DUNE Features

The following list gives a short overview over the main features of DUNE and refers you to more detailed documentation.

Grid Implementations

So far seven grid implementations are available through the DUNE grid interface. Each is geared towards a different purpose and thus has a different set of features. Further grid managers can be obtained by downloading additional modules.

So far seven grid implementations are available through the DUNE grid interface. Each is geared towards a different purpose and thus has a different set of features.

• AlbertaGrid: The grid manager of the Alberta toolbox
• ALUConformGrid, ALUCubeGrid, and ALUSimplexGrid: A family of grids in two and three space dimension based on the ALUGrid library.
• GeometryGrid: A metagrid exchanging the host grid’s geometry
• OneDGrid: A sequential locally adaptive grid in one space dimension
• UGGrid: The grid manager of the UG toolbox
• YaspGrid: A structured parallel grid in n space dimensions

Linear Algebra

DUNE contains ISTL (the Iterative Solver Template Library) for powerful (parallel) linear algebra. The main features are:

• Abstractions for block matrices (e.g. compressed row storage BCRSMatrix, block diagonal matrices DiagonalMatrix and block vectors BlockVector, see doxygen documentation)
• Block structure arbitrarily nestable
• High performance through generic programming
• Expression templates for BLAS1 routines
• Several standard solvers (Krylov methods and stationary iterative methods)
• Highly scalable parallel algebraic multigrid method available as preconditioner.

Quadrature Formulas

• Quadrature rules for all common element types
• Rules for hypercubes up to order 19, for simplices up to order 12
• Easy access

Shape Functions

• Lagrangian shape functions of arbitrary order
• Monomial shape functions of arbitrary order for Discontinuous Galerkin methods
• Orthonormal shape functions of arbitrary order
• Raviart-Thomas shape functions of lowest order for cube and of arbitrary order for simplex elements

Input/Output

• Reading grid files in the gmsh format
• Reading grid files in the grid independent Dune grid format DGF
• Reading simplex grids through DGF constructed using the tools Tetgen and Triangle
• Reading and writing in the AmiraMesh format
• Subsampling of high-order functions
• Write grids and data in the format of the visualization toolkit (vtk)
• Visualization using GRAPE
• Output in Data Explorer format

Discretization Module

There are some discretization modules available which provide

• Arbitrary order lagrange spaces for different grid structures
• Discontinuous Galerkin spaces of arbitrary order both with orthonormal and Lagrange basis function
• Further discrete function spaces include Raviart-Thomas, Nedelec, and others
• Linear and non-linear solvers
• Time discretization method, e.g., explicit, implicit, and IMEX Runge-Kutta methods or multistep methods
• Support for parallelization and adaptivity (both h and p refinement)