Quantum energies which are used in applications are usually composed of repulsive and attractive terms. The objective of this study is to use an accurate and efficient fitting of the repulsive energy instead of using ...
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Quantum energies which are used in applications are usually composed of repulsive and attractive terms. The objective of this study is to use an accurate and efficient fitting of the repulsive energy instead of using standard parametrizations. The investigation is based on Density Functional Theory and Tight Binding simulations. Our objective is not only to capture the values of the repulsive terms but also to efficiently reproduce the elastic properties and the forces. The elasticity values determine the rigidity of a material when some traction or load is applied on it. The pair-potential is based on an exponential term corrected by B-spline terms. In order to accelerate the computations, one uses a hierarchical optimization for the B-splines on different levels. Carbon graphenes constitute the configurations used in the simulations. We report on some results to show the efficiency of the B-splines on different levels.
In this paper, we present an algorithm for trigonometric interpolation of multivariate functions on generalized sparse grids and study its application for the approximation of functions in periodic Sobolev spaces of d...
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Robust optimization determines how the input variables dispersion is propagated on the output variables. This is of great practical relevance: For example, the quality of a product is influenced decisively by producti...
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ISBN:
(纸本)9789609999465
Robust optimization determines how the input variables dispersion is propagated on the output variables. This is of great practical relevance: For example, the quality of a product is influenced decisively by production tolerances. In industrial applications it is important to characterize the range of variation with appropriate measures. The industry is particularly interested in accurate limits of the output distribution or its centered part. In this article the mathematical characterization of robustness is discussed under the viewpoint of its practical applicability. It is shown, that the usually used robustness measures mean for central tendency and standard deviation for dispersion produce inaccurate limits. Instead several measures based on quantiles are proposed. The median is used as measure of central tendency while different quantile ranges are used as measure of dispersion. They are compared for the robust optimization of mathematical functions and industrial applications. The advantages of the quantile measures are pointed out. The computation of quantiles is expensive, because it needs many function evaluations. Due to their long runtime only a few simulations can be executed in practice. A methodology tailored to this situation is proposed. It is based on the use of metamodels. Starting with a few real simulations a metamodel for the system is build. Further ones for median and dispersion of the output variables are derived from it. This enables the user to perform a full multicriteria robust optimization on the whole parameter range. The methodology takes the tolerances of the metamodels into account. A new measure for the tolerance of metamodels which are derived from metamodels is presented. It is used to estimate the accuracy of the quantile models. The tolerance can easily be integrated in the robust optimization process.
Quantum energies which are used in applications are usually composed of repulsive and attractive terms. The objective of this study is to use an accurate and efficient fitting of the repulsive energy instead of using ...
详细信息
Quantum energies which are used in applications are usually composed of repulsive and attractive terms. The objective of this study is to use an accurate and efficient fitting of the repulsive energy instead of using standard parametrizations. The investigation is based on Density Functional Theory and Tight Binding simulations. Our objective is not only to capture the values of the repulsive terms but also to efficiently reproduce the elastic properties and the forces. The elasticity values determine the rigidity of a material when some traction or load is applied on it. The pair-potential is based on an exponential term corrected by B-spline terms. In order to accelerate the computations, one uses a hierarchical optimization for the B-splines on different levels. Carbon graphenes constitute the configurations used in the simulations. We report on some results to show the efficiency of the B-splines on different levels.
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 p...
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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.
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 ...
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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.
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 bee...
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Crash simulation results show both deterministic and stochastic behavior. For optimization in automotive design it is very important to distinguish between effects caused by variation of simulation parameters and effe...
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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 f...
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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
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