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

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

ISBN-10: 3642285880

ISBN-13: 9783642285882

ISBN-10: 3642285899

ISBN-13: 9783642285899

DUNE, the dispensed and Unified
Numerics atmosphere, is an open-source modular toolbox
for fixing partial differential equations with grid-based tools.
This publication covers contemporary advances within the improvement
and utilization of DUNE.
It involves a set of thirteen articles which normally advanced from talks given on the First DUNE person assembly in Stuttgart, Germany, 6.-8.10.2010.
The articles well illustrate the complex features and the powerful versatility of the DUNE framework. the 1st half provides extensions of the DUNE middle modules, together with the development of neighborhood finite point 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., lowered foundation tools, unfitted discontinuous Galerkin equipment, optimum regulate difficulties, and porous media functions.
Specific equipment and functions 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 point package.

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

Example text

Consider the initial value problem ∂t u + ∇g · u2 v(x) = 0 2 u(·, 0) = u0 in S2 ×]0, T [, (5) in S2 for a given, divergence-free velocity field v : S2 → T S2 and given initial data u0 ∈ L∞ (S2 ). Here, ∇g · denotes the divergence operator induced by the Riemannian metric g. For the numerical experiments, we use a shear flow v(ϕ , θ ) = a(θ ) sin ϕ , cos ϕ , 0 , where ϕ ∈ [0, 2π [ and θ ∈ [−π , π ] denote the spherical coordinates of a point. Fig. 2 Numerical solution to (5) with a standard finite volume method on 3 028 288 triangles distributed onto 16 processes.

Dedner and M. Nolte in this book. 3 Prismatic Grid Let H be a d-dimensional grid in a w-dimensional world, called the host grid. The 0 . Now, let L be a fixed set of entities of codimension 0 in H will be denoted by EH number of layers and α0 < α1 < . . < αL . 0 and By pe,i we will denote the prismatic cell constructed from an entity e ∈ EH the interval [αi , αi+1 ] for i = 0, 1, . . , L − 1. The domain occupied by the prismatic cell is given by dom(pe,i ) = e × [αi , αi+1 ] = { (x, xd+1 ) | x ∈ e, xd+1 ∈ [αi−1 , αi ] } ⊂ Rw+1 .

Thereby, internally only one full traversal of the host grid is needed. However, the default setting may easily be changed by the user. 3 Determining the Reference Element As described in Section 2, the reference element of an entity has to be determined dynamically. Let hostEntity denote a host grid entity of dimension dim. The method type() returns the GeometryType of an entity. Since the introduction of the generic reference elements this class has not to be extended any more for grids introducing new reference element types in D UNE -G RID.

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Advances in DUNE: Proceedings of the DUNE User Meeting, Held in October 6th–8th 2010 in Stuttgart, Germany by Andreas Dedner, Visit Amazon's Bernd Flemisch Page, search results, Learn about Author Central, Bernd Flemisch, , Robert Klöfkorn


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