Enhancing Energy Production with Exascale HPC Methods

High Performance Computing (HPC) resources have become the key actor for achieving more ambitious challenges in many disciplines. In this step beyond, an explosion on the available parallelism and the use of special purpose processors are crucial. With such a goal, the HPC4E project applies new exascale HPC techniques to energy industry simulations, customizing them if necessary, and going beyond the state-of-the-art in the required HPC exascale simulations for different energy sources. In this paper, a general overview of these methods is presented as well as some specific preliminary results.The research leading to these results has received funding from the European Union's Horizon 2020 Programme (2014-2020) under the HPC4E Project (www.hpc4e.eu), grant agreement n° 689772, the Spanish Ministry of Economy and Competitiveness under the CODEC2 project (TIN2015-63562-R), and from the Brazilian Ministry of Science, Technology and Innovation through Rede Nacional de Pesquisa (RNP). Computer time on Endeavour cluster is provided by the Intel Corporation, which enabled us to obtain the presented experimental results in uncertainty quantification in seismic imagingPostprint (author's final draft

Topology and grid adaption for high-speed flow computations

This study investigates the effects of grid topology and grid adaptation on numerical solutions of the Navier-Stokes equations. In the first part of this study, a general procedure is presented for computation of high-speed flow over complex three-dimensional configurations. The flow field is simulated on the surface of a Butler wing in a uniform stream. Results are presented for Mach number 3.5 and a Reynolds number of 2,000,000. The O-type and H-type grids have been used for this study, and the results are compared together and with other theoretical and experimental results. The results demonstrate that while the H-type grid is suitable for the leading and trailing edges, a more accurate solution can be obtained for the middle part of the wing with an O-type grid. In the second part of this study, methods of grid adaption are reviewed and a method is developed with the capability of adapting to several variables. This method is based on a variational approach and is an algebraic method. Also, the method has been formulated in such a way that there is no need for any matrix inversion. This method is used in conjunction with the calculation of hypersonic flow over a blunt-nose body. A movie has been produced which shows simultaneously the transient behavior of the solution and the grid adaption

The Smart Power Cell concept

This dissertation describes a novel architecture and operational concept for a future electric power system. The architecture and operational concept were developed as a solution to the technical challenges which result from the ongoing decommissioning of conventional power plants and the mass scale integration of distributed and renewable energy sources. In particular, the architecture aims at ensuring the efficient, secure and stable operation of a future power system by enabling the coordinated operation of its distribution and transmission grids. To this, in the first part of the dissertation, the Smart Power Cell concept is introduced. A Smart Power Cell is a subsection of the distribution domain of a future power system which is supervised and controlled by an ICT-based monitoring and control system. A Smart Power Cell can be controlled to adapt its dynamic behaviour on demand an thus be integrated into the operation of the transmission network. The dissertation then deals with the modelling and simulation of a power system organized according to the developed concept. Besides, methods for the description of the flexibility of Smart Power Cells to support the operation of a transmission network are described. In addition, a control scheme for controlling the power which a Smart Power Cell exchanges with the transmission network is presented. Finally, the developed methods are tested by means of steady-state and dynamic simulations using a combined transmission-distribution test system designed for this purpose. The dissertation closes with a summary of the main contributions and a discussion of the research efforts required to bring the Smart Power Cell concept into life

Graph Signal Processing: Overview, Challenges and Applications

Research in Graph Signal Processing (GSP) aims to develop tools for processing data defined on irregular graph domains. In this paper we first provide an overview of core ideas in GSP and their connection to conventional digital signal processing. We then summarize recent developments in developing basic GSP tools, including methods for sampling, filtering or graph learning. Next, we review progress in several application areas using GSP, including processing and analysis of sensor network data, biological data, and applications to image processing and machine learning. We finish by providing a brief historical perspective to highlight how concepts recently developed in GSP build on top of prior research in other areas.Comment: To appear, Proceedings of the IEE

Applying future Exascale HPC methodologies in the energy sector

The appliance of new exascale HPC techniques to energy industry simulations is absolutely needed nowadays. In this sense, the common procedure is to customize these techniques to the specific energy sector they are of interest in order to go beyond the state-of-the-art in the required HPC exascale simulations. With this aim, the HPC4E project is developing new exascale methodologies to three different energy sources that are the present and the future of energy: wind energy production and design, efficient combustion systems for biomass-derived fuels (biogas), and exploration geophysics for hydrocarbon reservoirs. In this work, the general exascale advances proposed as part of HPC4E and its outcome to specific results in different domains are presented.The research leading to these results has received funding from the European Union's Horizon 2020 Programme (2014-2020) under the HPC4E Project (www.hpc4e.eu), grant agreement n° 689772, the Spanish Ministry of Economy and Competitiveness under the CODEC2 project (TIN2015-63562-R), and from the Brazilian Ministry of Science, Technology and Innovation through Rede Nacional de Pesquisa (RNP). Computer time on Endeavour cluster is provided by the Intel Corporation, which enabled us to obtain the presented experimental results in uncertainty quantification in seismic imaging.Postprint (author's final draft

Differentiated Multiple Aggregations in Multidimensional Databases

International audienceMany models have been proposed for modeling multidimensional data warehouse and most consider a same function to determine how measure values are aggregated according to different data detail levels. We provide a conceptual model that supports (1) multiple aggregations, associating to the same measure a different aggregation function according to analysis axes or hierarchies, and (2) differentiated aggregation, allowing specific aggregations at each detail level. Our model is based on a graphical formalism that allows controlling the validity of aggregation functions (distributive, algebraic or holistic). We also show how conceptual modeling can be used, in an R-OLAP environment, for building lattices of pre-computed aggregates

Algebraically constrained finite element methods for hyperbolic problems with applications in geophysics and gas dynamics

The research conducted in this thesis is focused on property-preserving discretizations of hyperbolic partial differential equations. Computational methods for solving such problems need to be carefully designed to produce physically meaningful numerical solutions. In particular, approximations to some quantities of interest should satisfy local and global discrete maximum principles. Moreover, numerical methods need to obey certain conservation relations, and convergence of approximations to the physically relevant exact solution should be ensured if multiple solutions may exist. Many algorithms based on the aforementioned design principles fall into the category of algebraic flux correction (AFC) schemes. Modern AFC discretizations of nonlinear hyperbolic systems express approximate solutions as convex combinations of intermediate states and constrain these states to be admissible. The main focus of our work is on monolithic convex limiting (MCL) strategies that modify spatial semi-discretizations in this way. Contrary to limiting approaches of predictor-corrector type, their monolithic counterparts are well suited for transient and steady problems alike. Further benefits of the MCL framework presented in this thesis include the possibility of enforcing entropy stability conditions in addition to discrete maximum principles. Using the AFC methodology, we transform finite element discretizations into property-preserving low order methods and perform flux correction to recover higher orders of accuracy without losing any desirable properties. The presented methods produce physics-compatible approximations, which exhibit excellent shock capturing capabilities. One novelty of this work is the tailor-made extension of monolithic convex limiting to the shallow water equations with a nonconservative topography term. Our generalized MCL schemes are entropy stable, positivity preserving, and well balanced in the sense that lake at rest equilibria are preserved. Another desirable property of numerical methods for the shallow water equations is the capability to handle wet-dry transitions properly. We present two new approaches to dealing with this issue. To corroborate our computational results with theoretical investigations, we perform numerical analysis for property-preserving discretizations of the time-dependent linear advection equation. In this context, we prove stability and derive an a~priori error estimate in the semi-discrete setting. We also compare the monolithic convex limiting strategy to two representatives of related flux-corrected transport algorithms. Another highlight of this thesis is the chapter on MCL schemes for arbitrary order discontinuous Galerkin (DG) discretizations. Building on algorithms developed for continuous Lagrange and Bernstein finite elements, we extend our MCL schemes to the high order DG setting. This research effort involves the design of new AFC tools for numerical fluxes that appear in the DG weak formulation. Our limiting strategy for DG methods exploits the properties of high order Bernstein polynomials to construct sparse discrete operators leading to compact-stencil nonlinear approximations. The proposed numerical methods are applied to various hyperbolic problems. Scalar equations are considered mainly for testing purposes and to simplify numerical analysis. Besides the shallow water system, we study the Euler equations of gas dynamics

Three-points interfacial quadrature for geometrical source terms on nonuniform grids

International audienceThis paper deals with numerical (finite volume) approximations, on nonuniform meshes, for ordinary differential equations with parameter-dependent fields. Appropriate discretizations are constructed over the space of parameters, in order to guarantee the consistency in presence of variable cells' size, for which $L^p$-error estimates, $1\le p < +\infty$, are proven. Besides, a suitable notion of (weak) regularity for nonuniform meshes is introduced in the most general case, to compensate possibly reduced consistency conditions, and the optimality of the convergence rates with respect to the regularity assumptions on the problem's data is precisely discussed. This analysis attempts to provide a basic theoretical framework for the numerical simulation on unstructured grids (also generated by adaptive algorithms) of a wide class of mathematical models for real systems (geophysical flows, biological and chemical processes, population dynamics)

Towards a gauge-polyvalent Numerical Relativity code

The gauge polyvalence of a new numerical code is tested, both in harmonic-coordinate simulations (gauge-waves testbed) and in singularity-avoiding coordinates (simple Black-Hole simulations, either with or without shift). The code is built upon an adjusted first-order flux-conservative version of the Z4 formalism and a recently proposed family of robust finite-difference high-resolution algorithms. An outstanding result is the long-term evolution (up to 1000M) of a Black-Hole in normal coordinates (zero shift) without excision.Comment: to appear in Physical Review