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ICES Faculty Books

Ranging from introductory textbooks to compendiums of research, this collection of books represent the prolific writing and knowledge base within the core faculty in ICES. These books are authored, co-authored, edited or co-edited by current ICES core faculty, and are currently in print and offered for sale as new volumes. Available on www.amazon.com, they serve to advance computational science and engineering in a broad range of applications.

Faculty Books
Cover Title Author Abstract
The Finite Element Method and Its Reliability The Finite Element Method and Its Reliability The finite element method is a numerical method widely used in engineering. Experience shows that

The finite element method is a numerical method widely used in engineering. Experience shows that unreliable computation can lead to very serious consequences. Hence reliability questions stand are at the forefront of engineering and theoretical interests. This book presents the mathematical theory of the finite element method and is the first to focus on the questions of how reliable computed results really are. It addresses among other topics the local behaviour, errors caused by pollution, superconvergence, and optimal meshes. Many computational examples illustrate the importance of the theoretical conclusions for practical computations. Graduate students, lecturers, and researchers in mathematics, engineering, and scientific computation will benefit from the clear structure of the book, and will find this a very useful reference.

Finite Elements Error Estimation Finite Elements: An Introduction to the Method and Error Estimation Most books on finite elements are devoted either to mathematical theory or to engineering applications--but

Most books on finite elements are devoted either to mathematical theory or to engineering applications--but not to both. Finite Elements: An Introduction to the Method and Error Estimation, by Ivo Babuska, John J. Whiteman, and Theofanis Strouboulis, seeks to bridge this gap by presenting the main theoretical ideas of the finite element method and the analysis of its errors in an accessible way. At the same time, it also presents computed numbers, which not only illustrate the theory but can only be analyzed using the theory. This approach, both dual and interacting between theory and computation makes this book unique.

Much research is currently being done into reliability in computational modelling, involving both validation of the mathematical models and verification of the numerical schemes. By treating finite element error analysis in this way this book is a significant contribution to the verification process of finite element modelling in the context of reliability.

Uncertain Input Data Problems and the Worst Scenario Method Uncertain Input Data Problems and the Worst Scenario Method, Volume 46 (North-Holland Series in Applied Mathematics and Mechanics) This book deals with the impact of uncertainty in input data on the outputs of

This book deals with the impact of uncertainty in input data on the outputs of mathematical models. Uncertain inputs as scalars, tensors, functions, or domain boundaries are considered. In practical terms, material parameters or constitutive laws, for instance, are uncertain, and quantities as local temperature, local mechanical stress, or local displacement are monitored. The goal of the worst scenario method is to extremize the quantity over the set of uncertain input data.

A general mathematical scheme of the worst scenario method, including approximation by finite element methods, is presented, and then applied to various state problems modeled by differential equations or variational inequalities: nonlinear heat flow, Timoshenko beam vibration and buckling, plate buckling, contact problems in elasticity and thermoelasticity with and without friction, and various models of plastic deformation, to list some of the topics. Dozens of examples, figures, and tables are included.

Although the book concentrates on the mathematical aspects of the subject, a substantial part is written in an accessible style and is devoted to various facets of uncertainty in modeling and to the state of the art techniques proposed to deal with uncertain input data.

A chapter on sensitivity analysis and on functional and convex analysis is included for the reader's convenience.

  • Rigorous theory is established for the treatment of uncertainty in modeling
  • Uncertainty is considered in complex models based on partial differential equations or variational inequalities
  • Applications to nonlinear and linear problems with uncertain data are presented in detail: quasilinear steady heat flow, buckling of beams and plates, vibration of beams, frictional contact of bodies, several models of plastic deformation, and more
  • Although emphasis is put on theoretical analysis and approximation techniques, numerical examples are also present
  • Main ideas and approaches used today to handle uncertainties in modeling are described in an accessible form
  • Fairly self-contained book
Finite Element Analysis Introduction to Finite Element Analysis: Formulation, Verification and Validation (Wiley Series in Computational Mechanics) Whenever numerical simulation is employed in connection with engineering decision-making, there is an implied expectation

Whenever numerical simulation is employed in connection with engineering decision-making, there is an implied expectation of reliability: one cannot base decisions on computed information without believing that information is reliable enough to support those decisions. Using mathematical models to show the reliability of computer-generated information is an essential part of any modelling effort.

Giving users of finite element analysis (FEA) software an introduction to verification and validation procedures, this book thoroughly covers the fundamentals of assuring reliability in numerical simulation. The renowned authors systematically guide readers through the basic theory and algorithmic structure of the finite element method, using helpful examples and exercises throughout.

Delivers the tools needed to have a working knowledge of the finite element method
Illustrates the concepts and procedures of verification and validation
Explains the process of conceptualization supported by virtual experimentation
Describes the convergence characteristics of the h-, p- and hp-methods
Covers the hierarchic view of mathematical models and finite element spaces
Uses examples and exercises which illustrate the techniques and procedures of quality assurance
Ideal for mechanical and structural engineering students, practicing engineers and applied mathematicians
Includes parameter-controlled examples of solved problems in a companion website (www.wiley.com/go/szabo)

Finite Element Analysis Finite Element Analysis (Wiley Series in Computational Mechanics) Covers the fundamentals of linear theory of finite elements, from both mathematical and physical points

Covers the fundamentals of linear theory of finite elements, from both mathematical and physical points of view. Major focus is on error estimation and adaptive methods used to increase the reliability of results. Incorporates recent advances not covered by other books.

Introduction to Implicit Surfaces Introduction to Implicit Surfaces (The Morgan Kaufmann Series in Computer Graphics) Implicit surfaces offer special effects animators, graphic designers, CAD engineers, graphics students, and hobbyists a

Implicit surfaces offer special effects animators, graphic designers, CAD engineers, graphics students, and hobbyists a new range of capabilities for the modeling of complex geometric objects. In contrast to traditional parametric surfaces, implicit surfaces can easily describe smooth, intricate, and articulatable shapes. These powerful yet easily understood surfaces are finding use in a growing number of graphics applications.

This comprehensive introduction develops the fundamental concepts and techniques of implicit surface modeling, rendering, and animating in terms accessible to anyone with a basic background in computer graphics.

  • provides a thorough overview of implicit surfaces with a focus on their applications in graphics
  • explains the best methods for designing, representing, and visualizing implicit surfaces
  • surveys the latest research

With contributions from seven graphics authorities, this innovative guide establishes implicit surfaces as a powerful and practical tool for animation and rendering.

Algebra, Arithmetic and Geometry with Applications Algebra, Arithmetic and Geometry with Applications: Papers from Shreeram S. Abhyankar's 70th Birthday Conference Proceedings of the Conference on Algebra and Algebraic Geometry with Applications, July 19 – 26,

Proceedings of the Conference on Algebra and Algebraic Geometry with Applications, July 19 – 26, 2000, at Purdue University to honor Professor Shreeram S. Abhyankar on the occasion of his seventieth birthday. Eighty-five of Professor Abhyankar's students, collaborators, and colleagues were invited participants. Sixty participants presented papers related to Professor Abhyankar's broad areas of mathematical interest. Sessions were held on algebraic geometry, singularities, group theory, Galois theory, combinatorics, Drinfield modules, affine geometry, and the Jacobian problem. This volume offers an outstanding collection of papers by expert authors.

Data Visualization Techniques Data Visualization Techniques (Trends in Software) Data visualization techniques are a means to manipulate sampled and computed data for comprehensive display.

Data visualization techniques are a means to manipulate sampled and computed data for comprehensive display. Visualized data can be static or in motion, to provide visual explanations of algorithms or general information. This book draws on examples from a broad selection of subject areas, such as atmospheric sciences or biology, which deal with diverse data analysis and visualization techniques. The various visualization methodologies covered in this book also include moving images as well as static. It is an important source of information for computer graphics software engineers, graduates and researchers who work in the field of visualization techniques. Unique features in this book include:

Details of data visualization techniques for scalar, vector and tensor field data and accompanying data structures

Explanation of how to express visual images in computational terms and turn these into display, with minimum delay

Methodology for "probing" a displayed visualization, in order to elicit more detail

Collection of information from several interrelated subject areas in one volume

Trends in Software - edited by Balachander Krishnamurthy of AT&T Research - is a sister publication of the journal Software: Practice and Experience

Large-Scale Inverse Problems Large-Scale Inverse Problems and Quantification of Uncertainty (Wiley Series in Computational Statistics) This book focuses on computational methods for large-scale statistical inverse problems and provides an introduction

This book focuses on computational methods for large-scale statistical inverse problems and provides an introduction to statistical Bayesian and frequentist methodologies. Recent research advances for approximation methods are discussed, along with Kalman filtering methods and optimization-based approaches to solving inverse problems. The aim is to cross-fertilize the perspectives of researchers in the areas of data assimilation, statistics, large-scale optimization, applied and computational mathematics, high performance computing, and cutting-edge applications.

The solution to large-scale inverse problems critically depends on methods to reduce computational cost. Recent research approaches tackle this challenge in a variety of different ways. Many of the computational frameworks highlighted in this book build upon state-of-the-art methods for simulation of the forward problem, such as, fast Partial Differential Equation (PDE) solvers, reduced-order models and emulators of the forward problem, stochastic spectral approximations, and ensemble-based approximations, as well as exploiting the machinery for large-scale deterministic optimization through adjoint and other sensitivity analysis methods.

Key Features:

  • Brings together the perspectives of researchers in areas of inverse problems and data assimilation.

  • Assesses the current state-of-the-art and identify needs and opportunities for future research.

  • Focuses on the computational methods used to analyze and simulate inverse problems.

  • Written by leading experts of inverse problems and uncertainty quantification.

Graduate students and researchers working in statistics, mathematics and engineering will benefit from this book.

Electronic Matericals Book Electronic Materials: A New Era in Materials Science (Springer Series in Solid-State Sciences) This is a personal, innovative, and exciting view of the current status of the field

This is a personal, innovative, and exciting view of the current status of the field of electronic materials. It provides a graduate-level introduction to new classes of electronic materials and indicates the most promising new avenues of theoretical and experimental investigation, capturing the challenge of the coming age of modern materials science. Researchers in the field of electronic materials will find here a general introduction to some of the most modern techniques of computer-assisted modeling and the most powerful experimental characterization tools. Nonspecialists will appreciate the broad survey and should find this book useful as a reference work.

CMOS Gate-Stack Scaling The Optical Properties of Materials: Volume 579 (MRS Proceedings) Computational approaches for predicting the optical properties of materials are at a stage of rapid

Computational approaches for predicting the optical properties of materials are at a stage of rapid development. Because a quantitative description of the optical properties of materials depends on both ground-state and excited-state properties, progress has been slower here than in other areas. However, advances in computational resources and algorithmic developments have dramatically altered this situation. This book brings together researchers from many different disciplines to meet and share ideas. A major focus is on techniques to predict and understand the optical and dielectric properties of materials. Experimental developments, as well as future research areas, are also incorporated. Topics include: bulk materials - ab initio theory; surfaces and polymers; clusters and nanocrystals; confined quantum systems/ quantum dots; nonlinear optical effects; semiconductor lasers, heterostructures and alloys; light-emitting materials; materials and materials characterization techniques; and optical engineering and lightwave propagation.

Electronic Structure and Optical Properties of Semiconductor Electronic Structure and Optical Properties of Semiconductors (Springer Series in Solid-State Sciences) The optical and electronic properties of semiconductors is a subject which today presents a major

The optical and electronic properties of semiconductors is a subject which today presents a major area in solid state sciences. This book is the first attempt to gather together information which is otherwise scattered throughout the scientific literature into a single comprehensive work. As such, the book will serve as an excellent introductory text for newcomers to the field as well as an indispensible reference volume for research workers.

Quantum Theory of Real Materials Quantum Theory of Real Materials (The Springer International Series in Engineering and Computer Science) Quantum Theory of Real Materials is a collection of articles by leading researchers in condensed

Quantum Theory of Real Materials is a collection of articles by leading researchers in condensed matter physics, highlighting recent advances in the use of quantum theory to explain and predict the properties of real materials. Quantum Theory of Real Materials covers the many exciting developments at the forefront of quantum theory of materials research. The volume is divided into six major sections covering electronic structure and quantum dynamics; semiconductors, insulators and metals; surfaces, interfaces and clusters; materials under pressure; superconductivity; and fullerenes, superhard materials and other novel materials. Quantum Theory of Real Materials is an excellent resource for researchers interested in learning about the most advanced discoveries in quantum theory of materials and applying that knowledge in the laboratory. Students will also find this volume to be a clear introduction and reference.

Materials Fundamentals of Gate Dielectrics Materials Fundamentals of Gate Dielectrics This book presents the fundamentals of novel gate dielectrics that are being introduced into semiconductor

This book presents the fundamentals of novel gate dielectrics that are being introduced into semiconductor manufacturing to ensure the continuous scaling of CMOS devices. As this is a rapidly evolving field of research we choose to focus on the materials that determine the performance of device applications. Most of these materials are transition metal oxides. Ironically, the d-orbitals responsible for the high dielectric constant cause severe integration difficulties, thus intrinsically limiting high-k dielectrics. Though new in the electronics industry many of these materials are well-known in the field of ceramics, and we describe this unique connection. The complexity of the structure-property relations in TM oxides requires the use of state-of-the-art first-principles calculations. Several chapters give a detailed description of the modern theory of polarization, and heterojunction band discontinuity within the framework of the density functional theory. Experimental methods include oxide melt solution calorimetry and differential scanning calorimetry, Raman scattering and other optical characterization techniques, transmission electron microscopy, and X-ray photoelectron spectroscopy.

Many of the problems encountered in the world of CMOS are also relevant for other semiconductors such as GaAs. A comprehensive review of recent developments in this field is thus also given.

CMOS Gate-Stack Scaling CMOS Gate-Stack Scaling - Materials, Interfaces and Reliability Implications: Volume 1155 (MRS Proceedings) To address the increasing demands of device scaling, new materials are being introduced into conventional

To address the increasing demands of device scaling, new materials are being introduced into conventional Si CMOS processing at an unprecedented rate. Presentations collected here focus on understanding, from a chemistry and materials perspective, the mechanism of interface formation and defects at interfaces, for both conventional Si and alternative channel (Ge or III-V) systems. Several papers address reliability concerns for high-k/metal gate (basic physical models, charge trapping, etc.), while others cover characterization of the thin films and interfaces which comprise the gate stack. Topics include: advanced Si-based gate stacks; and alternate channel materials.

Integration of Functional Oxides with Semiconductors Integration of Functional Oxides with Semiconductors This unique book describes the basic physical principles of the oxide/semiconductor epitaxy and offers a

This unique book describes the basic physical principles of the oxide/semiconductor epitaxy and offers a view of the current state of the field. It shows how this technology enables large-scale integration of oxide electronic and photonic devices, and describes possible hybrid semiconductor/oxide systems. The book incorporates both theoretical and experimental advances to explore the heteroepitaxy of tuned functional oxides and semiconductors to identify material, device and characterization challenges, and to present the incredible potential in the realization of multifunctional devices and monolithic integration of materials and devices.

This book also:

· Discusses why semiconductor substrates are an excellent integration platform for making hybrid logic/sensor devices

· Provides a brief introduction to the methods accessible to non-experts, before going into details of interest to the experts

· Includes a detailed glossary that explains the specialized terminology and provides insight into the terminology and how it’s used

From Springer Summary

Computing with Hp-Adaptive Finite Elements Computing with Hp-Adaptive Finite Elements, Vol. 1: One and Two Dimensional Elliptic and Maxwell Problems Offering the only existing finite element (FE) codes for Maxwell equations that support hp refinements

Offering the only existing finite element (FE) codes for Maxwell equations that support hp refinements on irregular meshes, Computing with hp-ADAPTIVE FINITE ELEMENTS: Volume 1. One- and Two-Dimensional Elliptic and Maxwell Problems presents 1D and 2D codes and automatic hp adaptivity. This self-contained source discusses the theory and implementation of hp-adaptive FE methods, focusing on projection-based interpolation and the corresponding hp-adaptive strategy.

The book is split into three parts, progressing from simple to more advanced problems. Part I examines the hp elements for the standard 1D model elliptic problem. The author develops the variational formulation and explains the construction of FE basis functions. The book then introduces the 1D code (1Dhp) and automatic hp adaptivity. This first part ends with a study of a 1D wave propagation problem. In Part II, the book proceeds to 2D elliptic problems, discussing two model problems that are slightly beyond standard-level examples: 3D axisymmetric antenna problem for Maxwell equations (example of a complex-valued, indefinite problem) and 2D elasticity (example of an elliptic system). The author concludes with a presentation on infinite elements - one of the possible tools to solve exterior boundary-value problems. Part III focuses on 2D time-harmonic Maxwell equations. The book explains the construction of the hp edge elements and the fundamental de Rham diagram for the whole family of hp discretizations. Next, it explores the differences between the elliptic and Maxwell versions of the 2D code, including automatic hp adaptivity. Finally, the book presents 2D exterior (radiation and scattering) problems and sample solutions using coupled hp finite/infinite elements.

In Computing with hp-ADAPTIVE FINITE ELEMENTS, the information provided, including many unpublished details, aids in solving elliptic and Maxwell problems.

Computing with Hp-Adaptive Finite Elements Vol 2 Computing with Hp-Adaptive Finite Elements, Vol. 2: Frontiers: Three Dimensional Elliptic and Maxwell Problems with Applications With a focus on 1D and 2D problems, the first volume of Computing with hp-ADAPTIVE

With a focus on 1D and 2D problems, the first volume of Computing with hp-ADAPTIVE FINITE ELEMENTS prepared readers for the concepts and logic governing 3D code and implementation. Taking the next step in hp technology, Volume II Frontiers: Three-Dimensional Elliptic and Maxwell Problems with Applications presents the theoretical foundations of the 3D hp algorithm and provides numerical results using the 3Dhp code developed by the authors and their colleagues.

The first part of the book focuses on fundamentals of the 3D theory of hp methods as well as issues that arise when the code is implemented. After a review of boundary-value problems, the book examines exact hp sequences, projection-based interpolation, and De Rham diagrams. It also presents the 3D version of the automatic hp-adaptivity package, a two-grid solver for highly anisotropic hp meshes and goal-oriented Krylov iterations, and a parallel implementation of the 3D code.

The second part explores several recent projects in which the 3Dhp code was used and illustrates how these applications have greatly driven the development of 3D hp technology. It encompasses acoustic and electromagnetic (EM) scattering problems, an analysis of complex structures with thin-walled components, and challenging simulations of logging tools. The book concludes with a look at the future of hp methods.

Spearheaded by a key developer of this technology with more than 20 years of research in the field, this self-contained, comprehensive resource will help readers overcome the difficulties in coding hp-adaptive elements.

Applied Functional Analysis Demkowicz Applied Functional Analysis (Computational Mechanics and Applied Mathematics) Comprehensive and easy-to-understand, this innovative textbook progresses from the essentials of preparatory mathematics to sophiisticated

Comprehensive and easy-to-understand, this innovative textbook progresses from the essentials of preparatory mathematics to sophiisticated functional analysis. This text has few mathematical prerequisites and provides the fundamental concepts and therorems essential to mathematical analysis and modeling

Recent Developments In Theoretical Studies Of Proteins Recent Developments In Theoretical Studies Of Proteins (Advanced Series in Physical Chemistry) Experts provide a unique and broad perspective of the theoretical tools available today to analyze

Experts provide a unique and broad perspective of the theoretical tools available today to analyze protein structure and function. Topics at the frontier of computational biophysics, such as dynamics and thermodynamics of proteins, reaction path studies, optimization techniques, analytical theories of protein folding, sequence alignment algorithms and electrostatics of proteins are discussed in a pedagogical and complete way. Those entering the field will find the book to be a useful introduction. It will also serve as a complementary text to existing ones that focus on just one of the above subjects.

New Algorithms for Macromolecular Simulation New Algorithms for Macromolecular Simulation (Lecture Notes in Computational Science and Engineering) Molecular simulation is a widely used tool in biology, chemistry, physics and engineering. This book

Molecular simulation is a widely used tool in biology, chemistry, physics and engineering. This book contains a collection of articles by leading researchers who are developing new methods for molecular modelling and simulation. Topics addressed here include: multiscale formulations for biomolecular modelling, such as quantum-classical methods and advanced solvation techniques; protein folding methods and schemes for sampling complex landscapes; membrane simulations; free energy calculation; and techniques for improving ergodicity. The book is meant to be useful for practitioners in the simulation community and for those new to molecular simulation who require a broad introduction to the state of the art.

Numerical Analysis of Multiscale Computations Numerical Analysis of Multiscale Computations: Proceedings of a Winter Workshop at the Banff International Research Station 2009 (Lecture Notes in Computational Science and Engineering) This book is a snapshot of current research in multiscale modeling, computations and applications. It

This book is a snapshot of current research in multiscale modeling, computations and applications. It covers fundamental mathematical theory, numerical algorithms as well as practical computational advice for analysing single and multiphysics models containing a variety of scales in time and space. Complex fluids, porous media flow and oscillatory dynamical systems are treated in some extra depth, as well as tools like analytical and numerical homogenization, and fast multipole method.

Large-Scale PDE-Constrained Optimization Large-Scale PDE-Constrained Optimization Optimal design, optimal control, and parameter estimation of systems governed by partial differential equations (PDEs)

Optimal design, optimal control, and parameter estimation of systems governed by partial differential equations (PDEs) give rise to a class of problems known as PDE-constrained optimization. The size and complexity of the discretized PDEs often pose significant challenges for contemporary optimization methods. With the maturing of technology for PDE simulation, interest has now increased in PDE-based optimization. The chapters in this volume collectively assess the state of the art in PDE-constrained optimization, identify challenges to optimization presented by modern highly parallel PDE simulation codes, and discuss promising algorithmic and software approaches for addressing them. These contributions represent current research of two strong scientific computing communities, in optimization and PDE simulation. This volume merges perspectives in these two different areas and identifies interesting open questions for further research.

Real-Time PDE-Constrained Optimization Real-Time PDE-Constrained Optimization (Computational Science and Engineering) *"A timely contribution to a field of growing importance. This carefully edited book presents a

"A timely contribution to a field of growing importance. This carefully edited book presents a rich collection of chapters ranging from mathematical methodology to emerging applications. I recommend it to students as a rigorous and comprehensive presentation of simulation-based optimization and to researchers as an overview of recent advances and challenges in the field."
--Jorge Nocedal, Professor, Northwestern University.

Many engineering and scientific problems in design, control, and parameter estimation can be formulated as optimization problems that are governed by partial differential equations (PDEs). The complexities of the PDEs and the requirement for rapid solution pose significant difficulties. A particularly challenging class of PDE-constrained optimization problems is characterized by the need for real-time solution, i.e., in time scales that are sufficiently rapid to support simulation-based decision making.

Real-Time PDE-Constrained Optimization, the first book devoted to real-time optimization for systems governed by PDEs, focuses on new formulations, methods, and algorithms needed to facilitate real-time, PDE-constrained optimization. In addition to presenting state-of-the-art algorithms and formulations, the text illustrates these algorithms with a diverse set of applications that includes problems in the areas of aerodynamics, biology, fluid dynamics, medicine, chemical processes, homeland security, and structural dynamics.

Despite difficulties, there is a pressing need to capitalize on continuing advances in computing power to develop optimization methods that will replace simple rule-based decision making with optimized decisions based on complex PDE simulations.

Audience

The book is aimed at readers who have expertise in simulation and are interested in incorporating optimization into their simulations, who have expertise in numerical optimization and are interested in adapting optimization methods.

Large-Scale Inverse Problems Large-Scale Inverse Problems and Quantification of Uncertainty (Wiley Series in Computational Statistics) This book focuses on computational methods for large-scale statistical inverse problems and provides an introduction

This book focuses on computational methods for large-scale statistical inverse problems and provides an introduction to statistical Bayesian and frequentist methodologies. Recent research advances for approximation methods are discussed, along with Kalman filtering methods and optimization-based approaches to solving inverse problems. The aim is to cross-fertilize the perspectives of researchers in the areas of data assimilation, statistics, large-scale optimization, applied and computational mathematics, high performance computing, and cutting-edge applications.

The solution to large-scale inverse problems critically depends on methods to reduce computational cost. Recent research approaches tackle this challenge in a variety of different ways. Many of the computational frameworks highlighted in this book build upon state-of-the-art methods for simulation of the forward problem, such as, fast Partial Differential Equation (PDE) solvers, reduced-order models and emulators of the forward problem, stochastic spectral approximations, and ensemble-based approximations, as well as exploiting the machinery for large-scale deterministic optimization through adjoint and other sensitivity analysis methods.

Key Features:

  • Brings together the perspectives of researchers in areas of inverse problems and data assimilation.

  • Assesses the current state-of-the-art and identify needs and opportunities for future research.

  • Focuses on the computational methods used to analyze and simulate inverse problems.

  • Written by leading experts of inverse problems and uncertainty quantification.

Graduate students and researchers working in statistics, mathematics and engineering will benefit from this book.

Isogeometric Analysis Isogeometric Analysis: Toward Integration of CAD and FEA “The authors are the originators of isogeometric analysis, are excellent scientists and good educators. It

“The authors are the originators of isogeometric analysis, are excellent scientists and good educators. It is very original. There is no other book on this topic.”
—René de Borst, Eindhoven University of Technology

Written by leading experts in the field and featuring fully integrated colour throughout, Isogeometric Analysis provides a groundbreaking solution for the integration of CAD and FEA technologies. Tom Hughes and his researchers, Austin Cottrell and Yuri Bazilevs, present their pioneering isogeometric approach, which aims to integrate the two techniques of CAD and FEA using precise NURBS geometry in the FEA application. This technology offers the potential to revolutionise automobile, ship and airplane design and analysis by allowing models to be designed, tested and adjusted in one integrative stage.

Providing a systematic approach to the topic, the authors begin with a tutorial introducing the foundations of Isogeometric Analysis, before advancing to a comprehensive coverage of the most recent developments in the technique. The authors offer a clear explanation as to how to add isogeometric capabilities to existing finite element computer programs, demonstrating how to implement and use the technology. Detailed programming examples and datasets are included to impart a thorough knowledge and understanding of the material.

Provides examples of different applications, showing the reader how to implement isogeometric models
Addresses readers on both sides of the CAD/FEA divide
Describes Non-Uniform Rational B-Splines (NURBS) basis functions

Computational Inelasticity Computational Inelasticity (Interdisciplinary Applied Mathematics) (v. 7) A description of the theoretical foundations of inelasticity, its numerical formulation and implementation, constituting a

A description of the theoretical foundations of inelasticity, its numerical formulation and implementation, constituting a representative sample of state-of-the-art methodology currently used in inelastic calculations. Among the numerous topics covered are small deformation plasticity and viscoplasticity, convex optimisation theory, integration algorithms for the constitutive equation of plasticity and viscoplasticity, the variational setting of boundary value problems and discretization by finite element methods. Also addressed are the generalisation of the theory to non-smooth yield surface, mathematical numerical analysis issues of general return mapping algorithms, the generalisation to finite-strain inelasticity theory, objective integration algorithms for rate constitutive equations, the theory of hyperelastic-based plasticity models and small and large deformation viscoelasticity. Of great interest to researchers and graduate students in various branches of engineering, especially civil, aeronautical and mechanical, and applied mathematics.

Mathematical Foundations of Elasticity Mathematical Foundations of Elasticity (Dover Civil and Mechanical Engineering) This graduate-level study approaches mathematical foundations of three-dimensional elasticity using modern differential geometry and functional

This graduate-level study approaches mathematical foundations of three-dimensional elasticity using modern differential geometry and functional analysis. It is directed to mathematicians, engineers and physicists who wish to see this classical subject in a modern setting with examples of newer mathematical contributions. Relevant problems appear throughout the text. 1983 edition.

The Finite Element Method The Finite Element Method: Linear Static and Dynamic Finite Element Analysis (Dover Civil and Mechanical Engineering) Directed toward students without in-depth mathematical training, this text cultivates comprehensive skills in linear static

Directed toward students without in-depth mathematical training, this text cultivates comprehensive skills in linear static and dynamic finite element methodology. Included are a comprehensive presentation and analysis of algorithms of time-dependent phenomena plus beam, plate, and shell theories derived directly from three-dimensional elasticity theory. Solution guide available upon request.

Chemical Dynamics at Low Temperatures Chemical Dynamics at Low Temperatures (Advances in Chemical Physics) The first unified treatment of experimental and theoretical advances in low-temperature chemistry Chemical Dynamics at

The first unified treatment of experimental and theoretical advances in low-temperature chemistry Chemical Dynamics at Low Temperatures is a landmark publication. For the first time, the cumulative results of twenty years of experimental and theoretical research into low-temperature chemistry have been collected and presented in a unified treatment. The result is a text/reference that both offers an overview of the subject and contains sufficient detail to guide practicing researchers toward fertile ground for future research. Topics covered include:

  • Developmental history
  • Formulation of general problems and the main approximations used to solve them
  • Specific features of tunneling chemical dynamics
  • One-dimensional tunneling in the path integral formalism
  • Special problems of two- and multidimensional tunneling
  • An extended presentation of pertinent experimental results
Single Molecule Science: Physical Principles and Models Single Molecule Science: Physical Principles and Models The observation and manipulation of individual molecules is one of the most exciting developments in

The observation and manipulation of individual molecules is one of the most exciting developments in modern molecular science. Single Molecule Science: Physical Principles and Models provides an introduction to the mathematical tools and physical theories needed to understand, explain, and model single-molecule observations.

This book explains the physical principles underlying the major classes of single-molecule experiments such as fluorescence measurements, force-probe spectroscopy, and nanopore experiments. It provides the framework needed to understand single-molecule phenomena by introducing all the relevant mathematical and physical concepts, and then discussing various approaches to the problem of interpreting single-molecule data.

The essential concepts used throughout this book are explained in the appendices and the text does not assume any background beyond undergraduate chemistry, physics, and calculus. Every effort has been made to keep the presentation self-contained and derive results starting from a limited set of fundamentals, such as several simple models of molecular dynamics and the laws of probability. The result is a book that develops essential concepts in a simple yet rigorous way and in a manner that is accessible to a broad audience.

Contact Problems in Elasticity : A Study of Variational Ineq Contact Problems in Elasticity : A Study of Variational Inequalities and Finite Element Methods (SIAM Studies in Applied and Numerical Methematics) (Siam Studies in Applied Mathematics) The contact of one deformable body with another lies at the heart of almost every

The contact of one deformable body with another lies at the heart of almost every mechanical structure. Here, in a comprehensive treatment, two of the field's leading researchers present a systematic approach to contact problems. Using variational formulations, Kikuchi and Oden derive a multitude of new results, both for classical problems and for nonlinear problems involving large deflections and buckling of thin plates with unilateral supports, dry friction with nonclassical laws, large elastic and elastoplastic deformations with frictional contact, dynamic contacts with dynamic frictional effects, and rolling contacts. This method exposes properties of solutions obscured by classical methods, and it provides a basis for the development of powerful numerical schemes.

Finite Elements Intro Finite Elements: An Introduction. Volume I This book provides an introduction to the finite element method presented as a general approach

This book provides an introduction to the finite element method presented as a general approach to the approximation of solutions to boundary- and initial -value problems involving linear partial differential equations. The discussion beginning with the notion of weak forms of two-point boundary -value problems, trial and test function spaces, with an introduction to elementary properties of H1 and L2 spaces, the direct stiffness method of matrix assembly, finite element families, and extensions to two-dimensional elliptic problems. A chapter on the development of computer programs to implement the method , together with a code for one-dimensional problems is provided. A brief account of applications to time -dependent parabolic problems is included. Extensive examples and exercises are presented.

A Posterori Error Estimation in Finite Element Analysis A Posterori Error Estimation in Finite Element Analysis An up-to-date, one-stop reference-complete with applications This volume presents the most up-to-date information available on

An up-to-date, one-stop reference-complete with applications

This volume presents the most up-to-date information available on a posteriori error estimation for finite element approximation in mechanics and mathematics. It emphasizes methods for elliptic boundary value problems and includes applications to incompressible flow and nonlinear problems.

Recent years have seen an explosion in the study of a posteriori error estimators due to their remarkable influence on improving both accuracy and reliability in scientific computing. In an effort to provide an accessible source, the authors have sought to present key ideas and common principles on a sound mathematical footing.

Topics covered in this timely reference include:

  • Implicit and explicit a posteriori error estimators
  • Recovery-based error estimators
  • Estimators, indicators, and hierarchic bases
  • The equilibrated residual method
  • Methodology for the comparison of estimators
  • Estimation of errors in quantities of interest

A Posteriori Error Estimation in Finite Element Analysis is a lucid and convenient resource for researchers in almost any field of finite element methods, and for applied mathematicians and engineers who have an interest in error estimation and/or finite elements.

An Introduction to the Mathematical Theory of Finite Element An Introduction to the Mathematical Theory of Finite Elements This introduction to the basic mathematical theory of the finite element method is geared toward

This introduction to the basic mathematical theory of the finite element method is geared toward readers with limited mathematical backgrounds. Its coherent demonstrations explain the use of these techniques in developing the theory of finite elements, with detailed proofs of the major theorems and numerous examples. 1976 edition.

Finite Elements of Nonlinear Continua Finite Elements of Nonlinear Continua This text extends applications of the finite element method from linear problems in elastic structures

This text extends applications of the finite element method from linear problems in elastic structures to a broad class of practical, nonlinear problems in continuum mechanics. Its general and unified treatment of theory and applications emphasizes nonlinear problems in finite elasticity, viscoelasticity, heat conduction, and thermoviscoelasticity. 1972 edition.

Applied Functional Analysis Applied Functional Analysis, Second Edition Through numerous illustrative examples and comments, Applied Functional Analysis, Second Edition demonstrates the rigor of

Through numerous illustrative examples and comments, Applied Functional Analysis, Second Edition demonstrates the rigor of logic and systematic, mathematical thinking. It presents the mathematical foundations that lead to classical results in functional analysis. More specifically, the text prepares students to learn the variational theory of partial differential equations, distributions and Sobolev spaces, and numerical analysis with an emphasis on finite element methods.

While retaining the structure of its best-selling predecessor, this second edition includes revisions of many original examples, along with new examples that often reflect the authors’ own vast research experiences and perspectives. This edition also provides many more exercises as well as a solutions manual for qualifying instructors. Each chapter begins with an extensive introduction and concludes with a summary and historical comments that frequently refer to other sources.

An Introduction to Mathematical Modeling An Introduction to Mathematical Modeling: A Course in Mechanics A modern approach to mathematical modeling, featuring unique applications from the field of mechanics An

A modern approach to mathematical modeling, featuring unique applications from the field of mechanics

An Introduction to Mathematical Modeling: A Course in Mechanics is designed to survey the mathematical models that form the foundations of modern science and incorporates examples that illustrate how the most successful models arise from basic principles in modern and classical mathematical physics. Written by a world authority on mathematical theory and computational mechanics, the book presents an account of continuum mechanics, electromagnetic field theory, quantum mechanics, and statistical mechanics for readers with varied backgrounds in engineering, computer science, mathematics, and physics.

The author streamlines a comprehensive understanding of the topic in three clearly organized sections:

  1. Nonlinear Continuum Mechanics introduces kinematics as well as force and stress in deformable bodies; mass and momentum; balance of linear and angular momentum; conservation of energy; and constitutive equations

  2. Electromagnetic Field Theory and Quantum Mechanics contains a brief account of electromagnetic wave theory and Maxwell's equations as well as an introductory account of quantum mechanics with related topics including ab initio methods and Spin and Pauli's principles

  3. Statistical Mechanics presents an introduction to statistical mechanics of systems in thermodynamic equilibrium as well as continuum mechanics, quantum mechanics, and molecular dynamics

Each part of the book concludes with exercise sets that allow readers to test their understanding of the presented material. Key theorems and fundamental equations are highlighted throughout, and an extensive bibliography outlines resources for further study.

Extensively class-tested to ensure an accessible presentation, An Introduction to Mathematical Modeling is an excellent book for courses on introductory mathematical modeling and statistical mechanics.

Applied Functional Analysis Demkowicz Applied Functional Analysis (Computational Mechanics and Applied Mathematics) Comprehensive and easy-to-understand, this innovative textbook progresses from the essentials of preparatory mathematics to sophiisticated

Comprehensive and easy-to-understand, this innovative textbook progresses from the essentials of preparatory mathematics to sophiisticated functional analysis. This text has few mathematical prerequisites and provides the fundamental concepts and therorems essential to mathematical analysis and modeling

Numerical Recipes 3rd Edition: The Art of Scientific Computi Numerical Recipes 3rd Edition: The Art of Scientific Computing Co-authored by four leading scientists from academia and industry, Numerical Recipes Third Edition starts with

Co-authored by four leading scientists from academia and industry, Numerical Recipes Third Edition starts with basic mathematics and computer science and proceeds to complete, working routines. Widely recognized as the most comprehensive, accessible and practical basis for scientific computing, this new edition incorporates more than 400 Numerical Recipes routines, many of them new or upgraded. The executable C++ code, now printed in color for easy reading, adopts an object-oriented style particularly suited to scientific applications. The whole book is presented in the informal, easy-to-read style that made earlier editions so popular.

Please visit www.nr.com or www.cambridge.org/us/numericalrecipes for more details. More information concerning licenses is available at: www.nr.com/licenses

New key features:

  • 2 new chapters, 25 new sections, 25% longer than Second Edition
  • Thorough upgrades throughout the text
  • Over 100 completely new routines and upgrades
Problem Book in Relativity and Gravitation Problem Book in Relativity and Gravitation Important and useful to every student of relativity, this book is a unique collection of

Important and useful to every student of relativity, this book is a unique collection of some 475 problems--with solutions--in the fields of special and general relativity, gravitation, relativistic astrophysics, and cosmology. The problems are expressed in broad physical terms to enhance their pertinence to readers with diverse backgrounds.

In their solutions, the authors have attempted to convey a mode of approach to these kinds of problems, revealing procedures that can reduce the labor of calculations while avoiding the pitfall of too much or too powerful formalism. Although well suited for individual use, the volume may also be used with one of the modem textbooks in general relativity.

Numerical Analysis of Multiscale Computations Numerical Analysis of Multiscale Computations: Proceedings of a Winter Workshop at the Banff International Research Station 2009 (Lecture Notes in Computational Science and Engineering) This book is a snapshot of current research in multiscale modeling, computations and applications. It

This book is a snapshot of current research in multiscale modeling, computations and applications. It covers fundamental mathematical theory, numerical algorithms as well as practical computational advice for analysing single and multiphysics models containing a variety of scales in time and space. Complex fluids, porous media flow and oscillatory dynamical systems are treated in some extra depth, as well as tools like analytical and numerical homogenization, and fast multipole method.

Using PLAPACK: Parallel Linear Algebra Package Using PLAPACK: Parallel Linear Algebra Package PLAPACK is a library infrastructure for the parallel implementation of linear algebra algorithms and applications

PLAPACK is a library infrastructure for the parallel implementation of linear algebra algorithms and applications on distributed memory supercomputers such as the Intel Paragon, IBM SP2, Cray T3D/T3E, SGI PowerChallenge, and Convex Exemplar. This infrastructure allows library developers, scientists, and engineers to exploit a natural approach to encoding so-called blocked algorithms, which achieve high performance by operating on submatrices and subvectors. This feature, as well as the use of an alternative, more application-centric approach to data distribution, sets PLAPACK apart from other parallel linear algebra libraries, allowing for strong performance and significanltly less programming by the user.This book is a comprehensive introduction to all the components of a high-performance parallel linear algebra library, as well as a guide to the PLAPACK infrastructure.Scientific and Engineering Computation series

The Science of Programming Matrix Computations The Science of Programming Matrix Computations The Formal Linear Algebra Methods Environment (FLAME) encompasses a methodology for deriving an algorithm for

The Formal Linear Algebra Methods Environment (FLAME) encompasses a methodology for deriving an algorithm for a dense linear algebra operation hand-in-hand with its proof of correctness as well as an approach to represent (and code) the resulting algorithm. This books reviews the foundations of FLAME: the derivation methodology, the notation, and the high-level Application Programming Interfaces, which are applied to basic linear algebra operations as well as operations for the solution of linear systems. While the text targets the novice, its emphasis on high performance algorithms should also be of interest to the expert.