Advances in DUNE: Proceedings of the DUNE User Meeting, Held by Andreas Dedner, Visit Amazon's Bernd Flemisch Page, search

By Andreas Dedner, Visit Amazon's Bernd Flemisch Page, search results, Learn about Author Central, Bernd Flemisch, , Robert Klöfkorn

DUNE, the dispensed and Unified
Numerics surroundings, is an open-source modular toolbox
for fixing partial differential equations with grid-based equipment.
This booklet covers fresh advances within the improvement
and utilization of DUNE.
It comprises a suite of thirteen articles which ordinarily developed from talks given on the First DUNE person assembly in Stuttgart, Germany, 6.-8.10.2010.
The articles properly illustrate the complex features and the robust versatility of the DUNE framework. the 1st half provides extensions of the DUNE middle modules, together with the development of neighborhood finite aspect areas, a discretization toolbox, and meta-grids,
as good as a dialogue of functionality pitfalls. the second one half introduces a number of exterior DUNE modules facing, e.g., decreased foundation tools, unfitted discontinuous Galerkin tools, optimum keep an eye on difficulties, and porous media functions.
Specific tools and purposes are topic of the 3rd half,
ranging from two-phase circulate in porous media over the implementation of hybrid discontinuous Galerkin and heterogeneous multi-scale equipment as much as the coupling of DUNE with an latest finite aspect package.

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Extra resources for Advances in DUNE: Proceedings of the DUNE User Meeting, Held in October 6th–8th 2010 in Stuttgart, Germany

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By definition, top and bottom surface of the convex polytope pe,i are “flat”. Subentities parallel to the the newly added spatial direction are called “non-flat”. , 0 0 EP(H ) = { pe,i | e ∈ E (H ), i = 0, 1, . . , L − 1 }. The D UNE -P RISM G RID Module 37 The grid dimension of P(H ) is d + 1, and the world dimension is w + 1. In general, a prismatic grid will by hybrid. If H is a conforming grid, P(H ) will be conforming as well. In the newly added direction, grid cells will always align. At the time of this writing, the distribution of prismatic cells in this direction is restricted to the structured case αi = α0 + iΔ , Δ = (αL − α0 )/L.

Listing 5 Adapting and communicating a discrete function / / type of the default restriction and prolongation operator t y p e d e f R e s t r i c t P r o l o n g D e f a u l t RestrictProlongType ; / / type of the adaptation manager t y p e d e f A d a p t a t i o n M a n a g e r i AdaptationManagerType ; / / create restriction and prolongation operator for u and the adaptation manager RestrictProlongType uRestrictProlong ( u ) ; AdaptationManagerType adaptationManager ( hgrid , u R e s t r i c t P r o l o n g ) ; / / mark grid for refinement and coarsening using some external method mark mark ( h g r i d , u ) ; / / adapt the grid with automatic restriction and prolongation of the discrete function u adaptManager .

I n i t i a l i z e ( u ) ; / / time loop for ( t i m e P ro v i d e r . i n i t ( ) ; t i m e P ro v i d e r . time ( ) < T; timeProvider . next () ) { t i m e P r o v i d e r . p r o v i d e T i m e S t e p E s t i m a t e ( maxTimeStep ) ; odeSolver . solve ( u ) ; } We conclude our short survey of the module D UNE -F EM by demonstrating the concepts for including adaptivity and parallelization. Using the adaptation manager from D UNE -F EM and the default restriction/prolongation operators on the discrete D UNE -F EM: A general purpose discretization toolbox 25 function space, the few lines of code for adapting a grid and keeping the discrete functions consistent, are given in Listing 5.

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