Adaptive Space-time Finite Element Methods for Optimization Problems Governed by Nonlinear Parabolic Systems PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Adaptive Space-time Finite Element Methods for Optimization Problems Governed by Nonlinear Parabolic Systems PDF full book. Access full book title Adaptive Space-time Finite Element Methods for Optimization Problems Governed by Nonlinear Parabolic Systems by Dominik Meidner. Download full books in PDF and EPUB format.
Author: Dominik Meidner
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
Get Book Here
Book Description
Author: Dominik Meidner
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
Get Book Here
Book Description
Author: Jens Lang
Publisher: Springer Science & Business Media
ISBN: 3662044846
Category : Computers
Languages : en
Pages : 161
Get Book Here
Book Description
Nowadays there is an increasing emphasis on all aspects of adaptively gener ating a grid that evolves with the solution of a PDE. Another challenge is to develop efficient higher-order one-step integration methods which can handle very stiff equations and which allow us to accommodate a spatial grid in each time step without any specific difficulties. In this monograph a combination of both error-controlled grid refinement and one-step methods of Rosenbrock-type is presented. It is my intention to impart the beauty and complexity found in the theoretical investigation of the adaptive algorithm proposed here, in its realization and in solving non-trivial complex problems. I hope that this method will find many more interesting applications. Berlin-Dahlem, May 2000 Jens Lang Acknowledgements I have looked forward to writing this section since it is a pleasure for me to thank all friends who made this work possible and provided valuable input. I would like to express my gratitude to Peter Deuflhard for giving me the oppor tunity to work in the field of Scientific Computing. I have benefited immensly from his help to get the right perspectives, and from his continuous encourage ment and support over several years. He certainly will forgive me the use of Rosenbrock methods rather than extrapolation methods to integrate in time.
Author: Hans Georg Bock
Publisher: Springer Science & Business Media
ISBN: 3642303676
Category : Mathematics
Languages : en
Pages : 342
Get Book Here
Book Description
This judicious selection of articles combines mathematical and numerical methods to apply parameter estimation and optimum experimental design in a range of contexts. These include fields as diverse as biology, medicine, chemistry, environmental physics, image processing and computer vision. The material chosen was presented at a multidisciplinary workshop on parameter estimation held in 2009 in Heidelberg. The contributions show how indispensable efficient methods of applied mathematics and computer-based modeling can be to enhancing the quality of interdisciplinary research. The use of scientific computing to model, simulate, and optimize complex processes has become a standard methodology in many scientific fields, as well as in industry. Demonstrating that the use of state-of-the-art optimization techniques in a number of research areas has much potential for improvement, this book provides advanced numerical methods and the very latest results for the applications under consideration.
Author: Günter Leugering
Publisher: Springer Science & Business Media
ISBN: 3034801335
Category : Mathematics
Languages : en
Pages : 622
Get Book Here
Book Description
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 problems is still lacking. The contributions of this volume, some of which have the character of survey articles, therefore, aim at creating and developing further new ideas for optimization, control and corresponding numerical simulations of systems of possibly coupled nonlinear partial differential equations. The research conducted within this unique network of groups in more than fifteen German universities focuses on novel methods of optimization, control and identification for problems in infinite-dimensional spaces, shape and topology problems, model reduction and adaptivity, discretization concepts and important applications. Besides the theoretical interest, the most prominent question is about the effectiveness of model-based numerical optimization methods for PDEs versus a black-box approach that uses existing codes, often heuristic-based, for optimization.
Author: Christian A. Möller
Publisher: Logos Verlag Berlin GmbH
ISBN: 3832528156
Category : Mathematics
Languages : en
Pages : 259
Get Book Here
Book Description
Adaptivity is a crucial tool in state-of-the-art scientific computing. However, its theoretical foundations are only understood partially and are subject of current research. This self-contained work provides theoretical basics on partial differential equations and finite element discretizations before focusing on adaptive finite element methods for time dependent problems. In this context, aspects of temporal adaptivity and error control are considered in particular. Based on the gained insights, a specific adaptive algorithm is designed and analyzed thoroughly. Most importantly, it is proven that the presented adaptive method terminates within any demanded error tolerance. Moreover, the developed algorithm is analyzed from a numerical point of view and its performance is compared to well-known standard methods. Finally, it is applied to the real-life problem of concrete carbonation, where two different discretizations are compared.
Author: Thomas Carraro
Publisher: Springer
ISBN: 3319233211
Category : Mathematics
Languages : en
Pages : 424
Get Book Here
Book Description
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 challenging practical problems. The practicability and efficiency of the presented methods is illustrated by several case studies from fluid dynamics, data compression, image processing and computational biology, giving rise to possible new research topics. This volume, resulting from the workshop Multiple Shooting and Time Domain Decomposition Methods, held in Heidelberg in May 2013, will be of great interest to applied mathematicians, computer scientists and all scientists using mathematical methods.
Author: Alfio Borzi
Publisher: SIAM
ISBN: 1611972043
Category : Mathematics
Languages : en
Pages : 295
Get Book Here
Book Description
This book provides a bridge between continuous optimization and PDE modelling and focuses on the numerical solution of the corresponding problems. Intended for graduate students in PDE-constrained optimization, it is also suitable as an introduction for researchers in scientific computing or optimization.
Author: Slimane Adjerid
Publisher:
ISBN:
Category :
Languages : en
Pages : 39
Get Book Here
Book Description
Adaptive finite element methods are given for solving initial boundary value problems for vector systems of parabolic partial differential equations in one- and two-space dimensions. One-dimension systems are discretized using piecewise linear finite element approximations in space and a backward difference code for stiff ordinary differential systems in time. A spatial error estimate is calculated using piecewise quadratic approximations that employ nodal superconvergence to increase computational efficiency. This error estimate is used to move and refine the finite element mesh in order to equidistribute a measure of the total spatial error and to satisfy a prescribed error tolerance. Ordinary differential equations for the spatial error estimate and the mesh motion are integrated in time using the same backward difference software that is used to determine the finite element solution. Two-dimension systems are discretized using piecewise bilinear finite element approximations in space and backward difference software in time. A spatial error estimate is calculated using piecewise cubic approximations that take advantage of nodal superconvergence. This error estimate is used to locally refine a stationary finite element mesh in order to satisfy a prescribed spatial error tolerance.
Author: Fadi Aldakheel
Publisher: Springer Nature
ISBN: 3030873129
Category : Science
Languages : en
Pages : 587
Get Book Here
Book Description
This Festschrift is dedicated to Professor Dr.-Ing. habil. Peter Wriggers on the occasion of his 70th birthday. Thanks to his high dedication to research, over the years Peter Wriggers has built an international network with renowned experts in the field of computational mechanics. This is proven by the large number of contributions from friends and collaborators as well as former PhD students from all over the world. The diversity of Peter Wriggers network is mirrored by the range of topics that are covered by this book. To name only a few, these include contact mechanics, finite & virtual element technologies, micromechanics, multiscale approaches, fracture mechanics, isogeometric analysis, stochastic methods, meshfree and particle methods. Applications of numerical simulation to specific problems, e.g. Biomechanics and Additive Manufacturing is also covered. The volume intends to present an overview of the state of the art and current trends in computational mechanics for academia and industry.
Author: Andrea Cangiani
Publisher: Springer Science & Business Media
ISBN: 3642331343
Category : Mathematics
Languages : en
Pages : 811
Get Book Here
Book Description
The European Conferences on Numerical Mathematics and Advanced Applications (ENUMATH) are a series of conferences held every two years to provide a forum for discussion of new trends in numerical mathematics and challenging scientific and industrial applications at the highest level of international expertise. ENUMATH 2011 was hosted by the University of Leicester (UK) from the 5th to 9th September 2011. This proceedings volume contains more than 90 papers by speakers of the conference and gives an overview of recent developments in scientific computing, numerical analysis, and practical use of modern numerical techniques and algorithms in various applications. New results on finite element methods, multiscale methods, numerical linear algebra, and finite difference schemes are presented. A range of applications include computational problems from fluid dynamics, materials, image processing, and molecular dynamics.
