Adaptive Numerical Solution Of Pdes

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Adaptive Numerical Solution Of Pdes

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Author : Peter Deuflhard
language : en
Publisher: Walter de Gruyter
Release Date : 2012-08-31

Adaptive Numerical Solution Of Pdes written by Peter Deuflhard and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-31 with Mathematics categories.

This book deals with the general topic “Numerical solution of partial differential equations (PDEs)” with a focus on adaptivity of discretizations in space and time. By and large, introductory textbooks like “Numerical Analysis in Modern Scientific Computing” by Deuflhard and Hohmann should suffice as a prerequisite. The emphasis lies on elliptic and parabolic systems. Hyperbolic conservation laws are treated only on an elementary level excluding turbulence. Numerical Analysis is clearly understood as part of Scientific Computing. The focus is on the efficiency of algorithms, i.e. speed, reliability, and robustness, which directly leads to the concept of adaptivity in algorithms. The theoretical derivation and analysis is kept as elementary as possible. Nevertheless required somewhat more sophisticated mathematical theory is summarized in comprehensive form in an appendix. Complex relations are explained by numerous figures and illustrating examples. Non-trivial problems from regenerative energy, nanotechnology, surgery, and physiology are inserted. The text will appeal to graduate students and researchers on the job in mathematics, science, and technology. Conceptually, it has been written as a textbook including exercises and a software list, but at the same time it should be well-suited for self-study.

Adaptive Multilevel Solution Of Nonlinear Parabolic Pde Systems

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Author : Jens Lang
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29

Adaptive Multilevel Solution Of Nonlinear Parabolic Pde Systems written by Jens Lang and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Computers categories.

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.

Modeling Mesh Generation And Adaptive Numerical Methods For Partial Differential Equations

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Author : Ivo Babuska
language : en
Publisher:
Release Date : 1995-07-14

Modeling Mesh Generation And Adaptive Numerical Methods For Partial Differential Equations written by Ivo Babuska and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-07-14 with categories.

Adaptive Computational Methods For Partial Differential Equations

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Author : Ivo Babushka
language : en
Publisher: SIAM
Release Date : 1983-01-01

Adaptive Computational Methods For Partial Differential Equations written by Ivo Babushka and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983-01-01 with Mathematics categories.

List of participants; Elliptic equations; Parabolic equations; Hyperbolic equations.

Numerical Solution Of Pdes Using Adaptive Finite Difference Methods

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Author : Yiqi Qiu
language : en
Publisher:
Release Date : 1997

Numerical Solution Of Pdes Using Adaptive Finite Difference Methods written by Yiqi Qiu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with categories.

Adaptive Method Of Lines

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Author : A, Vande Wouwer
language : en
Publisher: CRC Press
Release Date : 2001-04-18

Adaptive Method Of Lines written by A, Vande Wouwer and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-04-18 with Mathematics categories.

The general Method of Lines (MOL) procedure provides a flexible format for the solution of all the major classes of partial differential equations (PDEs) and is particularly well suited to evolutionary, nonlinear wave PDEs. Despite its utility, however, there are relatively few texts that explore it at a more advanced level and reflect the method's

Adaptive Radial Basis Function Methods For The Numerical Solution Of Partial Differential Equations With Application To The Simulation Of The Human Tear Film

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Author : Alfa R. H. Heryudono
language : en
Publisher:
Release Date : 2008

Adaptive Radial Basis Function Methods For The Numerical Solution Of Partial Differential Equations With Application To The Simulation Of The Human Tear Film written by Alfa R. H. Heryudono and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Differential equations, Partial categories.

This thesis deals with meshless adaptive numerical methods for solving partial differential equations. Specifically, the type of meshless method used is the radial basis function (RBF) method. We did numerous numerical experiments, built the algorithm from scratch, analyzed it, and tested it on some common test problems. The emphasis of this thesis is on computations and not on proofs. During our journey, we found many interesting results and ideas. Our goal in developing the adaptive RBF based method is to use it in the future as a method for solving two dimensional tear film equations in a blink cycle. The problem is challenging involving complex moving geometries, fourth-order nonlinear PDEs, and nontrivial boundary conditions. To get some insight, we begin with the one dimensional versions and solve them with spectral collocation methods. In the one dimensional case, we are able to compare them with data from in vivo observations. Our first experiment regarding the adaptive RBF method started with one dimensional adaptive interpolation problem. We found out that the use of variable RBF shape parameters is substantial. Extending the method to handle more general problems including time-independent and time-dependent problems in one and two dimensions is straightforward. The method can be extended even more to the generalized adaptive finite difference method with no need of special stencils. This can overcome the ill-conditioning issue that is found in the adaptive global RBF methods when applied to problems that exhibit very steep slopes.

Adaptive Numerical Methods For Pdes

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Author : Mathematisches Forschungsinstitut Oberwolfach
language : en
Publisher:
Release Date : 2007

Adaptive Numerical Methods For Pdes written by Mathematisches Forschungsinstitut Oberwolfach and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with categories.

Adaptive Methods For Partial Differential Equations

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Author : Ivo Babushka
language : en
Publisher: SIAM
Release Date : 1989-01-01

Adaptive Methods For Partial Differential Equations written by Ivo Babushka and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-01-01 with Mathematics categories.

"Proceedings of the Workshop on Adaptive Computational Methods for Partial Differential Equations, Rensselaer Polytechnic Institute, October 13-15, 1988"--T.p. verso.

Adaptive Numerical Methods For High Dimensional Parametric Pdes

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Author : Martin Eigel
language : en
Publisher:
Release Date : 2022

Adaptive Numerical Methods For High Dimensional Parametric Pdes written by Martin Eigel and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022 with categories.