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Presents discretization methods on non-matching triangulations and iterative solvers with emphasis on mortar fine elements, Schwartz methods, and multigrid techniques. Also emphasizes the role of trace theorems, dual norms and weak interface conditions. Softcover. ... Read more

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This volume contains the latest developments in the use of iterative methods to block Toeplitz systems. These systems arise in a variety of applications in mathematics, scientific computing, and engineering, such as image processing, numerical differential equations and integral equations, time series analysis, and control theory. Iterative methods such as Krylov subspace methods and multigrid methods are proposed to solve block Toeplitz systems. One of the main advantages of these iterative methods is that the operation cost of solving a large class of mn × mn block Toeplitz systems only requires O (mn log mn) operations.

This book is the first book on Toeplitz iterative solvers and it includes recent research results. The author belongs to one of the most important groups in the field of structured matrix computation. The book is accessible to readers with a working knowledge of numerical linear algebra. It should be of interest to everyone who deals with block Toeplitz systems, numerical linear algebra, partial differential equations, ordinary differential equations, image processing, and approximation theory.

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Presenting innovative, promising and unconventional techniques, Post-modern Electromagnetics outlines the essential tools for the creation of numerical methods. Hafner offers a comparative analysis of the fundamental computational electromagnetics methods and proposes future adaptive strategies. Complementary to Max-1: A Visual Electromagnetics Platform, this unique text challenges current thinking and provides guidance through the solution of practical problems. Features Include:
* Outline of Maxwell theory from simple material properties to complex media and wave equations

* Discussion of intelligent optimization strategies such as genetic algorithms designed to improve the performance of existing techniques

* Applications section demonstrating solutions in statics, scattering, gratings, antenna, antenna arrays, guided waves, resonators, coupling and waveguide discontinuities

* Explanation of the background to numerical methods showing how the various approaches to computational electromagnetics can be generalized and combined
Students and researchers interested in advanced numerical approaches and design engineers developing new codes for computational electromagnetics will benefit from this exploration of creative electromagnetics solutions. ... Read more

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Designed for undergraduate students in the general science, engineering, and mathematics community, Introduction to the Simulation of Dynamics Using Simulink^® shows how to use the powerful tool of Simulink to investigate and form intuitions about the behavior of dynamical systems. Requiring no prior programming experience, it clearly explains how to transition from physical models described by mathematical equations directly to executable Simulink simulations.

Teaches students how to model and explore the dynamics of systems
Step by step, the author presents the basics of building a simulation in Simulink. He begins with finite difference equations and simple discrete models, such as annual population models, to introduce the concept of state. The text then covers ordinary differential equations, numerical integration algorithms, and time-step simulation. The final chapter offers overviews of some advanced topics, including the simulation of chaotic dynamics and partial differential equations.

A one-semester undergraduate course on simulation
Written in an informal, accessible style, this guide includes many diagrams and graphics as well as exercises embedded within the text. It also draws on numerous examples from the science, engineering, and technology fields. The book deepens students’ understanding of simulated systems and prepares them for advanced and specialized studies in simulation. Ancillary materials are available at http://nw08.american.edu/~gray

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This compact yet thorough tutorial is the perfect introduction to the basic concepts of solving partial differential equations (PDEs) using parallel numerical methods. In just eight short chapters, the authors provide readers with enough basic knowledge of PDEs, discretization methods, solution techniques, parallel computers, parallel programming, and the run-time behavior of parallel algorithms to allow them to understand, develop, and implement parallel PDE solvers. Examples throughout the book are intentionally kept simple so that the parallelization strategies are not dominated by technical details.

A Tutorial on Elliptic PDE Solvers and Their Parallelization is a valuable aid for learning about the possible errors and bottlenecks in parallel computing. One of the highlights of the tutorial is that the course material can run on a laptop, not just on a parallel computer or cluster of PCs, thus allowing readers to experience their first successes in parallel computing in a relatively short amount of time.

Audience
This tutorial is intended for advanced undergraduate and graduate students in computational sciences and engineering; however, it may also be helpful to professionals who use PDE-based parallel computer simulations in the field.

Contents
List of figures; List of algorithms; Abbreviations and notation; Preface; Chapter 1: Introduction; Chapter 2: A simple example; Chapter 3: Introduction to parallelism; Chapter 4: Galerkin finite element discretization of elliptic partial differential equations; Chapter 5: Basic numerical routines in parallel; Chapter 6: Classical solvers; Chapter 7: Multigrid methods; Chapter 8: Problems not addressed in this book; Appendix: Internet addresses; Bibliography; Index. ... Read more

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The first four chapters of this book give a comprehensive and unified theory of the Krylov methods. Many of these are shown to be particular examples of
the block conjugate-gradient algorithm and it is this observation that
permits the unification of the theory. The two major sub-classes of those
methods, the Lanczos and the Hestenes-Stiefel, are developed in parallel as
natural generalisations of the Orthodir (GCR) and Orthomin algorithms. These
are themselves based on Arnoldi's algorithm and a generalised Gram-Schmidt
algorithm and their properties, in particular their stability properties,
are determined by the two matrices that define the block conjugate-gradient
algorithm. These are the matrix of coefficients and the preconditioning
matrix.

In Chapter 5 the"transpose-free" algorithms based on the conjugate-gradient squared algorithm are presented while Chapter 6 examines the various ways in which the QMR technique has been exploited. Look-ahead methods and general block methods are dealt with in Chapters 7 and 8 while Chapter 9 is devoted to error analysis of two basic algorithms.

In Chapter 10 the results of numerical testing of the more important algorithms in their basic forms (i.e. without look-ahead or preconditioning) are presented and these are related to the structure of the algorithms and the general theory. Graphs illustrating the performances of various algorithm/problem combinations are given via a CD-ROM.

Chapter 11, by far the longest, gives a survey of preconditioning techniques. These range from the old idea of polynomial preconditioning via SOR and ILU preconditioning to methods like SpAI, AInv and the multigrid methods that were developed specifically for use with parallel computers. Chapter 12 is devoted to dual algorithms like Orthores and the reverse algorithms of Hegedus. Finally certain ancillary matters like reduction to Hessenberg form, Chebychev polynomials and the companion matrix are described in a series of appendices.

· comprehensive and unified approach
· up-to-date chapter on preconditioners
· complete theory of stability
· includes dual and reverse methods
· comparison of algorithms on CD-ROM
· objective assessment of algorithms ... Read more

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The subject of this book is the efficient solution of partial differential equations (PDEs) that arise when modelling incompressible fluid flow.The material is organized into four groups of two chapters each, covering the Poisson equation (chapters 1 & 2); the convection-diffucion equation (chapters 3 & 4); the Stokes equations (chapters 5 & 6); and the Navier-Stokes equations (chapters 7 & 8).These equations represent important models within the domain of computational fluid dynamics, but they also arise in many other settings.For each PDE model, there is a chapter concerned with finite element discretization.For each problem and associated solvers there is a description of how to compute along with theoretical analysis which guides the choice of approaches.Illustrative numerical results occur throughout the book, which have been computed with the freely downloadable IFISS software. All numerical results should be reproducible by readers who have access to MATLAB and there is considerable scope for experimentation in the 'computational laboratory' provided by the software. This book provides an excellent introduction to finite elements, iterative linear solvers and scientific computing aimed at graduates in engineering, numerical analysis, applied mathematics and interdisciplinary scientific computing.Including theoretical problems and practical exercises closely tied with freely downloadable MATLAB software, this book is an ideal teaching and learning resource. ... Read more

Product Description
This book presents a unifying theoretical framework for iterative solvers for linear systems. The focus is on parameter-free methods, i. e. methods that can be applied without a priori knowledge of inner properties of the systems. Despite the generality of the approach convergence estimates and geometrical properties can be derived.
State-of-the-art solvers are surveyed and classified. Many new relations between these methods are furnished leading to a deeper insight. Existing gaps in the theory are pointed out and some visions for the design of more efficient and robust solvers are given.
A valuation of established methods based on the theoretical results and on numerical tests is given. Recipes for the application of particular techniques are derived. The criteria are efficiency, robustness and the possibility of parallelization.
This book has a triple aim: to simplify the analysis by a unified theory, to survey and valuate state-of-the-art solvers and to give an introduction to iterative solvers for non-experts in the field. ... Read more

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In this thoroughly revised version of the successful first edition, the author has added new material that will prove useful for research or application of the finite element method. The most important application of finite elements is the numerical solution of elliptic partial differential equations. The author provides thorough coverage of this subject and includes aspects such as saddle point problems that require a more in-depth mathematical treatment. ... Read more

Customer Reviews (2)

A decent introduction to theory and methods for FEM
I would say I mostly agree with the previous reviewer.The description is pretty clear, despite being a translation, and it has actually proven useful to me during my time in grad school.One minor complaint I have is that some of the proofs he gives are not as clear as I would like them to be.Specifically, I am talking about the sections dealing with the INF-SUP condition.It seems that everyone who writes an FEM book either skirts this whole issue of the INF-SUP condition (which is what a lot of engineering texts do), or they just copy the 'standard' proofs, which suck.But other than that, this is a useful book to have.

A Good Book To Learn Finite Elements From
I recently read this book as part of an advanced numerical analysis class in grad school.I found it to be well written and easy to read.It was useful to me in learning about finite elements from both an abstract and practical perspective.I would recommend it to anyone familiar with the concept of a weak solution to an elliptic partial differential equation and with some experience with numerical linear algebra.
This book could have been improved by including some code or pseudo-code to help get novices started.This is not too severe of a drawback since the text is so well written that the reader should be able to implement many of the ideas without any other training in this area. ... Read more

Product Description
This volume deals with problems of modern effective algorithmsfor the numerical solution of the most frequently occurring ellipticpartial differential equations. From the point of view ofimplementation, attention is paid to algorithms for both classicalsequential and parallel computer systems.
The first two chapters are devoted to fast algorithms for solving thePoisson and biharmonic equation. In the third chapter, parallelalgorithms for model parallel computer systems of the SIMD and MIMDtypes are described. The implementation aspects of parallel algorithmsfor solving model elliptic boundary value problems are outlined forsystems with matrix, pipeline and multiprocessor parallel computerarchitectures. A modern and popular multigrid computational principlewhich offers a good opportunity for a parallel realization isdescribed in the next chapter. More parallel variants based in thisidea are presented, whereby methods and assignments strategies forhypercube systems are treated in more detail. The last chapterpresents VLSI designs for solving special tridiagonal linear systemsof equations arising from finite-difference approximations of ellipticproblems.
For researchers interested in the development and application of fastalgorithms for solving elliptic partial differential equations usingadvanced computer systems.
... Read more

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This digital document is a journal article from Coastal Engineering, published by Elsevier in . The article is delivered in HTML format and is available in your Amazon.com Media Library immediately after purchase. You can view it with any web browser.

Description:
The Lagrangian particle method is a superior tool for the modelling of violent behavior of the water surface, such as wave breaking and overtopping. To further develop the numerical wave flume by the particle method, there remain several issues: modelling of the sub-particle-scale turbulence, modelling of the gas-phase behavior, modelling of movable bed (sediment transport), and modelling of floating bodies. In this paper, the sub-particle-scale turbulence model, the solid-liquid and liquid-gas two-phase-flow models, and the floating-bodies model, which have been developed by the authors, are reviewed to present the performance of the particle method in a computation of wave breaking. ... Read more