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# Proper Orthogonal Decomposition Methods for Partial Differential Equations

• Author : Zhendong Luo
• Release : 26 November 2018
• ISBN : 0128167998
• Pages : 278 pages
• Rating : 4/5 from 21 ratings

Summary:
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

• Author : Zhendong Luo,Goong Chen
• Release : 26 November 2018

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,

## Multiple Shooting and Time Domain Decomposition Methods

• Author : Thomas Carraro,Michael Geiger,Stefan Körkel,Rolf Rannacher
• Publisher : Springer
• Release : 26 October 2015

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

## Certified Reduced Basis Methods for Parametrized Partial Differential Equations

• Author : Jan S Hesthaven,Gianluigi Rozza,Benjamin Stamm
• Publisher : Springer
• Release : 20 August 2015

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.

## Reduced Basis Methods for Partial Differential Equations

• Author : Alfio Quarteroni,Andrea Manzoni,Federico Negri
• Publisher : Springer
• Release : 19 August 2015

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

## 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

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

## Incremental Proper Orthogonal Decomposition for PDE Simulation Data

• Author : Hiba Ghassan Fareed
• Publisher : Anonim
• Release : 27 May 2022

"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

## Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018

• Author : Spencer J. Sherwin,David Moxey,Joaquim Peiró,Peter E. Vincent,Christoph Schwab
• Publisher : Springer Nature
• Release : 11 August 2020

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.

## Mathematical and Numerical Modeling of the Cardiovascular System and Applications

• Author : Daniele Boffi,Luca F. Pavarino,Gianluigi Rozza,Simone Scacchi,Christian Vergara
• Publisher : Springer
• Release : 03 November 2018

The book comprises contributions by some of the most respected scientists in the field of mathematical modeling and numerical simulation of the human cardiocirculatory system. It covers a wide range of topics, from the assimilation of clinical data to the development of mathematical and computational models, including with parameters, as well as their efficient numerical solution, and both in-vivo and in-vitro validation. It also considers applications of relevant clinical interest. This book is intended for graduate students and researchers in

## Snapshot-Based Methods and Algorithms

• Author : Peter Benner,et al.
• Publisher : Walter de Gruyter GmbH & Co KG
• Release : 16 December 2020

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.

## Multiscale Wavelet Methods for Partial Differential Equations

• Author : Wolfgang Dahmen,Andrew Kurdila,Peter Oswald
• Publisher : Elsevier
• Release : 13 August 1997

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

## Numerical and Evolutionary Optimization 2018

• Author : Adriana Lara,Marcela Quiroz,Efrén Mezura-Montes,Oliver Schütze
• Publisher : MDPI
• Release : 19 November 2019

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.

## Medical Image Computing and Computer-Assisted Intervention - MICCAI 2014

• Author : Polina Golland,Nobuhiko Hata,Christian Barillot,Joachim Hornegger,Robert Howe
• Publisher : Springer
• Release : 31 August 2014

The three-volume set LNCS 8673, 8674, and 8675 constitutes the refereed proceedings of the 17th International Conference on Medical Image Computing and Computer-Assisted Intervention, MICCAI 2014, held in Boston, MA, USA, in September 2014. Based on rigorous peer reviews, the program committee carefully selected 253 revised papers from 862 submissions for presentation in three volumes. The 100 papers included in the first volume have been organized in the following topical sections: microstructure imaging; image reconstruction and enhancement; registration; segmentation; intervention planning and guidance; oncology; and optical imaging.

## Recent Trends in Computational Engineering - CE2014

• Author : Miriam Mehl,Manfred Bischoff,Michael Schäfer
• Publisher : Springer
• Release : 12 October 2015

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