Iterative Splitting Methods for Differential Equations

Iterative Splitting Methods for Differential Equations PDF

Author: Juergen Geiser

Publisher: CRC Press

Published: 2011-06-01

Total Pages: 325

ISBN-13: 1439869839

DOWNLOAD EBOOK →

Iterative Splitting Methods for Differential Equations explains how to solve evolution equations via novel iterative-based splitting methods that efficiently use computational and memory resources. It focuses on systems of parabolic and hyperbolic equations, including convection-diffusion-reaction equations, heat equations, and wave equations.In th

Splitting Methods for Partial Differential Equations with Rough Solutions

Splitting Methods for Partial Differential Equations with Rough Solutions PDF

Author: Helge Holden

Publisher: European Mathematical Society

Published: 2010

Total Pages: 238

ISBN-13: 9783037190784

DOWNLOAD EBOOK →

Operator splitting (or the fractional steps method) is a very common tool to analyze nonlinear partial differential equations both numerically and analytically. By applying operator splitting to a complicated model one can often split it into simpler problems that can be analyzed separately. In this book one studies operator splitting for a family of nonlinear evolution equations, including hyperbolic conservation laws and degenerate convection-diffusion equations. Common for these equations is the prevalence of rough, or non-smooth, solutions, e.g., shocks. Rigorous analysis is presented, showing that both semi-discrete and fully discrete splitting methods converge. For conservation laws, sharp error estimates are provided and for convection-diffusion equations one discusses a priori and a posteriori correction of entropy errors introduced by the splitting. Numerical methods include finite difference and finite volume methods as well as front tracking. The theory is illustrated by numerous examples. There is a dedicated Web page that provides MATLABR codes for many of the examples. The book is suitable for graduate students and researchers in pure and applied mathematics, physics, and engineering.

Decomposition Methods for Differential Equations

Decomposition Methods for Differential Equations PDF

Author: Juergen Geiser

Publisher: CRC Press

Published: 2009-05-20

Total Pages: 320

ISBN-13: 1439810974

DOWNLOAD EBOOK →

Decomposition Methods for Differential Equations: Theory and Applications describes the analysis of numerical methods for evolution equations based on temporal and spatial decomposition methods. It covers real-life problems, the underlying decomposition and discretization, the stability and consistency analysis of the decomposition methods, and num

Finite Difference Methods. Theory and Applications

Finite Difference Methods. Theory and Applications PDF

Author: Ivan Dimov

Publisher: Springer

Published: 2019-01-28

Total Pages: 688

ISBN-13: 3030115399

DOWNLOAD EBOOK →

This book constitutes the refereed conference proceedings of the 7th International Conference on Finite Difference Methods, FDM 2018, held in Lozenetz, Bulgaria, in June 2018.The 69 revised full papers presented together with 11 invited papers were carefully reviewed and selected from 94 submissions. They deal with many modern and new numerical techniques like splitting techniques, Green’s function method, multigrid methods, and immersed interface method.

Multicomponent and Multiscale Systems

Multicomponent and Multiscale Systems PDF

Author: Juergen Geiser

Publisher: Springer

Published: 2015-08-21

Total Pages: 325

ISBN-13: 3319151177

DOWNLOAD EBOOK →

This book examines the latest research results from combined multi-component and multi-scale explorations. It provides theory, considers underlying numerical methods and presents brilliant computational experimentation. Engineering computations featured in this monograph further offer particular interest to many researchers, engineers and computational scientists working in frontier modeling and applications of multicomponent and multiscale problems. Professor Geiser gives specific attention to the aspects of decomposing and splitting delicate structures and controlling decomposition and the rationale behind many important applications of multi-component and multi-scale analysis. Multicomponent and Multiscale Systems: Theory, Methods and Applications in Engineering also considers the question of why iterative methods can be powerful and more appropriate for well-balanced multiscale and multicomponent coupled nonlinear problems. The book is ideal for engineers and scientists working in theoretical and applied areas.

Iterative Methods and Preconditioners for Systems of Linear Equations

Iterative Methods and Preconditioners for Systems of Linear Equations PDF

Author: Gabriele Ciaramella

Publisher: SIAM

Published: 2022-02-08

Total Pages: 285

ISBN-13: 1611976901

DOWNLOAD EBOOK →

Iterative methods use successive approximations to obtain more accurate solutions. This book gives an introduction to iterative methods and preconditioning for solving discretized elliptic partial differential equations and optimal control problems governed by the Laplace equation, for which the use of matrix-free procedures is crucial. All methods are explained and analyzed starting from the historical ideas of the inventors, which are often quoted from their seminal works. Iterative Methods and Preconditioners for Systems of Linear Equations grew out of a set of lecture notes that were improved and enriched over time, resulting in a clear focus for the teaching methodology, which derives complete convergence estimates for all methods, illustrates and provides MATLAB codes for all methods, and studies and tests all preconditioners first as stationary iterative solvers. This textbook is appropriate for undergraduate and graduate students who want an overview or deeper understanding of iterative methods. Its focus on both analysis and numerical experiments allows the material to be taught with very little preparation, since all the arguments are self-contained, and makes it appropriate for self-study as well. It can be used in courses on iterative methods, Krylov methods and preconditioners, and numerical optimal control. Scientists and engineers interested in new topics and applications will also find the text useful.

Coupled Systems

Coupled Systems PDF

Author: Juergen Geiser

Publisher: CRC Press

Published: 2014-02-14

Total Pages: 311

ISBN-13: 1466578025

DOWNLOAD EBOOK →

Theory, Models, and Applications in Engineering explains how to solve complicated coupled models in engineering using analytical and numerical methods. It presents splitting multiscale methods to solve multiscale and multi-physics problems and describes analytical and numerical methods in time and space for evolution equations arising in engineering problems. The book discusses the effectiveness, simplicity, stability, and consistency of the methods in solving problems that occur in real-life engineering tasks. It shows how MATLAB (R) and Simulink (R) are used to implement the methods. The author also covers the coupling of separate, multiple, and logical scales in applications, including microscale, macroscale, multiscale, and multi-physics problems. Covering mathematical, algorithmic, and practical aspects, this book brings together innovative ideas in coupled systems and extends standard engineering tools to coupled models in materials and flow problems with respect to their scale dependencies and their influence on each time and spatial scale

Lanterna Rally - Theme by Grace Themes