Increasing the Flexibility of the High Order Discontinuous Galerkin Framework FLEXI Towards Large Scale Industrial Applications

2021 ◽  
pp. 343-358
Author(s):  
Andrea Beck ◽  
Min Gao ◽  
Daniel Kempf ◽  
Patrick Kopper ◽  
Nico Krais ◽  
...  
Keyword(s):  
Discontinuous Galerkin ◽  
Large Scale ◽  
Industrial Applications ◽  
High Order

scholarly journals Asynchronous communication in spectral-element and discontinuous Galerkin methods for atmospheric dynamics – a case study using the High-Order Methods Modeling Environment (HOMME-homme_dg_branch)

2016 ◽  
Vol 9 (8) ◽  
pp. 2881-2892 ◽  
Author(s):  
Benjamin F. Jamroz ◽  
Robert Klöfkorn
Keyword(s):  
Discontinuous Galerkin ◽  
Large Scale ◽  
Discontinuous Galerkin Methods ◽  
Spectral Element ◽  
Asynchronous Communication ◽  
High Order ◽  
Galerkin Methods ◽  
High Order Methods ◽  
Data Movement ◽  
Modeling Environment

Abstract. The scalability of computational applications on current and next-generation supercomputers is increasingly limited by the cost of inter-process communication. We implement non-blocking asynchronous communication in the High-Order Methods Modeling Environment for the time integration of the hydrostatic fluid equations using both the spectral-element and discontinuous Galerkin methods. This allows the overlap of computation with communication, effectively hiding some of the costs of communication. A novel detail about our approach is that it provides some data movement to be performed during the asynchronous communication even in the absence of other computations. This method produces significant performance and scalability gains in large-scale simulations.

HIGH-ORDER EXPLICIT TIME-INTEGRATORS FOR DISCONTINUOUS GALERKIN DISCRETIZATIONS OF THE MAXWELL EQUATIONS

2012 ◽  
Vol 04 (01) ◽  
pp. 1250029
Author(s):  
H. FAHS ◽  
M. SAFA
Keyword(s):  
Discontinuous Galerkin ◽  
Large Scale ◽  
Formal Solution ◽  
High Order ◽  
Practical Implementation ◽  
Test Problems ◽  
Time Integrators ◽  
The Matrix ◽  
Long Time ◽  
Exponential Formula

We investigate the practical implementation of a high-order explicit time-stepping method based on polynomial approximations, for possible application to large-scale problems in electromagnetics. After the spatial discretization by a high-order discontinuous Galerkin method, we obtain a linear system of differential equations of the form, [Formula: see text], where [Formula: see text] is a matrix containing the spatial derivatives and t is the time variable. The formal solution can be written in terms of the matrix exponential, [Formula: see text], acting on some vectors. We introduce a general family of time-integrators based on the approximation of [Formula: see text] by Jacobi polynomial expansions. We discuss the efficient implementation of this technique, and based on some test problems, we compare the virtues and shortcomings of the algorithm. We also demonstrate how these schemes provide an efficient alternative to standard explicit integrators for computing solutions over long time intervals.

A new method to predict anomaly in brain network based on graph deep learning

2020 ◽  
Vol 31 (6) ◽  
pp. 681-689
Author(s):  
Jalal Mirakhorli ◽  
Hamidreza Amindavar ◽  
Mojgan Mirakhorli
Keyword(s):  
Deep Learning ◽  
Large Scale ◽  
Brain Plasticity ◽  
Brain Network ◽  
High Order ◽  
Brain Diseases ◽  
Simultaneous Occurrence ◽  
Generative Adversarial Network ◽  
The Brain ◽  
Brain Connections

AbstractFunctional magnetic resonance imaging a neuroimaging technique which is used in brain disorders and dysfunction studies, has been improved in recent years by mapping the topology of the brain connections, named connectopic mapping. Based on the fact that healthy and unhealthy brain regions and functions differ slightly, studying the complex topology of the functional and structural networks in the human brain is too complicated considering the growth of evaluation measures. One of the applications of irregular graph deep learning is to analyze the human cognitive functions related to the gene expression and related distributed spatial patterns. Since a variety of brain solutions can be dynamically held in the neuronal networks of the brain with different activity patterns and functional connectivity, both node-centric and graph-centric tasks are involved in this application. In this study, we used an individual generative model and high order graph analysis for the region of interest recognition areas of the brain with abnormal connection during performing certain tasks and resting-state or decompose irregular observations. Accordingly, a high order framework of Variational Graph Autoencoder with a Gaussian distributer was proposed in the paper to analyze the functional data in brain imaging studies in which Generative Adversarial Network is employed for optimizing the latent space in the process of learning strong non-rigid graphs among large scale data. Furthermore, the possible modes of correlations were distinguished in abnormal brain connections. Our goal was to find the degree of correlation between the affected regions and their simultaneous occurrence over time. We can take advantage of this to diagnose brain diseases or show the ability of the nervous system to modify brain topology at all angles and brain plasticity according to input stimuli. In this study, we particularly focused on Alzheimer’s disease.

An improvement of classical slope limiters for high-order discontinuous Galerkin method

2009 ◽  
Vol 59 (4) ◽  
pp. 423-442 ◽  
Author(s):  
R. Ghostine ◽  
G. Kesserwani ◽  
R. Mosé ◽  
J. Vazquez ◽  
A. Ghenaim
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
High Order ◽  
Slope Limiters

Decentralized adaptive tracking control for high-order interconnected stochastic nonlinear time-varying delay systems with stochastic input-to-state stable inverse dynamics by neural networks

2019 ◽  
Vol 41 (13) ◽  
pp. 3612-3625 ◽  
Author(s):  
Wang Qian ◽  
Wang Qiangde ◽  
Wei Chunling ◽  
Zhang Zhengqiang
Keyword(s):  
Neural Networks ◽  
Tracking Control ◽  
Large Scale ◽  
Inverse Dynamics ◽  
Small Neighborhood ◽  
High Order ◽  
Interconnected Systems ◽  
Delay Systems ◽  
Rbf Neural Networks ◽  
Stochastic Input

The paper solves the problem of a decentralized adaptive state-feedback neural tracking control for a class of stochastic nonlinear high-order interconnected systems. Under the assumptions that the inverse dynamics of the subsystems are stochastic input-to-state stable (SISS) and for the controller design, Radial basis function (RBF) neural networks (NN) are used to cope with the packaged unknown system dynamics and stochastic uncertainties. Besides, the appropriate Lyapunov-Krosovskii functions and parameters are constructed for a class of large-scale high-order stochastic nonlinear strong interconnected systems with inverse dynamics. It has been proved that the actual controller can be designed so as to guarantee that all the signals in the closed-loop systems remain semi-globally uniformly ultimately bounded, and the tracking errors eventually converge in the small neighborhood of origin. Simulation example has been proposed to show the effectiveness of our results.

scholarly journals Time-resolved PIV measurements of a deflected submerged jet interacting with liquid-gas and liquid-liquid interfaces

2021 ◽  
Author(s):  
Stefan Puttinger ◽  
Mahdi Saeedipour
Keyword(s):  
Liquid Layer ◽  
Large Scale ◽  
Free Surface Flow ◽  
Industrial Applications ◽  
Liquid Pool ◽  
Surface Flow ◽  
Two Phase ◽  
Time Resolved ◽  
Submerged Jet ◽  
Major Interest

AbstractThis paper presents an experimental investigation on the interactions of a deflected submerged jet into a liquid pool with its above interface in the absence and presence of an additional lighter liquid. Whereas the former is a free surface flow, the latter mimics a situation of two stratified liquids where the liquid-liquid interface is disturbed by large-scale motions in the liquid pool. Such configurations are encountered in various industrial applications and, in most cases, it is of major interest to avoid the entrainment of droplets from the lighter liquid into the main flow. Therefore, it is important to understand the fluid dynamics in such configurations and to analyze the differences between the cases with and without the additional liquid layer. To study this problem, we applied time-resolved particle image velocimetry experiments with high spatial resolution. A detailed data analysis of a small layer beneath the interface shows that although the presence of an additional liquid layer stabilizes the oscillations of the submerged jet significantly, the amount of kinetic energy, enstrophy, and velocity fluctuations concentrated in the proximity of the interface is higher when the oil layer is present. In addition, we analyze the energy distribution across the eigenmodes of a proper orthogonal distribution and the distribution of strain and vortex dominated regions. As the main objective of this study, these high-resolution time-resolved experimental data provide a validation platform for the development of new models in the context of the volume of fluid-based large eddy simulation of turbulent two-phase flows.

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