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

Separated Representations and PGD Based Model Reduction

Separated Representations and PGD Based Model Reduction
  • Author : Francisco Chinesta,Pierre Ladevèze
  • Publisher : Springer
  • Release : 02 September 2014
GET THIS BOOK Separated Representations and PGD Based Model Reduction

The papers in this volume start with a description of the construction of reduced models through a review of Proper Orthogonal Decomposition (POD) and reduced basis models, including their mathematical foundations and some challenging applications, then followed by a description of a new generation of simulation strategies based on the use of separated representations (space-parameters, space-time, space-time-parameters, space-space,...), which have led to what is known as Proper Generalized Decomposition (PGD) techniques. The models can be enriched by treating parameters as

Incremental Proper Orthogonal Decomposition for PDE Simulation Data

Incremental Proper Orthogonal Decomposition for PDE Simulation Data
  • Author : Hiba Ghassan Fareed
  • Publisher : Unknown
  • Release : 03 December 2021
GET THIS BOOK Incremental Proper Orthogonal Decomposition for PDE Simulation Data

"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

Snapshot Location in Proper Orthogonal Decomposition for Linear and Semi linear Parabolic Partial Differential Equations

Snapshot Location in Proper Orthogonal Decomposition for Linear and Semi linear Parabolic Partial Differential Equations
  • Author : Zhiheng Liu
  • Publisher : Unknown
  • Release : 03 December 2021
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

Certified Reduced Basis Methods for Parametrized Partial Differential Equations

Certified Reduced Basis Methods for Parametrized Partial Differential Equations
  • 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

Constrained Optimization and Optimal Control for Partial Differential Equations
  • 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

Proper Orthogonal Decomposition in Optimal Control of Fluids

Proper Orthogonal Decomposition in Optimal Control of Fluids
  • Author : National Aeronautics and Space Adm Nasa
  • Publisher : Independently Published
  • Release : 16 September 2018
GET THIS BOOK Proper Orthogonal Decomposition in Optimal Control of Fluids

In this article, we present a reduced order modeling approach suitable for active control of fluid dynamical systems based on proper orthogonal decomposition (POD). The rationale behind the reduced order modeling is that numerical simulation of Navier-Stokes equations is still too costly for the purpose of optimization and control of unsteady flows. We examine the possibility of obtaining reduced order models that reduce computational complexity associated with the Navier-Stokes equations while capturing the essential dynamics by using the POD. The

Multiscale Wavelet Methods for Partial Differential Equations

Multiscale Wavelet Methods for Partial Differential Equations
  • Author : Wolfgang Dahmen,Andrew Kurdila,Peter Oswald
  • Publisher : Elsevier
  • Release : 13 August 1997
GET THIS BOOK Multiscale Wavelet Methods for Partial Differential Equations

This latest volume in the Wavelets Analysis and Its Applications Series provides significant and up-to-date insights into recent developments in the field of wavelet constructions in connection with partial differential equations. Specialists in numerical applications and engineers in a variety of fields will find Multiscale Wavelet for Partial Differential Equations to be a valuable resource. Covers important areas of computational mechanics such as elasticity and computational fluid dynamics Includes a clear study of turbulence modeling Contains recent research on multiresolution

Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018

Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018
  • Author : Spencer J. Sherwin
  • Publisher : Springer Nature
  • Release : 03 December 2021
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.

Numerical and Evolutionary Optimization 2018

Numerical and Evolutionary Optimization 2018
  • Author : Adriana Lara,Marcela Quiroz,Efrén Mezura-Montes,Oliver Schütze
  • 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.

Trust region Proper Orthogonal Decomposition for Flow Control

Trust region Proper Orthogonal Decomposition for Flow Control
  • Author : E. Arian,Institute for Computer Applications in Science and Engineering
  • Publisher : Unknown
  • Release : 03 December 2021
GET THIS BOOK Trust region Proper Orthogonal Decomposition for Flow Control

The proper orthogonal decomposition (POD) is a model reduction technique for the simulation of physical processes governed by partial differential equations, e.g., fluid flows. It can also be used to develop reduced order control models. Fundamental is the computation of POD basis functions that represent the influence of the control action on the system in order to get a suitable control model. We present an approach where suitable reduced order models are derived successively and give global convergence results.

Recent Trends in Computational Engineering CE2014

Recent Trends in Computational Engineering   CE2014
  • Author : Miriam Mehl,Manfred Bischoff,Michael Schäfer
  • 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

Control and Optimization with PDE Constraints

Control and Optimization with PDE Constraints
  • 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