Wiley in Computational Mechanics

A hands-on introduction to computational statistics from a Bayesian point of view. Providing a solid grounding in statistics while uniquely covering the topics from a Bayesian perspective, “Understanding Computational Bayesian Statistics” successfully guides readers through this new, cutting-edge approach. With its hands-on treatment of the topic, the book shows how samples can be drawn from the posterior distribution when the formula giving its shape is all that is known, and how Bayesian inferences can be based on these samples from the posterior. These ideas are illustrated on common statistical models, including the multiple linear regression model, the hierarchical mean model, the logistic regression model, and the proportional hazards model. The book begins with an outline of the similarities and differences between Bayesian and the likelihood approaches to statistics. Subsequent chapters present key techniques for using computer software to draw Monte Carlo samples from the incompletely known posterior distribution and performing the Bayesian inference calculated from these samples. Topics of coverage include: • Direct ways to draw a random sample from the posterior by reshaping a random sample drawn from an easily sampled starting distribution • The distributions from the one-dimensional exponential family • Markov chains and their long-run behavior • The Metropolis-Hastings algorithm • Gibbs sampling algorithm and methods for speeding up convergence • Markov chain Monte Carlo sampling Using numerous graphs and diagrams, the author emphasizes a step-by-step approach to computational Bayesian statistics. At each step, important aspects of application are detailed, such as how to choose a prior for logistic regression model, the Poisson regression model, and the proportional hazards model. A related Web site houses R functions and Minitab macros for Bayesian analysis and Monte Carlo simulations, and detailed appendices in the book guide readers through the use of these software packages. “Understanding Computational Bayesian Statistics” is an excellent book for courses on computational statistics at the upper-level undergraduate and graduate levels. It is also a valuable reference for researchers and practitioners who use computer programs to conduct statistical analyses of data and solve problems in their everyday work.

Explore the multidisciplinary nature of complex networks through machine learning techniques. “Statistical and Machine Learning Approaches for Network Analysis” provides an accessible framework for structurally analyzing graphs by bringing together known and novel approaches on graph classes and graph measures for classification. By providing different approaches based on experimental data, the book uniquely sets itself apart from the current literature by exploring the application of machine learning techniques to various types of complex networks. Comprised of chapters written by internationally renowned researchers in the field of interdisciplinary network theory, the book presents current and classical methods to analyze networks statistically. Methods from machine learning, data mining, and information theory are strongly emphasized throughout. Real data sets are used to showcase the discussed methods and topics, which include: • A survey of computational approaches to reconstruct and partition biological networks • An introduction to complex networks-measures, statistical properties, and models • Modeling for evolving biological networks • The structure of an evolving random bipartite graph • Density-based enumeration in structured data • Hyponym extraction employing a weighted graph kernel “Statistical and Machine Learning Approaches for Network Analysis” is an excellent supplemental text for graduate-level, cross-disciplinary courses in applied discrete mathematics, bioinformatics, pattern recognition, and computer science. The book is also a valuable reference for researchers and practitioners in the fields of applied discrete mathematics, machine learning, data mining, and biostatistics.

Markov Chain Monte Carlo (MCMC) methods are now an indispensable tool in scientific computing. This book discusses recent developments of MCMC methods with an emphasis on those making use of past sample information during simulations. The application examples are drawn from diverse fields such as bioinformatics, machine learning, social science, combinatorial optimization, and computational physics. Key Features: • Expanded coverage of the stochastic approximation Monte Carlo and dynamic weighting algorithms that are essentially immune to local trap problems. • A detailed discussion of the Monte Carlo Metropolis-Hastings algorithm that can be used for sampling from distributions with intractable normalizing constants. • Up-to-date accounts of recent developments of the Gibbs sampler. • Comprehensive overviews of the population-based MCMC algorithms and the MCMC algorithms with adaptive proposals. This book can be used as a textbook or a reference book for a one-semester graduate course in statistics, computational biology, engineering, and computer sciences. Applied or theoretical researchers will also find this book beneficial.

Comprehensive introduction to finite elastoplasticity, addressing various analytical and numerical analyses & including state-of-the-art theories Introduction to Finite Elastoplasticity presents introductory explanations that can be readily understood by readers with only a basic knowledge of elastoplasticity, showing physical backgrounds of concepts in detail and derivation processes of almost all equations. The authors address various analytical and numerical finite strain analyses, including new theories developed in recent years, and explain fundamentals including the push-forward and pull-back operations and the Lie derivatives of tensors. As a foundation to finite strain theory, the authors begin by addressing the advanced mathematical and physical properties of continuum mechanics. They progress to explain a finite elastoplastic constitutive model, discuss numerical issues on stress computation, implement the numerical algorithms for stress computation into large-deformation finite element analysis and illustrate several numerical examples of boundary-value problems. Programs for the stress computation of finite elastoplastic models explained in this book are included in an appendix, and the code can be downloaded from an accompanying website.

Mechanics of Discontinua is the first book to comprehensively tackle both the theory of this rapidly developing topic and the applications that span a broad field of scientific and engineering disciplines, from traditional engineering to physics of particulates, nano-technology and micro-flows. Authored by a leading researcher who has been at the cutting edge of discontinua simulation developments over the last 15 years, the book is organized into four parts: introductory knowledge, solvers, methods and applications. In the first chapter a short revision of Continuum Mechanics together with tensorial calculus is introduced. Also, a short introduction to the finite element method is given. The second part of the book introduces key aspects of the subject. These include a diverse field of applications, together with fundamental theoretical and algorithmic aspects common to all methods of Mechanics of Discontinua. The third part of the book proceeds with the most important computational and simulation methods including Discrete Element Methods, the Combined Finite-Discrete Element Method, Molecular Dynamics Methods, Fracture and Fragmentation solvers and Fluid Coupling. After these the reader is introduced to applications stretching from traditional engineering and industry (such as mining, oil industry, powders) to nanotechnology, medical and science.

Computational Fluid-Structure Interaction: Methods and Applications takes the reader from the fundamentals of computational fluid and solid mechanics to the state-of-the-art in computational FSI methods, special FSI techniques, and solution of real-world problems. Leading experts in the field present the material using a unique approach that combines advanced methods, special techniques, and challenging applications. This book begins with the differential equations governing the fluid and solid mechanics, coupling conditions at the fluid–solid interface, and the basics of the finite element method. It continues with the ALE and space–time FSI methods, spatial discretization and time integration strategies for the coupled FSI equations, solution techniques for the fully-discretized coupled equations, and advanced FSI and space–time methods. It ends with special FSI techniques targeting cardiovascular FSI, parachute FSI, and wind-turbine aerodynamics and FSI. Key features: • First book to address the state-of-the-art in computational FSI • Combines the fundamentals of computational fluid and solid mechanics, the state-of-the-art in FSI methods, and special FSI techniques targeting challenging classes of real-world problems • Covers modern computational mechanics techniques, including stabilized, variational multiscale, and space–time methods, isogeometric analysis, and advanced FSI coupling methods • Is in full color, with diagrams illustrating the fundamental concepts and advanced methods and with insightful visualization illustrating the complexities of the problems that can be solved with the FSI methods covered in the book. • Authors are award winning, leading global experts in computational FSI, who are known for solving some of the most challenging FSI problems Computational Fluid-Structure Interaction: Methods and Applications is a comprehensive reference for researchers and practicing engineers who would like to advance their existing knowledge on these subjects. It is also an ideal text for graduate and senior-level undergraduate courses in computational fluid mechanics and computational FSI.

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: • 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 • 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 • 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 at the upper-undergraduate and graduate levels. The book also serves as a valuable reference for professionals working in the areas of modeling and simulation, physics, and computational engineering.

Introduces the theory and applications of the extended finite element method (XFEM) in the linear and nonlinear problems of continua, structures and geomechanics. • Explores the concept of partition of unity, various enrichment functions, and fundamentals of XFEM formulation. • Covers numerous applications of XFEM including fracture mechanics, large deformation, plasticity, multiphase flow, hydraulic fracturing and contact problems • Accompanied by a website hosting source code and examples

Built upon the two original books by Mike Crisfield and their own lecture notes, renowned scientist René de Borst and his team offer a thoroughly updated yet condensed edition that retains and builds upon the excellent reputation and appeal amongst students and engineers alike for which Crisfield's first edition is acclaimed. Together with numerous additions and updates, the new authors have retained the core content of the original publication, while bringing an improved focus on new developments and ideas. This edition offers the latest insights in non-linear finite element technology, including non-linear solution strategies, computational plasticity, damage mechanics, time-dependent effects, hyperelasticity and large-strain elasto-plasticity. The authors' integrated and consistent style and unrivalled engineering approach assures this book's unique position within the computational mechanics literature. Key features: • Combines the two previous volumes into one heavily revised text with obsolete material removed, an improved layout and updated references and notations • Extensive new material on more recent developments in computational mechanics • Easily readable, engineering oriented, with no more details in the main text than necessary to understand the concepts. • Pseudo-code throughout makes the link between theory and algorithms, and the actual implementation. “Non-linear Finite Element Analysis of Solids and Structures”, 2nd Edition is an essential reference for practising engineers and researchers that can also be used as a text for undergraduate and graduate students within computational mechanics.

An updated and comprehensive review of the theoretical foundation of the finite element method. The revised and updated second edition of “Finite Element Analysis: Method, Verification, and Validation” offers a comprehensive review of the theoretical foundations of the finite element method and highlights the fundamentals of solution verification, validation, and uncertainty quantification. Written by noted experts on the topic, the book covers the theoretical fundamentals as well as the algorithmic structure of the finite element method. The text contains numerous examples and helpful exercises that clearly illustrate the techniques and procedures needed for accurate estimation of the quantities of interest. In addition, the authors describe the technical requirements for the formulation and application of design rules. Designed as an accessible resource, the book has a companion website that contains a solutions manual, PowerPoint slides for instructors, and a link to finite element software. This important text: • Offers a comprehensive review of the theoretical foundations of the finite element method • Puts the focus on the fundamentals of solution verification, validation, and uncertainty quantification • Presents the techniques and procedures of quality assurance in numerical solutions of mathematical problems • Contains numerous examples and exercises Written for students in mechanical and civil engineering, analysts seeking professional certification, and applied mathematicians, “Finite Element Analysis: Method, Verification, and Validation”, Second Edition includes the tools, concepts, techniques, and procedures that help with an understanding of finite element analysis.

Covers everything readers need to know about clustering methodology for symbolic data-including new methods and headings-while providing a focus on multi-valued list data, interval data and histogram data This book presents all of the latest developments in the field of clustering methodology for symbolic data-paying special attention to the classification methodology for multi-valued list, interval-valued and histogram-valued data methodology, along with numerous worked examples. The book also offers an expansive discussion of data management techniques showing how to manage the large complex dataset into more manageable datasets ready for analyses. Filled with examples, tables, figures, and case studies, “Clustering Methodology for Symbolic Data” begins by offering chapters on data management, distance measures, general clustering techniques, partitioning, divisive clustering, and agglomerative and pyramid clustering. • Provides new classification methodologies for histogram valued data reaching across many fields in data science • Demonstrates how to manage a large complex dataset into manageable datasets ready for analysis • Features very large contemporary datasets such as multi-valued list data, interval-valued data, and histogram-valued data • Considers classification models by dynamical clustering • Features a supporting website hosting relevant data sets “Clustering Methodology for Symbolic Data” will appeal to practitioners of symbolic data analysis, such as statisticians and economists within the public sectors. It will also be of interest to postgraduate students of, and researchers within, web mining, text mining and bioengineering.