shape functions. Now we move one level up in the abstraction hierarchy and consider global function spaces and functions.