Authors:Oliver Sander, Markus Blatt, Bernd Flemisch Pages: 1 - 2 Abstract: Dune, the Distributed and Unified Numerics Environment has been under continuous development for more than 13 years. Several European institutions participate in this development, and over time, a substantial user community has evolved. In order to establish and foster personal contacts within the community as well as between users and developers, a first Dune User Meeting was held in Stuttgart in 2010, followed by a second one that took place in 2013 in Aachen. In 2015, the third Dune User Meeting was held in Heidelberg from 28th to 29th of September. More than 30 users and developers from five European countries attended, presented Dune-related work and engaged in lively discussions. Ten presentations resulted in contributions to these proceedings. PubDate: 2017-04-03 DOI: 10.11588/ans.2017.1.36872 Issue No:Vol. 5, No. 1 (2017)

Authors:Martin Alkämper, Andreas Langer Pages: 3 - 19 Abstract: The utility of Dune-ACFem is demonstrated to work well for solving a non-smooth minimization problem over bounded variation functions by implementing a primal-dual algo- rithm. The implementation is based on the simplification provided by Dune-ACFem. Moreover, the convergence of the discrete minimizer to the continuous one is shown theoretically.

Authors:Andreas Dedner, Stefan Girke, Robert Klöfkorn, Tobias Malkmus Pages: 21 - 61 Abstract: In this paper we discuss the new publicly released Dune-Fem-DG module. This module provides highly ecient implementations of the Discontinuous Galerkin (DG) method for solving a wide range of non linear partial dierential equations (PDE). The interfaces used are highly flexible and customizable, providing for example mechanisms for using distributed parallelization, local grid adaptivity with dynamic load balancing, and check pointing. We discuss methods for solving stationary problems as well as a matrix-free implementation for time dependent problems. Both parabolic and first order hyperbolic PDE are discussed in detail including models for compressible and incompressible flows, i.e., the compressible Navier-Stokes equations. For the spatial discretization a wide range of DG methods are implemented ranging from the standard interior penalty method to methods like LDG and CDG2. Upwinding numerical fluxes for first order terms are also available, including limiter bases stabilization for convection dominated PDEs. For the temporal discretization Runge-Kutta methods are used including higher order explicit, diagonally implicit and IMEX schemes. We discuss asynchronous communication, shared memory parallelization, and automated code generation which combined result in a high floating point performance of the code. PubDate: 2017-04-03 DOI: 10.11588/ans.2017.1.28602 Issue No:Vol. 5, No. 1 (2017)

Authors:Andreas Dedner, Alastair J Radcliffe Pages: 63 - 94 Abstract: A complete finite element (FEM) and boundary element (BEM) computational toolbox is presented, based on the Dune and Bem++ software packages respectively, for the efficient independent solution on parallel/multi-threaded multi-core computers of seperate finite and boundary element systems. Each system has very different memory resource requirements, but can be coupled together within a common computer program for solving multi-physics PDE problems for computational sciences and engineering applications.

Examples of both direct (to a fixed-point) and indirect FEM-BEM iterative coupling, and their performance results with increasing core/thread count, drawn from electromagnetic scattering and fluid mechanics are presented as illustration of the wide scope of applications for this package.

Authors:Christian Engwer, Carsten Gräser, Steffen Müthing, Oliver Sander Pages: 95 - 109 Abstract: The dune-functions Dune module introduces a new programmer interface for discrete and non-discrete functions. Unlike the previous interfaces considered in the existing Dune modules, it is based on overloading operator(), and returning values by-value. This makes user code much more readable, and allows the incorporation of newer C++ features such as lambda expressions. Run-time polymorphism is implemented not by inheritance, but by type erasure, generalizing the ideas of the std::function class from the C++11 standard library. We describe the new interface, show its possibilities, and measure the performance impact of type erasure and return-by-value. PubDate: 2017-04-03 DOI: 10.11588/ans.2017.1.27683 Issue No:Vol. 5, No. 1 (2017)

Authors:Felix Gruber, Angela Klewinghaus, Olga Mula Pages: 111 - 127 Abstract: In the numerical solution of partial differential equations (PDEs), a central question is the one of building variational formulations that are inf-sup stable not only at the infinite-dimensional level, but also at the finite-dimensional one. These properties are important since they represent the rigorous foundations for a posteriori error control and the development of adaptive strategies. The essential difficulty lies in finding systematic procedures to build variational formulations for which these desirable stability properties are (i) provable at the theoretical level while (ii) the approach remains implementable in practice and (iii) its computational complexity does not explode with the problem size. In this framework, the so-called Discontinuous Petrov–Galerkin (DPG) concept seems a promising approach to enlarge the scope of problems beyond second order elliptic PDEs for which this is possible. In the context of DPG, the result for the elliptic case was proven by Gopalakrishnan and Qiu [2014] and requires a p-enriched test space. Recently, the same type of result has been proven by Broersen et al. [2015] for certain classes of linear transport problems using an appropriate hp-enrichment to build the finite dimensional test space. In the light of this new result, we present Dune-DPG, a C++ library which allows to implement the test spaces introduced in Broersen et al. [2015]. The library is built upon the multi-purpose finite element package Dune (see Blatt et al. [2016]). In this paper, we present the current version 0.2 of Dune-DPG which has so far been tested only for elliptic and transport problems. An example of use via a simple transport equation is described. We conclude outlining future work and applications to more complex problems. Dune-DPG is licensed under the GPL 2 with runtime exception and a source code tarball is available together with this paper. PubDate: 2017-04-03 DOI: 10.11588/ans.2017.1.27719 Issue No:Vol. 5, No. 1 (2017)

Authors:Birane Kane Pages: 129 - 149 Abstract: We present higher order Discontinuous Galerkin discretizations schemes of two-phase flow model arising in the modelisation of subsurface flows in strongly heterogeneous porous media. The flow in the domain is immiscible and incompressible with no mass transfer between phases. We consider a fully implicit, locally conservative, higher order discretization on adaptively generated meshes. The implementation is based on the Open- Source PDE software framework DUNE. PubDate: 2017-04-03 DOI: 10.11588/ans.2017.1.28068 Issue No:Vol. 5, No. 1 (2017)

Authors:Dominic Kempf, Timo Koch Pages: 151 - 168 Abstract: We present dune-testtools, a collection of tools for system testing in scientific soft- ware using the example of the Distributed Unified Numerics Environment (Dune). Testing is acknowledged as indispensible support for scientific software development and assurance of software quality to produce trustworthy simulation results. Most of the time, testing in soft- ware frameworks developed at research facilities is restricted to either unit testing or simple benchmark programs. However, in a modern numerical software framework, the number of pos- sible feature combinations constituting a program is vast. Only system testing, meaning testing within a possible end user environment also emulating variability, can assess software quality and reproducibility of numerical results. We provide an easy-to-use interface taking workload off developers and administrators in open-source scientific numerical software framework projects. In our approach, the large number of possible combinations is reduced using the scientific expert knowledge of developers to identify the practically relevant combinations. Our approach to system testing is designed to be integrated in the workflow of a research software developing scientist.

Authors:Lars Lubkoll Pages: 169 - 191 Abstract: This document describes a C++-library for the generation of invariant-based models, including first three derivatives. Using expression templates, features of C++11/14, forward automatic differentiation and modern SFINAE-techniques admits a highly efficient implementation with a simple, intuitive interface. PubDate: 2017-04-03 DOI: 10.11588/ans.2017.1.27477 Issue No:Vol. 5, No. 1 (2017)

Authors:Rene Milk, Felix Tobias Schindler, Tobias Leibner Pages: 193 - 216 Abstract: : We present our effort to extend and complement the core modules of the Dis- tributed and Unified Numerics Environment DUNE (http://dune-project.org) by a well tested and structured collection of utilities and concepts. We describe key elements of our four modules dune-xt-common, dune-xt-grid, dune-xt-la and dune-xt-functions, which aim add further enabling the programming of generic algorithms within DUNE as well as adding an extra layer of usability and convenience. PubDate: 2017-04-03 DOI: 10.11588/ans.2017.1.27720 Issue No:Vol. 5, No. 1 (2017)

Authors:Oliver Sander, Timo Koch, Natalie Schröder, Bernd Flemisch Pages: 217 - 244 Abstract: We present FoamGrid, a new implementation of the Dune grid interface. FoamGrid implements one- and two-dimensional grids in a physical space of arbitrary dimension, which allows for grids for curved domains. Even more, the grids are not expected to have a manifold structure, i.e., more than two elements can share a common facet. This makes FoamGrid the grid data structure of choice for simulating structures such as foams, discrete fracture networks, or network flow problems. FoamGrid implements adaptive non-conforming refinement with element parametrizations. As an additional feature it allows removal and addition of elements in an existing grid, which makes FoamGrid suitable for network growth problems. We show how to use FoamGrid, with particular attention to the extensions of the grid interface needed to handle non-manifold topology and grid growth. Three numerical examples demonstrate the possibilities offered by FoamGrid.