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On DFT Molecular Simulation for Non-Adaptive Kernel Approximation

Advances in Materials Physics and Chemistry 2014年第6期4卷 105-115页

作者： Maharavo Randrianarivony Virtual Material Design Fraunhofer Institute for Algorithms and Scientific Computing SCAI Schloss Birlinghoven Sankt Augustin Germany

Using accurate quantum energy computations in nanotechnologic applications is usually very computationally intensive. That makes it difficult to apply in subsequent quantum simulation. In this paper, we present some preliminary results pertaining to stochastic methods for alleviating the numerical expense of quantum estimations. The initial information about the quantum energy originates from the Density Functional Theory. The determination of the parameters is performed by using methods stemming from machine learning. We survey the covariance method using marginal likelihood for the statistical simulation. More emphasis is put at the position of equilibrium where the total atomic energy attains its minimum. The originally intensive data can be reproduced efficiently without losing accuracy. A significant acceleration gain is perceived by using the proposed method.

关键词： DFT Energy Stochastic Covariance Hyperparameter

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VERCE Delivers a Productive E-science Environment for Seismology Research

VERCE Delivers a Productive E-science Environment for Seismo...

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IEEE International Conference on e-Science and Grid computing

作者： Malcolm Atkinson Michele Carpené Emanuele Casarotti Steffen Claus Rosa Filgueira Anton Frank Michelle Galea Tom Garth André Gemünd Heiner Igel Iraklis Klampanos Amrey Krause Lion Krischer Siew Hoon Leong Federica Magnoni Jonas Matser Alberto Michelini Andreas Rietbrock Horst Schwichtenberg Alessandro Spinuso Jean-Pierre Vilotte University of Edinburgh UK Supercomputing Applications and Innovation Department (CINECA) Italy Istituto Nazionale di Geofisica e Vulcanologia (INGV) Italy Fraunhofer Institute for Algorithms and Scientific Computing (SCAI) Germany The University of Edinburgh Edinburgh Edinburgh GB Leibniz Supercomputing Centre Germany University of Liverpool UK Ludwig-Maximilians-University Germany Royal Netherlands Meteorological Institute (KNMI) The Netherlands Institut de Physique du Globe de Paris (IPGP) France

The VERCE project has pioneered an e-Infrastructure to support researchers using established simulation codes on high-performance computers in conjunction with multiple sources of observational data. This is accessed and organised via the VERCE science gateway that makes it convenient for seismologists to use these resources from any location via the Internet. Their data handling is made flexible and scalable by two Python libraries, ObsPy and dispel4py and by data services delivered by ORFEUS and EUDAT. Provenance driven tools enable rapid exploration of results and of the relationships between data, which accelerates understanding and method improvement. These powerful facilities are integrated and draw on many other e-Infrastructures. This paper presents the motivation for building such systems, it reviews how solid-Earth scientists can make significant research progress using them and explains the architecture and mechanisms that make their construction and operation achievable. We conclude with a summary of the achievements to date and identify the crucial steps needed to extend the capabilities for seismologists, for solid-Earth scientists and for similar disciplines.

关键词： Computational modeling Data models Logic gates Context Earthquakes Analytical models Libraries

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A bond order dissection ANOVA approach for efficient electronic structure calculations

Lecture Notes in Computational Science and Engineering

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Lecture Notes in Computational Science and Engineering 2014年 102卷 211-235页

作者： Griebel, Michael Hamaekers, Jan Heber, Frederik Institute for Numerical Simulation University of Bonn Wegelerstr. 6 Bonn53115 Germany Fraunhofer Institute for Algorithms and Scientific Computing SCAI Schloss Birlinghoven Sankt Augustin53754 Germany

In this article, we present a new decomposition approach for the efficient approximate calculation of the electronic structure problem for molecules. It is based on a dimension-wise decomposition of the space the underlying Schrödinger equation lives in, i.e. 3(M+N), where M is the number of nuclei and N is the number of electrons. This decomposition is similar to the ANOVA-approach (analysis of variance) which is well-known in statistics. It represents the energy as a finite sum of contributions which depend on the positions of single nuclei, of pairs of nuclei, of triples of nuclei, and so on. Under the assumption of locality of electronicwave functions, the higher order terms in this expansion decay rapidly and may therefore be omitted. Furthermore, additional terms are eliminated according to the bonding structure of the molecule. This way, only the calculation of the electronic structure of local parts, i.e. small subsystems of the overall system, is necessary to approximate the total ground state energy. To determine the required subsystems, we employ molecular graph theory combined with molecular bonding knowledge. In principle, the local electronic subproblems may be approximately evaluated with whatever technique is appropriate, e.g. HF, CC, CI, or DFT. From these local energies, the total energy of the overall system is then approximately put together in a telescoping sum like fashion. Thus, if the size of the local subproblems is independent of the size of the overall molecular system, linear scaling is directly obtained. We discuss the details of our new approach and apply it to both, various small test systems and interferon alpha as an example of a large biomolecule. © Springer International Publishing Switzerland 2014.

关键词： Analysis of variance (ANOVA)

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Consideration of Process-Related Variations of Spot Welded Joints

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ATZ worldwide 2013年第12期115卷 44-49页

作者： Sommer, Silke Steffes-lai, Daniela Clees, Tanja Fraunhofer Institute for Mechanics of Materials IWM Freiburg Germany Fraunhofer Institute for Algorithms and Scientific Computing SCAI Sankt Augustin Germany

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Using LAMA for efficient AMG on hybrid clusters

Using LAMA for efficient AMG on hybrid clusters

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作者： Kraus, Jiri Förster, Malte Brandes, Thomas Soddemann, Thomas Fraunhofer Institute for Algorithms and Scientific Computing SCAI Schloss Birlinghoven 53754 Sankt Augustin Germany

In this paper, we describe the implementation of an AMG solver for a hybrid cluster that exploits distributed and shared memory parallelization and uses the available GPU accelerators on each node. This solver has been written by using LAMA (Library for Accelerated Math Applications). This library does not only provide an easy-to-use framework for solvers that might run on different devices with different matrix formats, but also comes with features to optimize and hide communication and memory transfers between CPUs and GPUs. These features are explained and their impact on the efficiency of the AMG solver is shown in this paper. The benchmark results show that an efficient use of hybrid clusters is even possible for multi-level methods like AMG where fast solutions are needed on all levels for multiple problem sizes. © 2012 Springer-Verlag.

关键词： Program processors

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Preconditioning for efficiently applying algebraic multigrid in fully implicit reservoir simulations

Preconditioning for efficiently applying algebraic multigrid...

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SPE Reservoir Simulation Symposium 2013

作者： Gries, Sebastian Stüben, Klaus Brown, Geoffrey L. Chen, Dingjun Collins, David A. Fraunhofer Institute for Algorithms and Scientific Computing SCAI Germany Computer Modelling Group Ltd. Canada

ISBN: (纸本)9781627480246

Fully implicit petroleum reservoir simulations result in huge, often very ill-conditioned linear systems of equations to solve for different unknowns, for example, pressure and saturations. It is well known that the full system matrix contains both hyperbolic as well as nearly elliptic sub-systems. Since the solution of the coupled system is mainly determined by the solution of their elliptic (typically pressure) components, (CPR-type) two-stage preconditioning methods still belong to the most popular approaches to tackle such coupled systems. After a suitable extraction and decoupling, the numerically most costly step in such two-stage methods consists in solving these elliptic sub-systems. It is known that algebraic multigrid (AMG) provides a technique to solve elliptic linear equations very efficiently. The main advantage of AMG-based solvers - their numerical scalability - makes them particularly efficient for solving huge linear systems. Depending on the application, the system's properties range from simple to highly indefinite. Unfortunately decoupling pressure and saturation related parts may introduce further difficulties. Consequently, in complex industrial simulations, the application of AMG to elliptic sub-systems might not be straightforward. In fact, an important goal in defining an efficient two-stage preconditioning strategy consists in extracting elliptic sub-systems that are suitable for an efficient AMG solution and, at the same time, ensure a fast overall convergence of the two-stage approach. The importance of this will be demonstrated for several industrial cases. In particular, some of these cases are very hard to solve by AMG if applied in a standard way. Preliminary results for a CPR-type coupling of SAMG to CMG's PARASOL, a variable degree variable ordering ILU preconditioner using FGMRES, are compared to using PARASOL by itself. Alternative preconditioning operators will be presented giving elliptic sub-systems which are not only more suit

关键词： Iterative methods

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Multiscale simulation of ion migration for battery systems

Multiscale simulation of ion migration for battery systems

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21st International Materials Research Congress, IMRC 2012

作者： Neuen, Christian Griebel, Michael Hamaekers, Jan Fraunhofer Institute for Algorithms and Scientific Computing SCAI Schloss Birlinghoven 53754 Sankt Augustin Germany Institute for Numerical Simulation Bonn University Wegelerstr. 6 53115 Bonn Germany

ISBN: (纸本)9781632661258

In this paper we describe a multi-scale approach to ion migration processes, which involves a bridging from the atomic scale to the macroscopic scale. To this end, the diffusion coefficient of a material i.e. a macroscopic physical quantity, will be appropriately determined from molecular dynamics simulations on the microscale. This way, performance predictions become possible prior to material synthesis. However, standard methods produce in general wrong results for ensemble setups which correspond to battery or capacitor applications. We introduce a novel method to derive correct values also for such problems. These values are then used in a macroscopic system of partial differential equation (Poisson-Nernst-Planck system) for the numerical simulation of ion migration in a battery. © 2013 Materials Research Society.

关键词： Molecular dynamics

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From integrative disease modeling to predictive, preventive, personalized and participatory (P4) medicine

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EPMA Journal 2014年第1期5卷 1-1页

作者： Erfan Younesi Martin Hofmann-Apitius Department of Bioinformatics Fraunhofer Institute for Algorithms and Scientific Computing (SCAI) Schloss Birlinghoven Sankt Augustin Germany Rheinische Friedrich-Wilhelms-Universität Bonn Bonn-Aachen International Center for IT Bonn Germany

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Multiscale Simulation of Ion Migration for Battery Systems

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MRS Online Proceedings Library (OPL) 2013年第1期1535卷 mmm2012-a-0099-mmm2012-a-0099页

作者： Christian Neuen Michael Griebel Jan Hamaekers Fraunhofer Institute for Algorithms and Scientific Computing SCAI Schloss Birlinghoven 53754 Sankt Augustin Germany Institute for Numerical Simulation Bonn University Wegelerstr. 6 53115 Bonn Germany

In this paper we describe a multi-scale approach to ion migration processes, which involves a bridging from the atomic scale to the macroscopic scale. To this end, the diffusion coefficient of a material i.e. a macroscopic physical quantity, will be appropriately determined from molecular dynamics simulations on the microscale. This way, performance predictions become possible prior to material synthesis. However, standard methods produce in general wrong results for ensemble setups which correspond to battery or capacitor *** introduce a novel method to derive correct values also for such problems. These values are then used in a macroscopic system of partial differential equation (Poisson-Nernst-Planck system) for the numerical simulation of ion migration in a battery.

关键词： diffusion simulation kinetics

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Loewy Decomposition of Linear Differential Equations 1

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丛书名： Texts & Monographs in Symbolic Computation

2012年

作者： Fritz Schwarz

ISBN: (数字)9783709112861

ISBN: (纸本)3709112850

The central subject of the book is the generalization of Loewy's decomposition - originally introduced by him for linear ordinary differential equations - to linear partial differential equations. Equations for a single function in two independent variables of order two or three are comprehensively discussed. A complete list of possible solution types is given. Various ad hoc results available in the literature are obtained algorithmically. The border of decidability for generating a Loewy decomposition are explicitly stated. The methods applied may be generalized in an obvious way to equations of higher order, in more variables or systems of such equations.

关键词： Symbolic and Algebraic Manipulation Differential Equations Mathematical and Computational Engineering Applications

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