Alfio Quarteroni's Books

Numerical Mathematics

By: Alfio Quarteroni,Riccardo Sacco,Fausto Saleri

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Numerical Mathematics

By: Alfio Quarteroni,Riccardo Sacco,Fausto Saleri

The purpose of this book is to provide the mathematical foundations of numerical methods, to analyze their basic theoretical properties and to demonstrate their performances on examples and counterexamples. Within any specific class of problems, the most appropriate scientific computing algorithms are reviewed, their theoretical analyses are carried out and the expected results are verified using the MATLAB software environment. Each chapter contains examples, exercises and applications of the theory discussed to the solution of real-life problems. While addressed to senior undergraduates and graduates in engineering, mathematics, physics and computer sciences, this text is also valuable for researchers and users of scientific computing in a large variety of professional fields.

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669

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Springer

Published Date

ISBN 10

0387227504

ISBN 13

9780387227504

Algorithms for a New World

When Big Data and Mathematical Models Meet

By: Alfio Quarteroni

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Algorithms for a New World

When Big Data and Mathematical Models Meet

By: Alfio Quarteroni

Covid-19 has shown us the importance of mathematical and statistical models to interpret reality, provide forecasts, and explore future scenarios. Algorithms, artificial neural networks, and machine learning help us discover the opportunities and pitfalls of a world governed by mathematics and artificial intelligence.

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Springer Nature

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ISBN 10

3030961664

ISBN 13

9783030961664

Numerical Models for Differential Problems

By: Alfio Quarteroni

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Numerical Models for Differential Problems

By: Alfio Quarteroni

In this text, we introduce the basic concepts for the numerical modelling of partial differential equations. We consider the classical elliptic, parabolic and hyperbolic linear equations, but also the diffusion, transport, and Navier-Stokes equations, as well as equations representing conservation laws, saddle-point problems and optimal control problems. Furthermore, we provide numerous physical examples which underline such equations. We then analyze numerical solution methods based on finite elements, finite differences, finite volumes, spectral methods and domain decomposition methods, and reduced basis methods. In particular, we discuss the algorithmic and computer implementation aspects and provide a number of easy-to-use programs. The text does not require any previous advanced mathematical knowledge of partial differential equations: the absolutely essential concepts are reported in a preliminary chapter. It is therefore suitable for students of bachelor and master courses in scientific disciplines, and recommendable to those researchers in the academic and extra-academic domain who want to approach this interesting branch of applied mathematics.

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668

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Springer Science & Business

Published Date

ISBN 10

8847055229

ISBN 13

9788847055223

Scientific Computing with MATLAB and Octave

By: Alfio Quarteroni,Fausto Saleri

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Scientific Computing with MATLAB and Octave

By: Alfio Quarteroni,Fausto Saleri

This introduction to Scientific Computing illustrates several numerical methods for the computer solution of certain classes of mathematical problems. The authors show how to compute the zeros or the integrals of continuous functions, solve linear systems, approximate functions by polynomials and construct accurate approximations for the solution of differential equations. To make the presentation concrete, the programming environment Matlab is adopted as a faithful companion.

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334

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Springer Science & Business Media

Published Date

ISBN 10

354032612X

ISBN 13

9783540326120

Numerical Mathematics

By: Alfio Quarteroni,Riccardo Sacco,Fausto Saleri

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Numerical Mathematics

By: Alfio Quarteroni,Riccardo Sacco,Fausto Saleri

This book provides the mathematical foundations of numerical methods and demonstrates their performance on examples, exercises and real-life applications. This is done using the MATLAB software environment, which allows an easy implementation and testing of the algorithms for any specific class of problems. The book is addressed to students in Engineering, Mathematics, Physics and Computer Sciences. In the second edition of this extremely popular textbook on numerical analysis, the readability of pictures, tables and program headings has been improved. Several changes in the chapters on iterative methods and on polynomial approximation have also been

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664

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Springer Science & Business Media

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ISBN 10

3540346589

ISBN 13

9783540346586

Multiscale and Adaptivity: Modeling, Numerics and Applications

C.I.M.E. Summer School, Cetraro, Italy 2009

By: Silvia Bertoluzza,Ricardo H. Nochetto,Alfio Quarteroni,Kunibert G. Siebert,Andreas Veeser

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Multiscale and Adaptivity: Modeling, Numerics and Applications

C.I.M.E. Summer School, Cetraro, Italy 2009

By: Silvia Bertoluzza,Ricardo H. Nochetto,Alfio Quarteroni,Kunibert G. Siebert,Andreas Veeser

This book is a collection of lecture notes for the CIME course on "Multiscale and Adaptivity: Modeling, Numerics and Applications," held in Cetraro (Italy), in July 2009. Complex systems arise in several physical, chemical, and biological processes, in which length and time scales may span several orders of magnitude. Traditionally, scientists have focused on methods that are particularly applicable in only one regime, and knowledge of the system on one scale has been transferred to another scale only indirectly. Even with modern computer power, the complexity of such systems precludes their being treated directly with traditional tools, and new mathematical and computational instruments have had to be developed to tackle such problems. The outstanding and internationally renowned lecturers, coming from different areas of Applied Mathematics, have themselves contributed in an essential way to the development of the theory and techniques that constituted the subjects of the courses.

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324

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Springer

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ISBN 10

3642240798

ISBN 13

9783642240799

Mathematical Modelling of the Human Cardiovascular System

Data, Numerical Approximation, Clinical Applications

By: Alfio Quarteroni,Luca Dede',Andrea Manzoni,Christian Vergara

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Mathematical Modelling of the Human Cardiovascular System

Data, Numerical Approximation, Clinical Applications

By: Alfio Quarteroni,Luca Dede',Andrea Manzoni,Christian Vergara

Addresses the mathematical and numerical modelling of the human cardiovascular system, from patient data to clinical applications.

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291

Publisher

Cambridge University Press

Published Date

ISBN 10

110848039X

ISBN 13

9781108480390

Formulation and Numerical Solution of Quantum Control Problems

By: Alfio Borzi,Gabriele Ciaramella,Martin Sprengel

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Formulation and Numerical Solution of Quantum Control Problems

By: Alfio Borzi,Gabriele Ciaramella,Martin Sprengel

This book provides an introduction to representative nonrelativistic quantum control problems and their theoretical analysis and solution via modern computational techniques. The quantum theory framework is based on the Schr?dinger picture, and the optimization theory, which focuses on functional spaces, is based on the Lagrange formalism. The computational techniques represent recent developments that have resulted from combining modern numerical techniques for quantum evolutionary equations with sophisticated optimization schemes. Both finite and infinite-dimensional models are discussed, including the three-level Lambda system arising in quantum optics, multispin systems in NMR, a charged particle in a well potential, Bose?Einstein condensates, multiparticle spin systems, and multiparticle models in the time-dependent density functional framework. This self-contained book covers the formulation, analysis, and numerical solution of quantum control problems and bridges scientific computing, optimal control and exact controllability, optimization with differential models, and the sciences and engineering that require quantum control methods.

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396

Publisher

SIAM

Published Date

ISBN 10

1611974844

ISBN 13

9781611974843

Numerical Models for Differential Problems

By: Alfio Quarteroni

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Numerical Models for Differential Problems

By: Alfio Quarteroni

In this text, we introduce the basic concepts for the numerical modelling of partial differential equations. We consider the classical elliptic, parabolic and hyperbolic linear equations, but also the diffusion, transport, and Navier-Stokes equations, as well as equations representing conservation laws, saddle-point problems and optimal control problems. Furthermore, we provide numerous physical examples which underline such equations. In particular, we discuss the algorithmic and computer implementation aspects and provide a number of easy-to-use programs. The text does not require any previous advanced mathematical knowledge of partial differential equations: the absolutely essential concepts are reported in a preliminary chapter. It is therefore suitable for students of bachelor and master courses in scientific disciplines, and recommendable to those researchers in the academic and extra-academic domain who want to approach this interesting branch of applied mathematics.

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611

Publisher

Springer Science & Business Media

Published Date

ISBN 10

8847010713

ISBN 13

9788847010710

Numerical Approximation of Partial Differential Equations

By: Alfio Quarteroni,Alberto Valli

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Numerical Approximation of Partial Differential Equations

By: Alfio Quarteroni,Alberto Valli

Everything is more simple than one thinks but at the same time more complex than one can understand Johann Wolfgang von Goethe To reach the point that is unknown to you, you must take the road that is unknown to you St. John of the Cross This is a book on the numerical approximation ofpartial differential equations (PDEs). Its scope is to provide a thorough illustration of numerical methods (especially those stemming from the variational formulation of PDEs), carry out their stability and convergence analysis, derive error bounds, and discuss the algorithmic aspects relative to their implementation. A sound balancing of theoretical analysis, description of algorithms and discussion of applications is our primary concern. Many kinds of problems are addressed: linear and nonlinear, steady and time-dependent, having either smooth or non-smooth solutions. Besides model equations, we consider a number of (initial-) boundary value problems of interest in several fields of applications. Part I is devoted to the description and analysis of general numerical methods for the discretization of partial differential equations. A comprehensive theory of Galerkin methods and its variants (Petrov Galerkin and generalized Galerkin), as wellas ofcollocationmethods, is devel oped for the spatial discretization. This theory is then specified to two numer ical subspace realizations of remarkable interest: the finite element method (conforming, non-conforming, mixed, hybrid) and the spectral method (Leg endre and Chebyshev expansion).

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551

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Springer Science & Business Media

Published Date

ISBN 10

3540852689

ISBN 13

9783540852681

Spectral Methods

Fundamentals in Single Domains

By: Claudio Canuto,M. Yousuff Hussaini,Alfio Quarteroni,Thomas A. Zang

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Spectral Methods

Fundamentals in Single Domains

By: Claudio Canuto,M. Yousuff Hussaini,Alfio Quarteroni,Thomas A. Zang

Since the publication of "Spectral Methods in Fluid Dynamics" 1988, spectral methods have become firmly established as a mainstream tool for scientific and engineering computation. The authors of that book have incorporated into this new edition the many improvements in the algorithms and the theory of spectral methods that have been made since then. This latest book retains the tight integration between the theoretical and practical aspects of spectral methods, and the chapters are enhanced with material on the Galerkin with numerical integration version of spectral methods. The discussion of direct and iterative solution methods is also greatly expanded.

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585

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Springer Science & Business Media

Published Date

ISBN 10

3540307265

ISBN 13

9783540307266

Reduced Basis Methods for Partial Differential Equations

An Introduction

By: Alfio Quarteroni,Andrea Manzoni,Federico Negri

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Reduced Basis Methods for Partial Differential Equations

An Introduction

By: Alfio Quarteroni,Andrea Manzoni,Federico Negri

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 using greedy algorithms and proper orthogonal decomposition techniques, investigate their approximation properties and analyze offline-online decomposition strategies aimed at the reduction of computational complexity. Furthermore, they carry out both a priori and a posteriori error analysis. The whole mathematical presentation is made more stimulating by the use of representative examples of applicative interest in the context of both linear and nonlinear PDEs. Moreover, the inclusion of many pseudocodes allows the reader to easily implement the algorithms illustrated throughout the text. The book will be ideal for upper undergraduate students and, more generally, people interested in scientific computing. All these pseudocodes are in fact implemented in a MATLAB package that is freely available at https://github.com/redbkit

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305

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Springer

Published Date

ISBN 10

3319154311

ISBN 13

9783319154312

Spectral Methods

Evolution to Complex Geometries and Applications to Fluid Dynamics

By: Claudio Canuto,M. Yousuff Hussaini,Alfio Quarteroni,Thomas A. Zang

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Spectral Methods

Evolution to Complex Geometries and Applications to Fluid Dynamics

By: Claudio Canuto,M. Yousuff Hussaini,Alfio Quarteroni,Thomas A. Zang

Following up the seminal Spectral Methods in Fluid Dynamics, Spectral Methods: Evolution to Complex Geometries and Applications to Fluid Dynamics contains an extensive survey of the essential algorithmic and theoretical aspects of spectral methods for complex geometries. These types of spectral methods were only just emerging at the time the earlier book was published. The discussion of spectral algorithms for linear and nonlinear fluid dynamics stability analyses is greatly expanded. The chapter on spectral algorithms for incompressible flow focuses on algorithms that have proven most useful in practice, has much greater coverage of algorithms for two or more non-periodic directions, and shows how to treat outflow boundaries. Material on spectral methods for compressible flow emphasizes boundary conditions for hyperbolic systems, algorithms for simulation of homogeneous turbulence, and improved methods for shock fitting. This book is a companion to Spectral Methods: Fundamentals in Single Domains.

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616

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Springer Science & Business Media

Published Date

ISBN 10

3540307281

ISBN 13

9783540307280

A Primer on Mathematical Modelling

By: Alfio Quarteroni,Paola Gervasio

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A Primer on Mathematical Modelling

By: Alfio Quarteroni,Paola Gervasio

In this book we describe the magic world of mathematical models: starting from real-life problems, we formulate them in terms of equations, transform equations into algorithms and algorithms into programs to be executed on computers. A broad variety of examples and exercises illustrate that properly designed models can, e.g.: predict the way the number of dolphins in the Aeolian Sea will change as food availability and fishing activity vary; describe the blood flow in a capillary network; calculate the PageRank of websites. This book also includes a chapter with an elementary introduction to Octave, an open-source programming language widely used in the scientific community. Octave functions and scripts for dealing with the problems presented in the text can be downloaded from https://paola-gervasio.unibs.it/quarteroni-gervasio This book is addressed to any student interested in learning how to construct and apply mathematical models.

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Page Count

238

Publisher

Springer Nature

Published Date

ISBN 10

3030445410

ISBN 13

9783030445416

Multiscale and Adaptivity: Modeling, Numerics and Applications

C.I.M.E. Summer School, Cetraro, Italy 2009

By: Silvia Bertoluzza,Ricardo H. Nochetto,Alfio Quarteroni,Kunibert G. Siebert,Andreas Veeser

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Multiscale and Adaptivity: Modeling, Numerics and Applications

C.I.M.E. Summer School, Cetraro, Italy 2009

By: Silvia Bertoluzza,Ricardo H. Nochetto,Alfio Quarteroni,Kunibert G. Siebert,Andreas Veeser

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324

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Springer Science & Business Media

Published Date

ISBN 10

364224078X

ISBN 13

9783642240782

Scientific Computing with MATLAB and Octave

By: Alfio Quarteroni,Fausto Saleri

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Scientific Computing with MATLAB and Octave

By: Alfio Quarteroni,Fausto Saleri

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334

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Springer Science & Business Media

Published Date

ISBN 10

3540326138

ISBN 13

9783540326137

Domain Decomposition Methods in Science and Engineering

The Sixth International Conference on Domain Decomposition, June 15-19, 1992, Como, Italy

By: Alfio Quarteroni

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Domain Decomposition Methods in Science and Engineering

The Sixth International Conference on Domain Decomposition, June 15-19, 1992, Como, Italy

By: Alfio Quarteroni

This book contains the proceedings of the Sixth International Conference on Domain Decomposition, held in June 1992 in Como, Italy. Developments in this area are driven by advances in computer technology as well as by a strengthening in the mathematical foundations of the subject. Compared to just a few years ago, experts have much more experience with difficult applications and have accumulated solid evidence that these methods provide valuable tools for solving problems in science and engineering. Much of the work in this field focuses on developing numerical methods for large algebraic systems, methods central to producing efficient codes for computational fluid dynamics, elasticity, and other core problems of continuum mechanics. These methods hold the promise of allowing simulations of very high resolution with relative ease. This approach allows for the flexibility of using different numerical methods and difference models, each appropriate for the subregion at hand, to solve large problems in a cost-effective way. Containing contributions by international experts in this area, this book reports on the state-of-the-art in the growing field of domain decomposition.

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512

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821854917

ISBN 13

9780821854914

Scientific Computing with MATLAB

By: Alfio Quarteroni,Fausto Saleri

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Scientific Computing with MATLAB

By: Alfio Quarteroni,Fausto Saleri

This textbook is an introduction to Scientific Computing, in which several numerical methods for the computer solution of certain classes of mathematical problems are illustrated. The authors show how to compute the zeros or the integrals of continuous functions, solve linear systems, approximate functions by polynomials and construct accurate approximations for the solution of differential equations. To make the presentation concrete and appealing, the programming environment Matlab is adopted as a faithful companion.

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Page Count

270

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Springer Science & Business Media

Published Date

ISBN 10

3642593399

ISBN 13

9783642593390

Optimal Control of Partial Differential Equations

Analysis, Approximation, and Applications

By: Andrea Manzoni,Alfio Quarteroni,Sandro Salsa

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Optimal Control of Partial Differential Equations

Analysis, Approximation, and Applications

By: Andrea Manzoni,Alfio Quarteroni,Sandro Salsa

This is a book on optimal control problems (OCPs) for partial differential equations (PDEs) that evolved from a series of courses taught by the authors in the last few years at Politecnico di Milano, both at the undergraduate and graduate levels. The book covers the whole range spanning from the setup and the rigorous theoretical analysis of OCPs, the derivation of the system of optimality conditions, the proposition of suitable numerical methods, their formulation, their analysis, including their application to a broad set of problems of practical relevance. The first introductory chapter addresses a handful of representative OCPs and presents an overview of the associated mathematical issues. The rest of the book is organized into three parts: part I provides preliminary concepts of OCPs for algebraic and dynamical systems; part II addresses OCPs involving linear PDEs (mostly elliptic and parabolic type) and quadratic cost functions; part III deals with more general classes of OCPs that stand behind the advanced applications mentioned above. Starting from simple problems that allow a “hands-on” treatment, the reader is progressively led to a general framework suitable to face a broader class of problems. Moreover, the inclusion of many pseudocodes allows the reader to easily implement the algorithms illustrated throughout the text. The three parts of the book are suitable to readers with variable mathematical backgrounds, from advanced undergraduate to Ph.D. levels and beyond. We believe that applied mathematicians, computational scientists, and engineers may find this book useful for a constructive approach toward the solution of OCPs in the context of complex applications.

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507

Publisher

Springer Nature

Published Date

ISBN 10

3030772268

ISBN 13

9783030772260

Cardiovascular Mathematics

Modeling and simulation of the circulatory system

By: Luca Formaggia,Alfio Quarteroni,Allesandro Veneziani

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Cardiovascular Mathematics

Modeling and simulation of the circulatory system

By: Luca Formaggia,Alfio Quarteroni,Allesandro Veneziani

Mathematical models and numerical simulations can aid the understanding of physiological and pathological processes. This book offers a mathematically sound and up-to-date foundation to the training of researchers and serves as a useful reference for the development of mathematical models and numerical simulation codes.

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528

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Springer Science & Business Media

Published Date

ISBN 10

8847011523

ISBN 13

9788847011526

Spectral Methods in Fluid Dynamics

By: Claudio Canuto,M.Yousuff Hussaini,Alfio Quarteroni,Thomas A., Jr. Zang

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Spectral Methods in Fluid Dynamics

By: Claudio Canuto,M.Yousuff Hussaini,Alfio Quarteroni,Thomas A., Jr. Zang

This is a book about spectral methods for partial differential equations: when to use them, how to implement them, and what can be learned from their of spectral methods has evolved rigorous theory. The computational side vigorously since the early 1970s, especially in computationally intensive of the more spectacular applications are applications in fluid dynamics. Some of the power of these discussed here, first in general terms as examples of the methods have been methods and later in great detail after the specifics covered. This book pays special attention to those algorithmic details which are essential to successful implementation of spectral methods. The focus is on algorithms for fluid dynamical problems in transition, turbulence, and aero dynamics. This book does not address specific applications in meteorology, partly because of the lack of experience of the authors in this field and partly because of the coverage provided by Haltiner and Williams (1980). The success of spectral methods in practical computations has led to an increasing interest in their theoretical aspects, especially since the mid-1970s. Although the theory does not yet cover the complete spectrum of applications, the analytical techniques which have been developed in recent years have facilitated the examination of an increasing number of problems of practical interest. In this book we present a unified theory of the mathematical analysis of spectral methods and apply it to many of the algorithms in current use.

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Page Count

582

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Springer Science & Business Media

Published Date

ISBN 10

3642841082

ISBN 13

9783642841088

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