Das unstetige Galerkinverfahren für Strömungen mit freier Oberfläche und im Grundwasserbereich in geophysikalischen Anwendungen

Free surface flows and subsurface flows appear in a broad range of geophysical applications and in many environmental settings situations arise which even require the coupling of free surface and subsurface flows. Many of these application scenarios are characterized by large domain sizes and long simulation times. Hence, they need considerable amounts of computational work to achieve accurate solutions and the use of efficient algorithms and high performance computing resources to obtain results within a reasonable time frame is mandatory. Discontinuous Galerkin methods are a class of numerical methods for solving differential equations that share characteristics with methods from the finite volume and finite element frameworks. They feature high approximation orders, offer a large degree of flexibility, and are well-suited for parallel computing. This thesis consists of eight articles and an extended summary that describe the application of discontinuous Galerkin methods to mathematical models including free surface and subsurface flow scenarios with a strong focus on computational aspects. It covers discretization and implementation aspects, the parallelization of the method, and discrete stability analysis of the coupled model.Für viele geophysikalische Anwendungen spielen Strömungen mit freier Oberfläche und im Grundwasserbereich oder sogar die Kopplung dieser beiden eine zentrale Rolle. Oftmals charakteristisch für diese Anwendungsszenarien sind große Rechengebiete und lange Simulationszeiten. Folglich ist das Berechnen akkurater Lösungen mit beträchtlichem Rechenaufwand verbunden und der Einsatz effizienter Lösungsverfahren sowie von Techniken des Hochleistungsrechnens obligatorisch, um Ergebnisse innerhalb eines annehmbaren Zeitrahmens zu erhalten. Unstetige Galerkinverfahren stellen eine Gruppe numerischer Verfahren zum Lösen von Differentialgleichungen dar, und kombinieren Eigenschaften von Methoden der Finiten Volumen- und Finiten Elementeverfahren. Sie ermöglichen hohe Approximationsordnungen, bieten einen hohen Grad an Flexibilität und sind für paralleles Rechnen gut geeignet. Diese Dissertation besteht aus acht Artikeln und einer erweiterten Zusammenfassung, in diesen die Anwendung unstetiger Galerkinverfahren auf mathematische Modelle inklusive solcher für Strömungen mit freier Oberfläche und im Grundwasserbereich beschrieben wird. Die behandelten Themen umfassen Diskretisierungs- und Implementierungsaspekte, die Parallelisierung der Methode sowie eine diskrete Stabilitätsanalyse des gekoppelten Modells

EuroEXA - D2.6: Final ported application software

This document describes the ported software of the EuroEXA applications to the single CRDB testbed and it discusses the experiences extracted from porting and optimization activities that should be actively taken into account in future redesign and optimization. This document accompanies the ported application software, found in the EuroEXA private repository (https://github.com/euroexa). In particular, this document describes the status of the software for each of the EuroEXA applications, sketches the redesign and optimization strategy for each application, discusses issues and difficulties faced during the porting activities and the relative lesson learned. A few preliminary evaluation results have been presented, however the full evaluation will be discussed in deliverable 2.8

Utglesning av simplex-nät för storskaliga parallellaFEM-beräkningar med DOLFIN HPC

Adaptive mesh refinement and coarsening methods are effective techniques to reduce the computation time of finite element based solvers. Parallel imple- mentations of such adaption routines, suitable for large scale computations on distributed memory machines, need additional care. In this thesis, a coarsening technique based on edge collapses is presented, its implementation and opti- mization for parallel computations explained and it is analyzed with respect to coarsening efficiency and performance. As a possible application the use of mesh coarsening in adaptive flow simulations is demonstratedAdaptiv förfining ochutglesning av element-nät är effektiva tekniker för att minska beräkningstidenför finita-element-lösare. Implementering av sådana adaptions-rutiner, passandeför stora beräkningar på maskiner med distribuerat minne, kräver stor omsorg. Idetta arbete presenteras en utglesnings-metod baserad på kant-sammanslagningar.Dess implementering och optimering för parallell-beräkningar förklaras ochanalyseras med avseende på glesnings-effektivitet och tidsåtgång. Somtillämpning visas nätutglesning i adaptiv strömningssimulerin

The production and conservation of fats and oils in the United States /

no.769 (1919

FESTUNG: A MATLAB/GNU Octave toolbox for the discontinuous Galerkin method. Part III: Hybridized discontinuous Galerkin (HDG) formulation

The third paper in our series on open source MATLAB / GNU Octave implementation of the discontinuous Galerkin (DG) method(s) focuses on a hybridized formulation. The main aim of this ongoing work is to develop rapid prototyping techniques covering a range of standard DG methodologies and suitable for small to medium sized applications. Our FESTUNG package relies on fully vectorized matrix / vector operations throughout, and all details of the implementation are fully documented. Once again, great care was taken to maintain a direct mapping between discretization terms and code routines as well as to ensure full compatibility to GNU Octave. The current work formulates a hybridized DG scheme for linear advection problem, describes hybrid approximation spaces on the mesh skeleton, and compares the performance of this discretization to the standard (element-based) DG method for different polynomial orders.Comment: Updated with accepted manuscript. Among other (mostly editorial) changes, parts of Sec. 3 were rewritten to improve the presentation of the metho

The production and conservation of fats and oils in the United States

no.769:suppl. (1919