Numerical Analysis of Nonlinear Partial Differential-Algebraic Equations: A Coupled and an Abstract Systems Approach

Various mathematical models in many application areas give rise to systems of partial differential equations and differential-algebraic equations (DAEs). These systems are called partial or abstract differential-algebraic equations (ADAEs). Being usually discretized by the method of lines the semi-discretized system yields in general a DAE. A substantial mathematical treatment of nonlinear ADAEs is still at an initial stage. We present two approaches treating nonlinear ADAEs. We investigate them with regard to the solvability and uniqueness of solutions and the convergence of solutions of semi-dicretized systems to the original solution. Furthermore we study the sensitivity of a solution with regard to perturbations on the right hand side and in the initial value. The first approach represents an extension of an approach by Tischendorf for the treatment of a specific class of linear ADAEs to the nonlinear case. It is based on the Galerkin approach and the theory of monotone operators for evolution equations. We prove unique solvability of the ADAE and strong convergence of the Galerkin solutions. Furthermore we prove that this class of ADAEs has Perturbation Index 1 and at most ADAE Index 1. In the second approach we formulate two prototypes of coupled systems, an elliptic and a parabolic one. Here a semi-explicit DAE is coupled to an infinite dimensional algebraic operator equation or an evolution equation. For both prototypes we prove unique solvability, strong convergence of Galerkin solutions and a Perturbation Index 1 result. Both prototypes are applied to concrete coupled systems in circuit simulation. In this context we also prove a global solvability result for the nonlinear equations of the Modified Nodal Analysis under suitable topological assumptions

Auctioning of EU ETS Phase II allowances: how and why?

The European Directive on the EU ETS allows governments to auction up to 10% of the allowances issued in phase II 2008-2012, without constraints being specified thereafter. This article reviews and extends the long-standing debate about auctioning, in which economists have generally supported and industries opposed a greater use of auctioning. The article clarifies the key issues by reviewing six `traditional' considerations, examines several credible options for auction design, and then proposes some new issues relevant to auctioning. It is concluded that greater auctioning in aggregate need not increase adverse competitiveness impacts, and could in some respects alleviate them, particularly by supporting border-tax adjustments. Auctioning within the 10% limit might also be used to dampen price volatility during 2008-2012 and, in subsequent periods, it offers the prospect of supporting a long-term price signal to aid investor confidence. The former is only possible, however, if Member States are willing to coordinate their decision-making (though not revenue-raising) powers in defining and implementing the intended pricing mechanisms

German companies relaxed about Brexit

The United Kingdom intends to leave the single market, yet still wants to retain broad access to it by means of a comprehensive free trade agreement. But the question remains as to whether the European Union is prepared to play ball. Brexiteers claim that German companies in particular, worried about their exports to the UK, will push for a gentle compromise in the favour of the UK, so that trade can continue with as little disruption as possible. Yet a survey by the Cologne Institute for Economic Research (IW Köln) has cast doubt on this view

Deutsche Unternehmen sehen den Brexit gelassen

Das Vereinigte Königreich (UK) will zwar aus dem Binnenmarkt austreten, mit einem umfassenden Freihandelsabkommen aber einen weitgehenden Zugang zu den EU-Absatzmärkten behalten. Es ist jedoch fraglich, ob sich die Europäische Union darauf einlässt. Die Brexiteers behaupten, dass vor allem deutsche Unternehmen, die sich um ihre Exporte in das UK sorgen, auf weiche Kompromisse zugunsten der Briten drängen, um weiterhin möglichst ungehindert Handel treiben zu können. Eine Umfrage des Instituts der deutschen Wirtschaft Köln (IW Köln) stellt diese Sichtweise jedoch infrage

Tuning and optimization for a variety of many-core architectures without changing a single line of implementation code using the Alpaka library

We present an analysis on optimizing performance of a single C++11 source code using the Alpaka hardware abstraction library. For this we use the general matrix multiplication (GEMM) algorithm in order to show that compilers can optimize Alpaka code effectively when tuning key parameters of the algorithm. We do not intend to rival existing, highly optimized DGEMM versions, but merely choose this example to prove that Alpaka allows for platform-specific tuning with a single source code. In addition we analyze the optimization potential available with vendor-specific compilers when confronted with the heavily templated abstractions of Alpaka. We specifically test the code for bleeding edge architectures such as Nvidia's Tesla P100, Intel's Knights Landing (KNL) and Haswell architecture as well as IBM's Power8 system. On some of these we are able to reach almost 50\% of the peak floating point operation performance using the aforementioned means. When adding compiler-specific #pragmas we are able to reach 5 TFLOPS/s on a P100 and over 1 TFLOPS/s on a KNL system.Comment: Accepted paper for the P\^{}3MA workshop at the ISC 2017 in Frankfur

Wächst die deutsche Industrie nur durch den Export?

Die deutsche Wirtschaftsstruktur mit ihrem relativ hohen Industriegewicht und der damit einhergehenden Weltmarktorientierung stehen derzeit in der Kritik. Auf Basis von Wachstumsbeiträgen und der Input-Output-Rechnung lässt sich zeigen, wie die Wertschöpfung ausgewählter industrieller Güterbereiche durch die heimische Endnachfrage, die Vorleistungen und den Außenbeitrag erklärt werden kann. Im Ergebnis hat - anders als zuweilen behauptet - nicht nur der Außenhandel das Wachstum der Wertschöpfung wichtiger Produktgruppen angetrieben, sondern auch die steigende Inlandsnachfrage auf der Vorleistungs- und Endverbrauchsebene. Bei Maschinen und Chemieprodukten dominiert zwar der Außenbeitrag. Dies erklärt sich aber vor allem aus dem globalen Investitionsboom und weniger aus den Ausfuhren in konsumorientierte Staaten mit Leistungsbilanzdefiziten. Mit diesem Konzept kann auch der weitgehend konstante Anteil der Industriegüter an der gesamtwirtschaftlichen Wertschöpfung erklärt werden. -- The high share of manufacturing and the strong export orientation of Germany's economy are presently drawing fire by some critics. A concept of growth contributions based on input-output statistics explains to which extent final domestic demand, inputs and net exports contribute to the growth of value added of selected industrial product groups. Contrary to popular allegations, it shows that, in general, net exports are only one growth driver for major product groups. The others are domestic demand of inputs and of final consumption and investment. While the influence of net exports dominates for machinery and chemical products, this is largely a result of the global investment boom rather than of exports to consumption-oriented countries with large current account deficits. The concept also explains the principally constant share of industrial goods in total value added in Germany.

Detection of Water Hazards for Autonomous Robotic Vehicles

Four methods of detection of bodies of water are under development as means to enable autonomous robotic ground vehicles to avoid water hazards when traversing off-road terrain. The methods involve processing of digitized outputs of optoelectronic sensors aboard the vehicles. It is planned to implement these methods in hardware and software that would operate in conjunction with the hardware and software for navigation and for avoidance of solid terrain obstacles and hazards. The first method, intended for use during the day, is based on the observation that, under most off-road conditions, reflections of sky from water are easily discriminated from the adjacent terrain by their color and brightness, regardless of the weather and of the state of surface waves on the water. Accordingly, this method involves collection of color imagery by a video camera and processing of the image data by an algorithm that classifies each pixel as soil, water, or vegetation according to its color and brightness values (see figure). Among the issues that arise is the fact that in the presence of reflections of objects on the opposite shore, it is difficult to distinguish water by color and brightness alone. Another issue is that once a body of water has been identified by means of color and brightness, its boundary must be mapped for use in navigation. Techniques for addressing these issues are under investigation. The second method, which is not limited by time of day, is based on the observation that ladar returns from bodies of water are usually too weak to be detected. In this method, ladar scans of the terrain are analyzed for returns and the absence thereof. In appropriate regions, the presence of water can be inferred from the absence of returns. Under some conditions in which reflections from the bottom are detectable, ladar returns could, in principle, be used to determine depth. The third method involves the recognition of bodies of water as dark areas in short-wavelength infrared (SWIR) images. This method is based on the fact, well known among experts in remote sensing, that water bodies of any appreciable depth appear very dark in near-infrared, overhead imagery. Even under a thick layer of marine fog, SWIR illumination is present. Hence, this method may work even in the presence of clouds, though it is unlikely to work at night. Snow and ice also exhibit very strong absorption at wavelengths greater than about 1.4 m. Hence, the wavelength range of about 1.5 to 1.6 m might be useable in this method for recognizing water, snow, and ice. One notable drawback of this method is that useful look-ahead distance could be limited by surface reflections. The fourth method, intended for use at night, involves the contrast between water and terrain in thermal-infrared (medium-wavelength infrared) imagery. This method is based on the fact that at night, water is usually warmer than the adjacent terrain. Look-ahead distance could be limited in this method because, for reasons not yet fully understood, water appears to darken in the thermal infrared with increasing distance

On the Scalability of Data Reduction Techniques in Current and Upcoming HPC Systems from an Application Perspective

We implement and benchmark parallel I/O methods for the fully-manycore driven particle-in-cell code PIConGPU. Identifying throughput and overall I/O size as a major challenge for applications on today's and future HPC systems, we present a scaling law characterizing performance bottlenecks in state-of-the-art approaches for data reduction. Consequently, we propose, implement and verify multi-threaded data-transformations for the I/O library ADIOS as a feasible way to trade underutilized host-side compute potential on heterogeneous systems for reduced I/O latency.Comment: 15 pages, 5 figures, accepted for DRBSD-1 in conjunction with ISC'1

Prosperity in a changing world: Structural change and economic growth

Structural change is both a challenge and an opportunity for countries and companies. However, there is no silver bullet in terms of superior economic models. Instead, different economic models can deal with structural change in a successful way. Both economies with a focus on services and those with a high share of manufacturing are able to achieve a high degree of economic growth and prosperity. Success factors are related to a solid performance with regard to the key drivers of structural change: globalisation, interconnectedness, innovation and knowledge as well as the economic framework. Economic policy - also at the EU level - should support companies and economies in reaping these potential benefits: fostering open and flexible markets as well as supporting European value chains and an intensification of knowledge in the production of goods and services are key success factors in this respect