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 setting, is an open-source modular toolbox
for fixing partial differential equations with grid-based equipment.
This booklet covers contemporary advances within the improvement
and utilization of DUNE.
It involves a suite of thirteen articles which frequently advanced from talks given on the First DUNE person assembly in Stuttgart, Germany, 6.-8.10.2010.
The articles properly illustrate the complex functions and the robust versatility of the DUNE framework. the 1st half offers 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 numerous exterior DUNE modules facing, e.g., diminished foundation tools, unfitted discontinuous Galerkin equipment, optimum regulate difficulties, and porous media functions.
Specific equipment and purposes are topic of the 3rd half,
ranging from two-phase move in porous media over the implementation of hybrid discontinuous Galerkin and heterogeneous multi-scale tools 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

Example text

2) In [3, 6] a Local Discontinuous Galerkin discretization for this system is presented. In order to overcome the difficulty of the time-dependent domain the so-called σ coordinate transformation tˆ = t, xˆ = x, zˆ = σ (x, z,t) = z − b(x) . h(x,t) is applied to the system. Then, the transformed computational domain is fixed in time, Ωˆ = {(x, ˆ zˆ) | (x, z) ∈ Ωt } = Ωx × (0, 1), (3) see Figure 5b. The geometry of Ωx may be very complex and may be captured by unstructured grids only. However, using an unstructured grid in all spatial dimensions would make the evaluation of of depth-averaged quantities as in (2) a nontrivial task.

To facility this step, special axpy like methods are provided on the local functions and matrices: • void axpy ( const PointType &x, const RangeType &s ); be,ϕ += s · ϕ (x) for all ϕ ∈ Veˆ . • void axpy ( const PointType &x, const JacobianRangeType &ds ); be,ϕ += ds : Dϕ (x) for all ϕ ∈ Veˆ . • void axpy ( const PointType &x, const RangeType &s, const JacobianRangeType &ds ); Equivalent to axpy( x, s ) ; axpy( x, ds ) ; Listing 2 Assembling mass matrix and right hand side // M. M. b. initialization of M and b reserve () ; clear () ; clear () ; / / create some temporary storage for the values of the local base functions Veˆ e s t d : : v e c t o r v a l u e s ; / / walk over the grid Th c o n s t I t e r a t o r T y p e end = s p a c e .

NumBaseFunctions ( ) ; va lue s . r e s i z e ( numBaseFunctions ) ; / / compute the integrals e ϕi ϕ j and e f ϕi using a quadrature with base function caching t y p e d e f C a c h i n g Q u a d r a t u r e Q u a d r a t u r e T y p e ; Q u a d r a t u r e T y p e q u a d r a t u r e ( e n t i t y , 2∗ s p a c e . o r d e r ( ) +1 ) ; c o n s t u n s i g n e d i n t nop = q u a d r a t u r e . nop ( ) ; f o r ( u n s i g n e d i n t qp = 0 ; qp < nop ; ++ qp ) { c o n s t Q u a d r a t u r e T y p e : : C o o r d i n a t e T y p e &x = q u a d r a t u r e .

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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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