Proper Orthogonal Decomposition Methods for Partial Differential Equations

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  • Author : Zhendong Luo
  • Publisher : Academic Press
  • Pages : 278 pages
  • ISBN : 0128167998
  • Rating : /5 from reviews
CLICK HERE TO GET THIS BOOK >>>Proper Orthogonal Decomposition Methods for Partial Differential Equations

Download or Read online Proper Orthogonal Decomposition Methods for Partial Differential Equations full in PDF, ePub and kindle. this book written by Zhendong Luo and published by Academic Press which was released on 26 November 2018 with total page 278 pages. We cannot guarantee that Proper Orthogonal Decomposition Methods for Partial Differential Equations book is available in the library, click Get Book button and read full online book in your kindle, tablet, IPAD, PC or mobile whenever and wherever You Like. Proper Orthogonal Decomposition Methods for Partial Differential Equations evaluates the potential applications of POD reduced-order numerical methods in increasing computational efficiency, decreasing calculating load and alleviating the accumulation of truncation error in the computational process. Introduces the foundations of finite-differences, finite-elements and finite-volume-elements. Models of time-dependent PDEs are presented, with detailed numerical procedures, implementation and error analysis. Output numerical data are plotted in graphics and compared using standard traditional methods. These models contain parabolic, hyperbolic and nonlinear systems of PDEs, suitable for the user to learn and adapt methods to their own R&D problems. Explains ways to reduce order for PDEs by means of the POD method so that reduced-order models have few unknowns Helps readers speed up computation and reduce computation load and memory requirements while numerically capturing system characteristics Enables readers to apply and adapt the methods to solve similar problems for PDEs of hyperbolic, parabolic and nonlinear types

Proper Orthogonal Decomposition Methods for Partial Differential Equations

Proper Orthogonal Decomposition Methods for Partial Differential Equations
  • Author : Zhendong Luo,Goong Chen
  • Publisher : Academic Press
  • Release : 26 November 2018
GET THIS BOOK Proper Orthogonal Decomposition Methods for Partial Differential Equations

Proper Orthogonal Decomposition Methods for Partial Differential Equations evaluates the potential applications of POD reduced-order numerical methods in increasing computational efficiency, decreasing calculating load and alleviating the accumulation of truncation error in the computational process. Introduces the foundations of finite-differences, finite-elements and finite-volume-elements. Models of time-dependent PDEs are presented, with detailed numerical procedures, implementation and error analysis. Output numerical data are plotted in graphics and compared using standard traditional methods. These models contain parabolic, hyperbolic and nonlinear systems of PDEs,

Reduced Basis Methods for Partial Differential Equations

Reduced Basis Methods for Partial Differential Equations
  • Author : Alfio Quarteroni,Andrea Manzoni,Federico Negri
  • Publisher : Springer
  • Release : 19 August 2015
GET THIS BOOK Reduced Basis Methods for Partial Differential Equations

This book provides a basic introduction to reduced basis (RB) methods for problems involving the repeated solution of partial differential equations (PDEs) arising from engineering and applied sciences, such as PDEs depending on several parameters and PDE-constrained optimization. The book presents a general mathematical formulation of RB methods, analyzes their fundamental theoretical properties, discusses the related algorithmic and implementation aspects, and highlights their built-in algebraic and geometric structures. More specifically, the authors discuss alternative strategies for constructing accurate RB spaces

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  • Author : Jan S Hesthaven,Gianluigi Rozza,Benjamin Stamm
  • Publisher : Springer
  • Release : 20 August 2015
GET THIS BOOK Certified Reduced Basis Methods for Parametrized Partial Differential Equations

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.

Constrained Optimization and Optimal Control for Partial Differential Equations

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  • Author : Günter Leugering,Sebastian Engell,Andreas Griewank,Michael Hinze,Rolf Rannacher,Volker Schulz,Michael Ulbrich,Stefan Ulbrich
  • Publisher : Springer Science & Business Media
  • Release : 03 January 2012
GET THIS BOOK Constrained Optimization and Optimal Control for Partial Differential Equations

This special volume focuses on optimization and control of processes governed by partial differential equations. The contributors are mostly participants of the DFG-priority program 1253: Optimization with PDE-constraints which is active since 2006. The book is organized in sections which cover almost the entire spectrum of modern research in this emerging field. Indeed, even though the field of optimal control and optimization for PDE-constrained problems has undergone a dramatic increase of interest during the last four decades, a full theory for nonlinear

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  • Author : Zhiheng Liu
  • Publisher : Unknown
  • Release : 03 October 2022
GET THIS BOOK Snapshot Location in Proper Orthogonal Decomposition for Linear and Semi linear Parabolic Partial Differential Equations

It is well-known that the performance of POD and POD-DEIM methods depends on the selection of the snapshot locations. In this work, we consider the selections of the locations for POD and POD-DEIM snapshots for spatially semi-discretized linear or semi-linear parabolic PDEs. We present an approach that for a fixed number of snapshots the optimal locations may be selected such that the global discretization error is approximately the same in each associated sub-interval. The global discretization error is assessed by

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  • Author : Spencer J. Sherwin,David Moxey,Joaquim Peiró,Peter E. Vincent,Christoph Schwab
  • Publisher : Springer Nature
  • Release : 11 August 2020
GET THIS BOOK Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018

This open access book features a selection of high-quality papers from the presentations at the International Conference on Spectral and High-Order Methods 2018, offering an overview of the depth and breadth of the activities within this important research area. The carefully reviewed papers provide a snapshot of the state of the art, while the extensive bibliography helps initiate new research directions.

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  • Publisher : MDPI
  • Release : 19 November 2019
GET THIS BOOK Numerical and Evolutionary Optimization 2018

This book was established after the 6th International Workshop on Numerical and Evolutionary Optimization (NEO), representing a collection of papers on the intersection of the two research areas covered at this workshop: numerical optimization and evolutionary search techniques. While focusing on the design of fast and reliable methods lying across these two paradigms, the resulting techniques are strongly applicable to a broad class of real-world problems, such as pattern recognition, routing, energy, lines of production, prediction, and modeling, among others.

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  • Publisher : Walter de Gruyter GmbH & Co KG
  • Release : 16 December 2020
GET THIS BOOK Snapshot Based Methods and Algorithms

An increasing complexity of models used to predict real-world systems leads to the need for algorithms to replace complex models with far simpler ones, while preserving the accuracy of the predictions. This two-volume handbook covers methods as well as applications. This second volume focuses on applications in engineering, biomedical engineering, computational physics and computer science.

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  • Publisher : Springer
  • Release : 12 October 2015
GET THIS BOOK Recent Trends in Computational Engineering CE2014

This book presents selected papers from the 3rd International Workshop on Computational Engineering held in Stuttgart from October 6 to 10, 2014, bringing together innovative contributions from related fields with computer science and mathematics as an important technical basis among others. The workshop discussed the state of the art and the further evolution of numerical techniques for simulation in engineering and science. We focus on current trends in numerical simulation in science and engineering, new requirements arising from rapidly increasing parallelism in computer

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  • Publisher : Springer Nature
  • Release : 01 March 2021
GET THIS BOOK Advances on Links Between Mathematics and Industry

This book results from the talks presented at the First Conference on Transfer between Mathematics & Industry (CTMI 2019). Its goal is to promote and disseminate the mathematical tools for Statistics & Big Data, MSO (Modeling, Simulation and Optimization) and their industrial applications. In this volume, the reader will find innovative advances in the automotive, energy, railway, logistics, and materials sectors. In addition, Advances CTMI 2019 promotes the opening of new research lines aiming to provide suitable solutions for the industrial and societal challenges.

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  • Author : Kristian Bredies,Christian Clason,Karl Kunisch,Gregory Winckel
  • Publisher : Springer Science & Business Media
  • Release : 12 June 2013
GET THIS BOOK Control and Optimization with PDE Constraints

Many mathematical models of physical, biological and social systems involve partial differential equations (PDEs). The desire to understand and influence these systems naturally leads to considering problems of control and optimization. This book presents important topics in the areas of control of PDEs and of PDE-constrained optimization, covering the full spectrum from analysis to numerical realization and applications. Leading scientists address current topics such as non-smooth optimization, Hamilton–Jacobi–Bellmann equations, issues in optimization and control of stochastic partial differential

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  • Publisher : Springer
  • Release : 26 October 2015
GET THIS BOOK Multiple Shooting and Time Domain Decomposition Methods

This book offers a comprehensive collection of the most advanced numerical techniques for the efficient and effective solution of simulation and optimization problems governed by systems of time-dependent differential equations. The contributions present various approaches to time domain decomposition, focusing on multiple shooting and parareal algorithms. The range of topics covers theoretical analysis of the methods, as well as their algorithmic formulation and guidelines for practical implementation. Selected examples show that the discussed approaches are mandatory for the solution of

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  • Author : Winfried Keiper,Anja Milde,Stefan Volkwein
  • Publisher : Springer
  • Release : 11 April 2018
GET THIS BOOK Reduced Order Modeling ROM for Simulation and Optimization

This edited monograph collects research contributions and addresses the advancement of efficient numerical procedures in the area of model order reduction (MOR) for simulation, optimization and control. The topical scope includes, but is not limited to, new out-of-the-box algorithmic solutions for scientific computing, e.g. reduced basis methods for industrial problems and MOR approaches for electrochemical processes. The target audience comprises research experts and practitioners in the field of simulation, optimization and control, but the book may also be beneficial