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Proper Orthogonal Decomposition Of Direct Numerical Simulation Data Data Reduction And Observer Construction
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Book Synopsis Proper Orthogonal Decomposition of Direct Numerical Simulation Data: Data Reduction and Observer Construction by :
Download or read book Proper Orthogonal Decomposition of Direct Numerical Simulation Data: Data Reduction and Observer Construction written by and published by . This book was released on 2000 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, direct numerical simulation (DNS) data of an opposed-jet hydrogen/air diffusion flame are in a postprocessing step, analyzed using the proper orthogonal decomposition (POD) technique. The aim of this work is twofold. The first goal is to compute a small number of space-dependent empirical eigenfunctions, so that a low-dimensional representation of the data generated by the large model of the discretized partial differential equations can be obtained using a weighted sum of these few eigenfunctions (POD modes). It is found that only six modes are needed for an accurate representation of the data in an extended range of inflow velocities. This large data reduction takes into account not only chemical kinetics but also transport phenomena in a full two-dimensional context and constitutes the first step toward the construction of low-dimensional dynamic models for the opposed-jet system. It is also found that the PODs have very good interpolatory properties. The second goal is to use part of the available data (i.e., partial measurements), together with the computed modes, to estimate, or, in the terminology of process control, to observe, the "unmeasured" quantities. It is found that only a small number of measurements are needed to obtain accurate estimates of the rest of the data.
Book Synopsis Data Analysis for Direct Numerical Simulations of Turbulent Combustion by : Heinz Pitsch
Download or read book Data Analysis for Direct Numerical Simulations of Turbulent Combustion written by Heinz Pitsch and published by Springer Nature. This book was released on 2020-05-28 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents methodologies for analysing large data sets produced by the direct numerical simulation (DNS) of turbulence and combustion. It describes the development of models that can be used to analyse large eddy simulations, and highlights both the most common techniques and newly emerging ones. The chapters, written by internationally respected experts, invite readers to consider DNS of turbulence and combustion from a formal, data-driven standpoint, rather than one led by experience and intuition. This perspective allows readers to recognise the shortcomings of existing models, with the ultimate goal of quantifying and reducing model-based uncertainty. In addition, recent advances in machine learning and statistical inferences offer new insights on the interpretation of DNS data. The book will especially benefit graduate-level students and researchers in mechanical and aerospace engineering, e.g. those with an interest in general fluid mechanics, applied mathematics, and the environmental and atmospheric sciences.
Book Synopsis Proper Orthogonal Decomposition and Tomographic Analysis of Combustion Systems for Control Applications by : Jennifer Leslie Edwards
Download or read book Proper Orthogonal Decomposition and Tomographic Analysis of Combustion Systems for Control Applications written by Jennifer Leslie Edwards and published by . This book was released on 2007 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Analysis of Kinetic Reaction Mechanisms by : Tamás Turányi
Download or read book Analysis of Kinetic Reaction Mechanisms written by Tamás Turányi and published by Springer. This book was released on 2014-12-29 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: Chemical processes in many fields of science and technology, including combustion, atmospheric chemistry, environmental modelling, process engineering, and systems biology, can be described by detailed reaction mechanisms consisting of numerous reaction steps. This book describes methods for the analysis of reaction mechanisms that are applicable in all these fields. Topics addressed include: how sensitivity and uncertainty analyses allow the calculation of the overall uncertainty of simulation results and the identification of the most important input parameters, the ways in which mechanisms can be reduced without losing important kinetic and dynamic detail, and the application of reduced models for more accurate engineering optimizations. This monograph is invaluable for researchers and engineers dealing with detailed reaction mechanisms, but is also useful for graduate students of related courses in chemistry, mechanical engineering, energy and environmental science and biology.
Book Synopsis AIAA Journal by : American Institute of Aeronautics and Astronautics
Download or read book AIAA Journal written by American Institute of Aeronautics and Astronautics and published by . This book was released on 2005 with total page 960 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Proper Orthogonal Decomposition by : Sarah Katherine Locke
Download or read book Proper Orthogonal Decomposition written by Sarah Katherine Locke and published by . This book was released on 2021 with total page 95 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Proper orthogonal decomposition (POD) projection errors and error bounds for POD reduced order models of partial differential equations have been studied by many. In this research we obtain new results regarding POD data approximation theory and present a new difference quotient (DQ) approach for computing the POD modes of the data. First, we improve on earlier results concerning POD projection errors by extending to a more general framework that allows for non-orthogonal POD projections and seminorms. We obtain new exact error formulas and convergence results for POD data approximation errors, and also prove new pointwise convergence results and error bounds for POD projections. We consider both the discrete and continuous cases of POD within this generalized framework. We also apply our results to several example problems, and show how the new results improve on previous work. Next, we consider the relationship between POD, difference quotients (DQs), and pointwise ROM error bounds. It is known that including DQs is necessary in order to prove optimal pointwise in time error bounds for POD reduced order models of the heat equation. We introduce a new approach to including DQs in the POD procedure to further investigate the role DQs play in POD numerical analysis. Instead of computing the POD modes using all of the snapshot data and DQs, we only use the first snapshot along with all of the DQs and special POD weights. We show that this approach retains all of the numerical analysis benefits of the standard POD DQ approach, while using a POD data set that has half the number of snapshots as the standard POD DQ approach, i.e., the new approach is more computationally efficient. We illustrate our theoretical results with numerical experiments"--Abstract, page iii.
Book Synopsis Incremental Proper Orthogonal Decomposition for PDE Simulation Data by : Hiba Ghassan Fareed
Download or read book Incremental Proper Orthogonal Decomposition for PDE Simulation Data written by Hiba Ghassan Fareed and published by . This book was released on 2018 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt: "We propose an incremental algorithm to compute the proper orthogonal decomposition (POD) of simulation data for a partial differential equation. Specifically, we modify an incremental matrix SVD algorithm of Brand to accommodate data arising from Galerkin-type simulation methods for time dependent PDEs. We introduce an incremental SVD algorithm with respect to a weighted inner product to compute the proper orthogonal decomposition (POD). The algorithm is applicable to data generated by many numerical methods for PDEs, including finite element and discontinuous Galerkin methods. We also modify the algorithm to initialize and incrementally update both the SVDand an error bound during the time stepping in a PDE solver without storing the simulation data. We show the algorithm produces the exact SVD of an approximate data matrix, and the operator norm error between the approximate and exact data matrices is bounded above by the computed error bound. This error bound also allows us to bound the error in the incrementally computed singular values and singular vectors. We demonstrate the effectiveness of the algorithm using finite element computations for a 1D Burgers' equation, a 1D FitzHugh-Nagumo PDE system, and a 2D Navier-Stokes problem"--Abstract, page iv.
Book Synopsis Dynamic Mode Decomposition by : J. Nathan Kutz
Download or read book Dynamic Mode Decomposition written by J. Nathan Kutz and published by SIAM. This book was released on 2016-11-23 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: Data-driven dynamical systems is a burgeoning field?it connects how measurements of nonlinear dynamical systems and/or complex systems can be used with well-established methods in dynamical systems theory. This is a critically important new direction because the governing equations of many problems under consideration by practitioners in various scientific fields are not typically known. Thus, using data alone to help derive, in an optimal sense, the best dynamical system representation of a given application allows for important new insights. The recently developed dynamic mode decomposition (DMD) is an innovative tool for integrating data with dynamical systems theory. The DMD has deep connections with traditional dynamical systems theory and many recent innovations in compressed sensing and machine learning. Dynamic Mode Decomposition: Data-Driven Modeling of Complex Systems, the first book to address the DMD algorithm, presents a pedagogical and comprehensive approach to all aspects of DMD currently developed or under development; blends theoretical development, example codes, and applications to showcase the theory and its many innovations and uses; highlights the numerous innovations around the DMD algorithm and demonstrates its efficacy using example problems from engineering and the physical and biological sciences; and provides extensive MATLAB code, data for intuitive examples of key methods, and graphical presentations.
Book Synopsis Certified Reduced Basis Methods for Parametrized Partial Differential Equations by : Jan S Hesthaven
Download or read book Certified Reduced Basis Methods for Parametrized Partial Differential Equations written by Jan S Hesthaven and published by Springer. This book was released on 2015-08-20 with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a thorough introduction to the mathematical and algorithmic aspects of certified reduced basis methods for parametrized partial differential equations. Central aspects ranging from model construction, error estimation and computational efficiency to empirical interpolation methods are discussed in detail for coercive problems. More advanced aspects associated with time-dependent problems, non-compliant and non-coercive problems and applications with geometric variation are also discussed as examples.
Book Synopsis Reduced Order Methods for Modeling and Computational Reduction by : Alfio Quarteroni
Download or read book Reduced Order Methods for Modeling and Computational Reduction written by Alfio Quarteroni and published by Springer. This book was released on 2014-06-05 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph addresses the state of the art of reduced order methods for modeling and computational reduction of complex parametrized systems, governed by ordinary and/or partial differential equations, with a special emphasis on real time computing techniques and applications in computational mechanics, bioengineering and computer graphics. Several topics are covered, including: design, optimization, and control theory in real-time with applications in engineering; data assimilation, geometry registration, and parameter estimation with special attention to real-time computing in biomedical engineering and computational physics; real-time visualization of physics-based simulations in computer science; the treatment of high-dimensional problems in state space, physical space, or parameter space; the interactions between different model reduction and dimensionality reduction approaches; the development of general error estimation frameworks which take into account both model and discretization effects. This book is primarily addressed to computational scientists interested in computational reduction techniques for large scale differential problems.
Book Synopsis Approximation of Large-Scale Dynamical Systems by : Athanasios C. Antoulas
Download or read book Approximation of Large-Scale Dynamical Systems written by Athanasios C. Antoulas and published by SIAM. This book was released on 2009-06-25 with total page 489 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical models are used to simulate, and sometimes control, the behavior of physical and artificial processes such as the weather and very large-scale integration (VLSI) circuits. The increasing need for accuracy has led to the development of highly complex models. However, in the presence of limited computational accuracy and storage capabilities model reduction (system approximation) is often necessary. Approximation of Large-Scale Dynamical Systems provides a comprehensive picture of model reduction, combining system theory with numerical linear algebra and computational considerations. It addresses the issue of model reduction and the resulting trade-offs between accuracy and complexity. Special attention is given to numerical aspects, simulation questions, and practical applications.
Book Synopsis Computational Engineering - Introduction to Numerical Methods by : Michael Schäfer
Download or read book Computational Engineering - Introduction to Numerical Methods written by Michael Schäfer and published by Springer Nature. This book was released on 2021-07-19 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical simulation methods in all engineering disciplines gains more and more importance. The successful and efficient application of such tools requires certain basic knowledge about the underlying numerical techniques. The text gives a practice-oriented introduction in modern numerical methods as they typically are applied in mechanical, chemical, or civil engineering. Problems from heat transfer, structural mechanics, and fluid mechanics constitute a thematical focus of the text. For the basic understanding of the topic aspects of numerical mathematics, natural sciences, computer science, and the corresponding engineering area are simultaneously important. Usually, the necessary information is distributed in different textbooks from the individual disciplines. In the present text the subject matter is presented in a comprehensive multidisciplinary way, where aspects from the different fields are treated insofar as it is necessary for general understanding. Overarching aspects and important questions related to accuracy, efficiency, and cost effectiveness are discussed. The topics are presented in an introductory manner, such that besides basic mathematical standard knowledge in analysis and linear algebra no further prerequisites are necessary. The book is suitable either for self-study or as an accompanying textbook for corresponding lectures. It can be useful for students of engineering disciplines as well as for computational engineers in industrial practice.
Book Synopsis Turbulence, Coherent Structures, Dynamical Systems and Symmetry by : Philip Holmes
Download or read book Turbulence, Coherent Structures, Dynamical Systems and Symmetry written by Philip Holmes and published by Cambridge University Press. This book was released on 2012-02-23 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: Describes methods revealing the structures and dynamics of turbulence for engineering, physical science and mathematics researchers working in fluid dynamics.
Book Synopsis High Performance Computing by : Heike Jagode
Download or read book High Performance Computing written by Heike Jagode and published by Springer Nature. This book was released on 2020-10-19 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed post-conference proceedings of 10 workshops held at the 35th International ISC High Performance 2020 Conference, in Frankfurt, Germany, in June 2020: First Workshop on Compiler-assisted Correctness Checking and Performance Optimization for HPC (C3PO); First International Workshop on the Application of Machine Learning Techniques to Computational Fluid Dynamics Simulations and Analysis (CFDML); HPC I/O in the Data Center Workshop (HPC-IODC); First Workshop \Machine Learning on HPC Systems" (MLHPCS); First International Workshop on Monitoring and Data Analytics (MODA); 15th Workshop on Virtualization in High-Performance Cloud Computing (VHPC). The 25 full papers included in this volume were carefully reviewed and selected. They cover all aspects of research, development, and application of large-scale, high performance experimental and commercial systems. Topics include high-performance computing (HPC), computer architecture and hardware, programming models, system software, performance analysis and modeling, compiler analysis and optimization techniques, software sustainability, scientific applications, deep learning.
Book Synopsis Discrete Choice Methods with Simulation by : Kenneth Train
Download or read book Discrete Choice Methods with Simulation written by Kenneth Train and published by Cambridge University Press. This book was released on 2009-07-06 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes the new generation of discrete choice methods, focusing on the many advances that are made possible by simulation. Researchers use these statistical methods to examine the choices that consumers, households, firms, and other agents make. Each of the major models is covered: logit, generalized extreme value, or GEV (including nested and cross-nested logits), probit, and mixed logit, plus a variety of specifications that build on these basics. Simulation-assisted estimation procedures are investigated and compared, including maximum stimulated likelihood, method of simulated moments, and method of simulated scores. Procedures for drawing from densities are described, including variance reduction techniques such as anithetics and Halton draws. Recent advances in Bayesian procedures are explored, including the use of the Metropolis-Hastings algorithm and its variant Gibbs sampling. The second edition adds chapters on endogeneity and expectation-maximization (EM) algorithms. No other book incorporates all these fields, which have arisen in the past 25 years. The procedures are applicable in many fields, including energy, transportation, environmental studies, health, labor, and marketing.
Book Synopsis Interpolatory Methods for Model Reduction by : A. C. Antoulas
Download or read book Interpolatory Methods for Model Reduction written by A. C. Antoulas and published by SIAM. This book was released on 2020-01-13 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dynamical systems are a principal tool in the modeling, prediction, and control of a wide range of complex phenomena. As the need for improved accuracy leads to larger and more complex dynamical systems, direct simulation often becomes the only available strategy for accurate prediction or control, inevitably creating a considerable burden on computational resources. This is the main context where one considers model reduction, seeking to replace large systems of coupled differential and algebraic equations that constitute high fidelity system models with substantially fewer equations that are crafted to control the loss of fidelity that order reduction may induce in the system response. Interpolatory methods are among the most widely used model reduction techniques, and Interpolatory Methods for Model Reduction is the first comprehensive analysis of this approach available in a single, extensive resource. It introduces state-of-the-art methods reflecting significant developments over the past two decades, covering both classical projection frameworks for model reduction and data-driven, nonintrusive frameworks. This textbook is appropriate for a wide audience of engineers and other scientists working in the general areas of large-scale dynamical systems and data-driven modeling of dynamics.
Book Synopsis Recent Numerical Advances in Fluid Mechanics by : Omer San
Download or read book Recent Numerical Advances in Fluid Mechanics written by Omer San and published by MDPI. This book was released on 2020-07-03 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent decades, the field of computational fluid dynamics has made significant advances in enabling advanced computing architectures to understand many phenomena in biological, geophysical, and engineering fluid flows. Almost all research areas in fluids use numerical methods at various complexities: from molecular to continuum descriptions; from laminar to turbulent regimes; from low speed to hypersonic, from stencil-based computations to meshless approaches; from local basis functions to global expansions, as well as from first-order approximation to high-order with spectral accuracy. Many successful efforts have been put forth in dynamic adaptation strategies, e.g., adaptive mesh refinement and multiresolution representation approaches. Furthermore, with recent advances in artificial intelligence and heterogeneous computing, the broader fluids community has gained the momentum to revisit and investigate such practices. This Special Issue, containing a collection of 13 papers, brings together researchers to address recent numerical advances in fluid mechanics.
