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$H(\mathrm {div})$ preconditioning for a mixed finite element formulation of the diffusion problem with random data

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Mathematics of Computation 2010年第270期79卷 733-760页

作者： Elman, Howard Furnival, Darran Powell, Catherine Department of Computer Science and Institute for Advanced Computer Studies University of Maryland College Park Maryland 20742 Applied Mathematics and Scientific Computing Program University of Maryland College Park Maryland 20742 National Oceanographic Centre Southampton S014 32H School of Mathematics University of Manchester Oxford Road Manchester M13 9PL United Kingdom

Abstract: We study $H(\mathrm {div})$ preconditioning for the saddle-point systems that arise in a stochastic Galerkin mixed formulation of the steady-state diffusion problem with random data. The key ingredient is a multigrid V-cycle for an $H(\mathrm {div})$ operator with random weight function acting on a certain tensor product space of random fields with finite variance. We build on the Arnold-Falk-Winther multigrid algorithm presented in 1997 by varying the spatial discretization from grid to grid whilst keeping the stochastic discretization fixed. We extend the deterministic analysis to accommodate the modified $H(\mathrm {div})$ operator and establish spectral equivalence bounds with a new multigrid V-cycle operator that are independent of the spatial and stochastic discretization parameters. We implement multigrid within a block-diagonal preconditioner for the full saddle-point problem, derive eigenvalue bounds for the preconditioned system matrices and investigate the impact of all the discretization parameters on the convergence rate of preconditioned minres.

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Immersive Paleontological Experience Through Virtual and Augmented Reality Representation

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Immersive Paleontological Experience Through Virtual and Aug...

IEEE International Symposium on Geoscience and Remote Sensing (IGARSS)

作者： Gustavo C. Almeida Daniel C. Zanotta Taina T. Guimaraes Ademir Marques Rodrigo S. Horodyski Luiz Gonzaga Maurício R. Veronez Vinícius C. Souza Vizlab — X-Reality and GeoInformatics Lab UNISINOS São Leopoldo RS Brazil Graduate Program in Applied Computing at Vale do Rio dos Sinos University São Leopoldo RS Brazil Rio Grande do Sul Geological History Museum UNISINOS São Leopoldo RS Brazil

Virtual reality systems have been extending their usability in many areas that could not be contemplated before. One of these fields is paleontology, which can now use virtual reality to build realistic models of real fossils with many goals, including preservation of originals, optimized visualization, or even for restoring missing parts. In this paper we present an immersive system where a entire scenario is reconstructed using digital photogrammetry and Mosis LAB application. The system has shown useful for many applications from touristic purposes and paleontological studies, since the immersive system provides an increased sense of manipulation, as well as the possibility of detailed inspection both inside and outside structures.

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Modeling subgrid-scale force and divergence of heat flux of compressible isotropic turbulence by artificial neural network

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Physical Review Fluids 2019年第10期4卷 104605-104605页

作者： Chenyue Xie Ke Li Chao Ma Jianchun Wang Shenzhen Key Laboratory of Complex Aerospace Flows Center for Complex Flows and Soft Matter Research Department of Mechanics and Aerospace Engineering Southern University of Science and Technology Shenzhen 518055 People's Republic of China Institute of Computational Mathematics and Scientific Engineering Computing Chinese Academy of Sciences Beijing 100190 People's Republic of China The Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

In this paper, the subgrid-scale (SGS) force and the divergence of SGS heat flux of compressible isotropic turbulence are modeled directly by an artificial neural network (ANN), which serves as a data-driven SGS modeling tool for large-eddy simulations (LESs). The unclosed SGS force and divergence of SGS heat flux are modeled based on the local stencil geometry with Galilean invariance. The input features include the first-order and second-order derivatives of filtered velocity and temperature, filtered density, and its first-order derivative. It is shown that the proposed ANN-F7 model shows an advantage over the gradient model in the a priori test. Specifically, the ANN-F7 model gives larger correlation coefficients and smaller relative errors than the gradient model. In an a posteriori analysis, the ANN-F7 model performs better than the dynamic Smagorinsky model (DSM) and dynamic mixed model (DMM) in the prediction of the statistical properties of flow fields at the Taylor microscale Reynolds number Reλ ranging from 180 to 250. The DSM and DMM models lead to the typical tilted spectral distribution of velocity, where low wave numbers are too energy rich, while those near the cutoff are damped too strongly. In contrast, it is shown that the velocity spectrum predicted by the ANN-F7 model almost overlaps with the filtered direct numerical simulation data. Besides, the ANN-F7 model reconstructs the probability density functions of SGS force and divergence of SGS heat flux much better than the DSM and DMM models. An artificial neural network with reasonable physical input features can deepen our understanding of turbulence modeling.

关键词： Compressible flows Turbulence Artificial neural networks

Methodology for Acquisition of Intensity Data in Forest Targets Using Terrestrial Laser Scanner

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IERI Procedia 2013年 5卷 238-244页

作者： Fabiane Bordin Elba Calesso Teixeira Sílvia Beatriz Alves Rolim Francisco Manoel Wohnrath Tognoli Maurício Roberto Veronez Luiz Gonzaga da Silveira Junior Camila Fernandes Natus de Souza Graduate Program in Remote Sensing Federal University of Rio Grande do Sul (UFRGS) Porto Alegre - RS Brazil Remote Sensing and Digital Cartography Laboratory (LASERCA) University of Vale do Rio dos Sinos (UNISINOS) São Leopoldo-RS Brazil State Foundation of Environmental Protection Luiz Henrique Roessler (FEPAM) Porto Alegre - RS Brazil Graduate Program in Geology University of Vale do Rio dos Sinos (UNISINOS) São Leopoldo-RS Brazil Graduate Program in Applied Computing University of Vale do Rio dos Sinos (UNISINOS) São Leopoldo-RS Brazil

The advance of technology and the availability of high-resolution and accurate systems have permitted the development of new methods for studies in forests. Terrestrial laser scanners have been consolidated as one of the most effective technologies for geospatial data acquisition since the last decade. They have offered the possibility of mapping tridimensionally with high positional accuracy a great number of targets, including forests. However, it is quite difficult to find methodological approaches for acquisition of forest data involving these type of systems. Thus, based on a mid and long range laser scanner with an electromagnetic spectrum ranging into the mid-infrared, 1535 nm, different distances and radiometric resolutions were tested in order to establish a method of acquisition of intensity data in forest targets. After processing, data were analyzed with a clustering algorithm to test the possibility of identifying different elements. Trunk, branches and leaves as well as an edge effect were satisfactorily grouped. Besides defining a method for acquisition of intensity, it opens good perspectives in terms of integrating the classification obtained by the clustering technique with the point cloud. Future studies can contribute to develop a method for quantifying the volume of forest elements and, consequently, estimate biomass.

关键词： Remote sensing Radiometric resolution Distance K-means algorithm LIDAR Mid-infrared Edge effect

A novel strong duality-based reformulation for trilevel infrastructure models in energy systems development

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arXiv 2023年

作者： Herrala, Olli Gabriel, Steven A. Oliveira, Fabricio Ekholm, Tommi Aalto University Department of Mathematics and Systems Analysis Espoo Finland University of Maryland Department of Mechanical Engineering/Applied Mathematics Statistics & Scientific Computing Program College ParkMD United States Norwegian University of Science and Technology Department of Industrial Economics and Technology Management Trondheim Norway Finnish Meteorological Institute Helsinki Finland

We explore the class of trilevel equilibrium problems with a focus on energy-environmental applications and present a novel single-level reformulation for such problems, based on strong duality. To the best of our knowledge, only one alternative single-level reformulation for trilevel problems exists. This reformulation uses a representation of the bottom-level solution set, whereas we propose a reformulation based on strong duality. Our novel reformulation is compared to this existing formulation, discussing both model sizes and computational performance. In particular, we apply this trilevel framework to a power market model, exploring the possibilities of an international policymaker in reducing emissions of the system. Using the proposed methods, we are able to obtain globally optimal solutions for a five-node case study representing the Nordic countries and assess the impact of a carbon tax on the electricity production portfolio. Copyright © 2023, The Authors. All rights reserved.

关键词： Energy resources

CEMCO: A Novel Competitive Evolutionary Multi-Colony Optimization Algorithm for Constrained Problems

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CEMCO: A Novel Competitive Evolutionary Multi-Colony Optimiz...

International Conference on Fuzzy Systems and Knowledge Discovery (FSKD)

作者： Mário Tasso Ribeiro Serra Neto Marco Antônio Florenzano Mollinetti Demison Rolins de Souza Alves Rodrigo Lisbôa Pereira Otávio Noura Teixeira University Centre of the State of Pará (CESUPA) Computational Intelligence Laboratory (LINCOMP) Belém Pará Brazil Systems Optimization Laboratory Tsukuba University Tsukuba Ibaraki Japan Federal Rural University of Amazon (UFRA) Electrical Engineering Post Graduation Program of the Federal University of Par (UFPA) Paragominas Pará Brazil Applied Computing Post Graduation Program (PPCA) Federal University of Pará Tucuruí (UFPA-TUC) Tucuruí Pará Brazil

ISBN: (纸本)9781538680988;9781538680971

The following paper presents a hybrid Swarm Intelligence algorithm, named Competitive Evolutionary Multi-Colony Optimization (CEMCO). CEMCO is based on the well-known bee inspired algorithm Artificial Bee Colony (ABC), introducing Evolutionary Strategies (ES)under a parallel master-slave architecture utilizing the General Purpose computing on Graphics Processing Units (GPGPU)paradigm. The goal of this approach is to enhance the overall performance of the master algorithm, producing high quality solutions, and significant solutions under a reduced processing time. Performance evaluation of CEMCO is performed by two large scale constrained optimization problems: Design of Pressure Vessel (DPV)and Welded Beam Design (WBD). Results obtained are compared against prominent techniques found in the literature.

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OnsagerNet: Learning stable and interpretable dynamics using a generalized Onsager principle

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arXiv 2020年

作者： Yu, Haijun Tian, Xinyuan Weinan, E. Li, Qianxiao NCMIS LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China Department of Mathematics The Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Department of Mathematics National University of Singapore Singapore119077 Singapore Institute of High Performance Computing A*STAR Singapore138632 Singapore

We propose a systematic method for learning stable and physically interpretable dynamical models using sampled trajectory data from physical processes based on a generalized Onsager principle. The learned dynamics are autonomous ordinary differential equations parameterized by neural networks that retain clear physical structure information, such as free energy, diffusion, conservative motion and external forces. For high dimensional problems with a low dimensional slow manifold, an autoencoder with metric preserving regularization is introduced to find the low dimensional generalized coordinates on which we learn the generalized Onsager dynamics. Our method exhibits clear advantages over existing methods on benchmark problems for learning ordinary differential equations. We further apply this method to study Rayleigh-Bénard convection and learn Lorenz-like low dimensional autonomous reduced order models that capture both qualitative and quantitative properties of the underlying dynamics. This forms a general approach to building reduced order models for forced dissipative *** Codes 76E30, 34D20, 68T05/07, 82C35 Copyright © 2020, The Authors. All rights reserved.

关键词： Ordinary differential equations

Toward single particle reconstruction without particle picking: Breaking the detection limit

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arXiv 2018年

作者： Bendory, Tamir Boumal, Nicolas Leeb, William Levin, Eitan Singer, Amit The School of Electrical Engineering Tel Aviv University Tel Aviv Israel Lausanne Switzerland School of Mathematics University of Minnesota MinneapolisMN United States Department of Computing and Mathematical Sciences California Institute of Technology PasadenaCA United States The Program in Applied and Computational Mathematics Department of Mathematics Princeton University PrincetonNJ United States

Single-particle cryo-electron microscopy (cryo-EM) has recently joined X-ray crystallography and NMR spectroscopy as a high-resolution structural method to resolve biological macromolecules. In a cryo-EM experiment, the microscope produces images called micrographs. Projections of the molecule of interest are embedded in the micrographs at unknown locations, and under unknown viewing directions. Standard imaging techniques first locate these projections (detection) and then reconstruct the 3-D structure from them. Unfortunately, high noise levels hinder detection. When reliable detection is rendered impossible, the standard techniques fail. This is a problem, especially for small molecules. In this paper, we pursue a radically different approach: we contend that the structure could, in principle, be reconstructed directly from the micrographs, without intermediate detection. The aim is to bring small molecules within reach for cryo-EM. To this end, we design an autocorrelation analysis technique that allows to go directly from the micrographs to the sought structures. This involves only one pass over the micrographs, allowing online, streaming processing for large experiments. We show numerical results and discuss challenges that lay ahead to turn this proof-of-concept into a complementary approach to state-of-the-art algorithms. Copyright © 2018, The Authors. All rights reserved.

关键词： X ray crystallography

Some Entanglement Survives Most Measurements

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arXiv 2023年

作者： Gonzales, Alvin Dilley, Daniel Byrd, Mark Intelligence Community Postdoctoral Research Fellowship Program Argonne National Laboratory 9700 S. Cass Avenue LemontIL60439 United States School of Computing Southern Illinois University Carbondale CarbondaleIL62901 United States School of Physics and Applied Physics Southern Illinois University Carbondale CarbondaleIL62901 United States

To prepare quantum states and extract information, it is often assumed that one can perform a perfectly projective measurement. Such measurements can achieve an uncorrelated system and environment state. However, perfectly projective measurements can be difficult or impossible to perform in practice. We investigate the limitations of repeated non-projective measurements in preparing a quantum system. For an n-qubit system initially entangled with its environment and subsequently prepared with measurements, using a sequence of weak measurements, we show that some entanglement remains unless one of the measurement operators becomes perfectly projective through an extreme limiting process. Removing initial (unentangled) correlations between a system and its environment and the scenario where measurement outcomes are not tracked are also discussed. We present results for n-qubit and n-dimensional input states. Copyright © 2023, The Authors. All rights reserved.

关键词： Quantum entanglement