Numerical analysis Books

Book SynopsisPacked with illustrations, amusing facts, puzzles, brainteasers and anecdotes - an enthralling and thought-provoking numerical voyage through the history of mathematics. A must-have for trivia addicts, maths-lovers and even numberphobes.Trade Review'This book is a complete joy. It made me smile. A lot' Carol Vorderman'There's more to maths than just numbers - but, as this entertaining and engaging book amply demonstrates, the depth and variety of mathematical ideas that appear when you start with 1, 2, 3 and keep going is astonishing. Once you start reading 'Number Freak' it's just like the number system itself - impossible to stop' Ian Stewart, author of Professor Stewart's Cabinet of Mathematical Curiosities'A great maths book for geeks and non-geeks alike' Johnny Ball'A fun book... definitely challenging' Vanity Fair'A fascinating parade of diverse numerical characters... An entertaining mix of numerical fun and theory' Booklist'All sorts of fascinating mathematical minutiae' Time Out (Chicago)

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Book SynopsisLearning Data Science is the first book to cover foundational skills in both programming and statistics that encompass the entire data science lifecycle: the process of collecting, wrangling, analyzing, and drawing conclusions from data.

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Book SynopsisHaskell is a purely functional language that allows programmers to rapidly develop clear, concise, and correct software. The language has grown in popularity in recent years, both in teaching and in industry. This book is based on the author''s experience of teaching Haskell for more than twenty years. All concepts are explained from first principles and no programming experience is required, making this book accessible to a broad spectrum of readers. While Part I focuses on basic concepts, Part II introduces the reader to more advanced topics. This new edition has been extensively updated and expanded to include recent and more advanced features of Haskell, new examples and exercises, selected solutions, and freely downloadable lecture slides and example code. The presentation is clean and simple, while also being fully compliant with the latest version of the language, including recent changes concerning applicative, monadic, foldable, and traversable types.Trade Review'The skills you acquire by studying this book will make you a much better programmer no matter what language you use to actually program in.' Erik Meijer, Facebook, from the ForewordReview of previous edition: 'The best introduction to Haskell available. There are many paths towards becoming comfortable and competent with the language but I think studying this book is the quickest path. I urge readers of this magazine to recommend Programming in Haskell to anyone who has been thinking about learning the language.' Duncan Coutts, The Monad.ReaderReview of previous edition: 'Where this book excels is in the order and style of its exposition … With its ripe selection of examples and its careful clarity of exposition, the book is a welcome addition to the introductory functional programming literature.' Journal of Functional ProgrammingTable of ContentsForeword; Preface; Part I. Basic Concepts: 1. Introduction; 2. First steps; 3. Types and classes; 4. Defining functions; 5. List comprehensions; 6. Recursive functions; 7. Higher-order functions; 8. Declaring types and classes; 9. The countdown problem; Part II. Going Further: 10. Interactive programming; 11. Unbeatable tic-tac-toe; 12. Monads and more; 13. Monadic parsing; 14. Foldables and friends; 15. Lazy evaluation; 16. Reasoning about programs; 17. Calculating compilers; Appendix A. Selected solutions; Appendix B. Standard prelude; Bibliography; Index.

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Book SynopsisThis outrageous graphic novel investigates key concepts in mathematics by taking readers on a voyage of forensic discovery, exploring some of the most fundamental ideas in mathematics within a thrilling murder mystery.Trade Review"Prime Suspects will appeal to a variety of readers in a variety of venues . . . . For the mathematician who eats, sleeps, and drinks numbers, start on page one and just enjoy the story . . . the book is fun, and interesting, and a challenge on many levels."---Judith Reveal, New York Journal of Books"Prime Suspects blends together the worlds of mathematics and forensic science to give readers both an interesting mystery and an education in numbers."---Anelise Farris, Rogues Portal"A total one-off."---Matthew Reisz, Times Educational Supplement"This is really a great book with so many references to mathematical ideas, that you can read and reread and find every time new details hidden in the graphics."---Adhemar Bultheel, European Mathematical Society"What a spectacular book! I am rather blown away by it."---Jonathan Shock, MathemAfrica"Granville and Granville have performed something of a feat. They've written a graphic detective novel that is both interesting to read and yet simultaneously teaches its readers some deep mathematics . . . . It's very difficult to write a book on an advanced topic in mathematics that's accessible to math students and enthusiasts yet touches on contemporary research that is of interest to a broad swath of practicing mathematicians. Prime Suspects is such a book. And it's entertaining to boot. I recommend it in the strongest terms."---Benjamin Linowitz, MAA Reviews"Bringing in elements from film noir, TV police shows and famous movies, coupled with some amazing art work, subtlemathematical humour and corny science jokes, and what you have is a one-of-a-kind creation – indeed, Prime Suspects has it all from minus to plus infinity."---David Appell, Physics World"Renowned number-theorist Andrew Granville here explores the graphic novel as a format to popularize mathematical discoveries. This absolutely brilliantly illustrated book arose from an earlier play and an accompanying commissioned musical piece. The mathematics too is astonishing—but explained understandably." * Mathematics Magazine *"If you are a mathematician, I definitely recommend reading (and listening to) Prime Suspects. If you are not a mathematician, you might miss a number of references, and some passages might be too mysterious or technical, but still it makes for interesting reading; it might be good for you, too."---Marco Abate, The Mathematical Intelligencer"The artwork and presentation are both well up to the standard of a mainstream graphic novel."---Andrew Ruddle, Mathematics Today"Prime Suspects is a work of art which anyone with a passion for maths will appreciate and enjoy."---Lennie Wells, Mathematical Gazette"I definitely recommend."---Marco Abate, Mathematical Intelligencer

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Book SynopsisProvides avenues for applying functional analysis to the practical study of natural sciences as well as mathematics. Contains worked problems on Hilbert space theory and on Banach spaces and emphasizes concepts, principles, methods and major applications of functional analysis.Table of ContentsMetric Spaces.Normed Spaces;Banach Spaces.Inner Product Spaces;Hilbert Spaces.Fundamental Theorems for Normed and Banach Spaces.Further Applications: Banach Fixed Point Theorem.Spectral Theory of Linear Operators in Normed Spaces.Compact Linear Operators on Normed Spaces and Their Spectrum.Spectral Theory of Bounded Self-Adjoint Linear Operators.Unbounded Linear Operators in Hilbert Space.Unbounded Linear Operators in Quantum Mechanics.Appendices.References.Index.

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Book SynopsisThis book investigates in detail the emerging deep learning (DL) technique in computational physics, assessing its promising potential to substitute conventional numerical solvers for calculating the fields in real-time. After good training, the proposed architecture can resolve both the forward computing and the inverse retrieve problems.Pursuing a holistic perspective, the book includes the following areas. The first chapter discusses the basic DL frameworks. Then, the steady heat conduction problem is solved by the classical U-net in Chapter 2, involving both the passive and active cases. Afterwards, the sophisticated heat flux on a curved surface is reconstructed by the presented Conv-LSTM, exhibiting high accuracy and efficiency. Additionally, a physics-informed DL structure along with a nonlinear mapping module are employed to obtain the space/temperature/time-related thermal conductivity via the transient temperature in Chapter 4. Finally, in Chapter 5, a series of thTable of Contents1. Deep Learning Framework and Paradigm in Computational Physics 2. Application of U-net in 3D Steady Heat Conduction Solver 3. Inversion of complex surface heat flux based on ConvLSTM 4. Time-domain electromagnetic inverse scattering based on deep learning 5. Reconstruction of thermophysical parameters based on deep learning 6. Advanced Deep Learning Techniques in Computational Physics

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Book SynopsisWhat sets Numerical Methods and Analysis with Mathematical Modelling apart are the modelling aspects utilizing numerical analysis (methods) to obtain solutions. The authors cover first the basic numerical analysis methods with simple examples to illustrate the techniques and discuss possible errors. The modelling prospective reveals the practical relevance of the numerical methods in context to real-world problems.At the core of this text are the real-world modelling projects. Chapters are introduced and techniques are discussed with common examples. A modelling scenario is introduced that will be solved with these techniques later in the chapter. Often, the modelling problems require more than one previously covered technique presented in the book.Fundamental exercises to practice the techniques are included. Multiple modelling scenarios per numerical methods illustrate the applications of the techniques introduced. Each chapter has several modelling

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Book SynopsisEste livro é uma introdução ao Cálculo Científico. O seu objectivo consiste em apresentar vários métodos numéricos para resolver no computador certos problemas matemáticos que não podem ser tratados de maneira mais simples. São abordadas questões clássicas como o cálculo de zeros ou de integrais de funções contínuas, a resolução de sistemas lineares, a aproximação de funções por polinómios e a construção de aproximações precisas de soluções de equações diferenciais. Todos os algoritmos são apresentados nas linguagens de programação MATLAB e Octave, cujos comandos e instruções principais se introduzem de forma gradual, visando em particular a sua compatibilidade nas duas linguagens. O leitor pode assim verificar experimentalmente propriedades teóricas como a estabilidade, a precisão e a complexidade. O livro inclui ainda a resolução de problemas através de numerosos exercícios e exemplos, frequentemente ligados a aplicações concretas. No fim de cada capítulo encontra-se uma secção específica que apresenta assuntos não abordados e as referências bibliográficas que permitem ao leitor aprofundar os conhecimentos adquiridos.Table of ContentsO que não se pode ignorar.- Equações não lineares.- Aproximação de funções e de dados.- Derivação e integração numéricas.- Sistemas lineares.- Valores próprios e vectores próprios.- Equações diferenciais ordinárias.- Métodos numéricos para problemas de valores iniciais e na fronteira.- Soluções dos exercícios.

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Book SynopsisThis book’s aim is to study the mathematical and computational models to analyze the progress, prognosis, prevention, and panacea of breast cancer. The book discusses application of Markov chains and transient mappings, Charlie–Simpson numerical algorithm, models represented by nonlinear reaction–diffusion-type partial differential equations, and related techniques. The book also attempts to design mathematical model of targeted strategic treatments by using Skilled Killer Drugs (SKD1 and SKD2) to suggest the improvisation of future cancer treatments. Both graduate students and researchers of computational biology and oncologists will benefit by studying this book. Researchers of cancer studies and biological sciences will also find this work helpful.Table of ContentsIntroduction.- Statistics: The Backgrounds & The Basis.- Attacker & Defender Model: The Dynamics of the Immune System.- Mathematical Modeling of Metastatic Cancer.- Mathematical/Computational Modeling of Advanced Immunotherapy.- Mathematical Modeling & Computational Studies On The War Against Breast Cancer.- Gene Therapy.- The Smartest Fighters.- Nutritional Therapy.- The Fateful Code & The Future Course.- Conclusion.

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Book SynopsisThis book helps the reader make use of the mathematical models of biological phenomena starting from the basics of programming and computer simulation. Computer simulations based on a mathematical model enable us to find a novel biological mechanism and predict an unknown biological phenomenon. Mathematical biology could further expand the progress of modern life sciences. Although many biologists are interested in mathematical biology, they do not have experience in mathematics and computer science. An educational course that combines biology, mathematics, and computer science is very rare to date. Published books for mathematical biology usually explain the theories of established mathematical models, but they do not provide a practical explanation for how to solve the differential equations included in the models, or to establish such a model that fits with a phenomenon of interest. MATLAB is an ideal programming platform for the beginners of computer science. This book starts from the very basics about how to write a programming code for MATLAB (or Octave), explains how to solve ordinary and partial differential equations, and how to apply mathematical models to various biological phenomena such as diabetes, infectious diseases, and heartbeats. Some of them are original models, newly developed for this book. Because MATLAB codes are embedded and explained throughout the book, it will be easy to catch up with the text. In the final chapter, the book focuses on the mathematical model of the proneural wave, a phenomenon that guarantees the sequential differentiation of neurons in the brain. This model was published as a paper from the author’s lab (Sato et al., PNAS 113, E5153, 2016), and was intensively explained in the book chapter “Notch Signaling in Embryology and Cancer”, published by Springer in 2020. This book provides the reader who has a biological background with invaluable opportunities to learn and practice mathematical biology.Table of Contents1. Preparation.- 2. Introduction to MATLAB programming .- 3. Simulating time variations in life phenomena.- 4. Simulating temporal and spatial changes in biological phenomena.

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Book SynopsisOptimization is an important tool used in decision science and for the analysis of physical systems used in engineering. It begins with very simple ideas progressing through more complicated concepts, concentrating on methods for both unconstrained and constrained optimization.Trade ReviewMMOR Mathematical Methods of Operations Research, 2001: "The books looks very suitable to be used in an graduate-level course in optimization for students in mathematics, operations research, engineering, and others. Moreover, it seems to be very helpful to do some self-studies in optimization, to complete own knowledge and can be a source of new ideas... I recommend this excellent book to everyone who is interested in optimization problems."Table of ContentsPreface.-Preface to the Second Edition.-Introduction.-Fundamentals of Unconstrained Optimization.-Line Search Methods.-Trust-Region Methods.-Conjugate Gradient Methods.-Quasi-Newton Methods.-Large-Scale Unconstrained Optimization.-Calculating Derivatives.-Derivative-Free Optimization.-Least-Squares Problems.-Nonlinear Equations.-Theory of Constrained Optimization.-Linear Programming: The Simplex Method.-Linear Programming: Interior-Point Methods.-Fundamentals of Algorithms for Nonlinear Constrained Optimization.-Quadratic Programming.-Penalty and Augmented Lagrangian Methods.-Sequential Quadratic Programming.-Interior-Point Methods for Nonlinear Programming.-Background Material.- Regularization Procedure.

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Book SynopsisThis book provides an extensive introduction to the numerical solution of a large class of integral equations. The initial chapters provide a general framework for the numerical analysis of Fredholm integral equations of the second kind, covering degenerate kernel, projection and Nystrom methods. Additional discussions of multivariable integral equations and iteration methods update the reader on the present state of the art in this area. The final chapters focus on the numerical solution of boundary integral equation (BIE) reformulations of Laplace's equation, in both two and three dimensions. Two chapters are devoted to planar BIE problems, which include both existing methods and remaining questions. Practical problems for BIE such as the set up and solution of the discretised BIE are also discussed. Each chapter concludes with a discussion of the literature and a large bibliography serves as an extended resource for students and researchers needing more information on solving particTrade Review' This outstanding monograph ... represents a major milestone in the list of books on the numerical solution of integral equations ... deserves to be on the shelf of any researcher and graduate student interested in the numerical solution of elliptic boundary-value problems.' H. Brunner, Mathematics Abstracts 'It will become the standard reference in the area.' Zietschrift fur Angwandte Mathematik und PhysikTable of ContentsPreface; 1. A brief discussion of integral equations; 2. Degenerate kernel methods; 3. Projection methods; 4. The Nystrom method; 5. Solving multivariable integral equations; 6. Iteration methods; 7. Boundary integral equations on a smooth planar boundary; 8. Boundary integral equations on a piecewise smooth planar boundary; 9. Boundary integral equations in three dimensions; Discussion of the literature; Appendix; Bibliography; Index.

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Book SynopsisThe book combines topics in mathematics (geometry and topology), computer science (algorithms), and engineering (mesh generation). The motivation for these topics is the difficulty, both conceptually and in the technical execution, of combining elements of combinatorial and of numerical algorithms. Mesh generation is a topic where a meaningful combination of these different approaches to problem solving is inevitable. The book develops methods from both areas that are amenable to combination, and explains breakthrough solutions to meshing that fit into this category. This book emphasizes topics that are elementary, attractive, useful, interesting, and lend themselves to teaching, making it an ideal graduate text for courses on mesh generation.Trade Review'… a very readable exposition …'. Monatshefte für Mathematik'… well organised … We recommend the book to graduate students and researchers in computational geometry.' János Kincses, Acta Sci. Math.Table of Contents1. Delaunay triangulations; 2. Triangle meshes; 3. Combinatorial topology; 4. Surface simplification; 5. Delaunay tetrahedrizations; 6. Tetrahedron meshes; 7. Open problems.

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Book SynopsisWritten in easy to understand language, this self-explanatory guide introduces the fundamentals of finite element methods and its application to differential equations. Beginning with a brief introduction to Sobolev spaces and elliptic scalar problems, the text progresses through an explanation of finite element spaces and estimates for the interpolation error. The concepts of finite element methods for parabolic scalar parabolic problems, object-oriented finite element algorithms, efficient implementation techniques, and high dimensional parabolic problems are presented in different chapters. Recent advances in finite element methods, including non-conforming finite elements for boundary value problems of higher order and approaches for solving differential equations in high dimensional domains are explained for the benefit of the reader. Numerous solved examples and mathematical theorems are interspersed throughout the text for enhanced learning.Trade Review'The book is written in a very traditional and straightforward style of theory and proof. The organization of the material makes it accessible for the reader to gain a foundational understanding of the topics … This book provides a readable, concise introduction to finite elements. Summing Up: Recommended.' S. L. Sullivan, CHOICETable of ContentsPreface; 1. Sobolev spaces; 1.1. Banach and Hilbert spaces; 1.2. Weak derivatives; 1.3. Sobolev spaces; 2. Elliptic scalar problems; 2.1. A general elliptic problem of second order; 2.2. Weak solution; 2.3. Standard Galerkin method; 2.4. Abstract error estimate; 3. Finite element spaces; 3.1. Simplices and barycentric coordinates; 3.2. Simplicial finite elements and local spaces; 3.3. Construction of finite elements spaces; 3.4. The concept of mapped finite elements: affine mappings; 3.5. Finite elements on rectangular and brick meshes; 3.6. Mapped finite elements: general bijective mappings; 3.7. Mapped Qk finite elements; 3.8. Isoparametric finite elements; 3.9. Further examples of finite elements in C0 and C1; 4. Interpolation and discretization error; 4.1. Transformation formulas; 4.2. Affine equivalent finite elements; 4.3. Canonical interpolation; 4.4. Local and global interpolation error; 4.5. Improved L2 error estimates by duality; 4.6. Interpolation of less smooth functions; 5. Biharmonic equation; 5.1. Deflection of a thin clamped plate; 5.2. Weak formulation of the biharmonic equation; 5.3. Conforming finite element methods; 5.4. Nonconforming finite element methods; 6. Parabolic problems; 6.1. Conservation of energy; 6.2. A general parabolic problem of initial boundary value problems; 6.3. Weak formulation of initial boundary value problems; 6.4. Semidiscretization by finite elements; 6.5. Time discretization; 6.6. Finite elements for high-dimensional parabolic problems; 7. Systems in solid mechanics; 7.1. Linear elasticity; 7.2. Mindlin–Reissner plate; 8. Systems in fluid mechanics; 8.1. Conservation of mass and momentum; 8.2. Weak formulation of the Stokes problem; 8.3. Conforming discretizations of the Stokes problem; 8.4. Nonconforming discretizations of the Stokes problem; 8.5. The nonconforming Crouzeix–Raviart element; 8.6. Further inf–sup stable finite element pairs; 8.7. Equal order stabilized finite elements; 8.8. Navier–Stokes problem with mixed boundary conditions; 8.9. Time discretization and linearization of the Navier–Stokes problem; 9. Implementation of the finite element method; 9.1. Mesh handling and data structure; 9.2. Numerical integration; 9.3. Sparse matrix storage; 9.4. Assembling of system matrices and load vectors; 9.5. Inclusion of boundary conditions; 9.6. Solution of the algebraic systems; 9.7. Object-oriented C++ programming; Bibliography; Index.

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Book SynopsisThis is a practical guide to P-splines, a simple, flexible and powerful tool for smoothing. P-splines combine regression on B-splines with simple, discrete, roughness penalties. They were introduced by the authors in 1996 and have been used in many diverse applications. The regression basis makes it straightforward to handle non-normal data, like in generalized linear models. The authors demonstrate optimal smoothing, using mixed model technology and Bayesian estimation, in addition to classical tools like cross-validation and AIC, covering theory and applications with code in R. Going far beyond simple smoothing, they also show how to use P-splines for regression on signals, varying-coefficient models, quantile and expectile smoothing, and composite links for grouped data. Penalties are the crucial elements of P-splines; with proper modifications they can handle periodic and circular data as well as shape constraints. Combining penalties with tensor products of B-splines extends theseTrade Review'The title says it all. This is a practical book which shows how P-splines are used in an astonishingly wide range of settings. If you use P-splines already the book is indispensable; if you don't, then reading it will convince you it's time to start. Every example comes with an R-program available on the book's web-site, an important feature for the experienced user and novice alike.' Iain Currie, Heriot-Watt University'This book is an enlightening and at the same time extremely enjoyable read. It will serve the applied statistician who is looking for practical solutions but also the connoisseur in search of elegant concepts. The accompanying website offers reproducible code and invites to promptly enter the fascinating universe of P-splines.' Jutta Gampe, Max Planck Institute for Demographic Research'Everything you always wanted to know about P-splines, from the inventors themselves. Paul H.C. Eilers and Brian D. Marx make a compelling case for their claim that P-splines are the best practical smoother out there, providing intuition, methodology, applications, and R code that clearly demonstrate the power, flexibility, and wide applicability of this approach to smoothing.' Jeffrey Simonoff, New York University'This is the book that everyone working on smoothing models should keep handy. At last we have a manuscript that shows the real power of P-splines, their versatility, and the different perspectives you can take to use them. Chapters 1 to 3 will certainly appeal to those who want to start working in this field, and to researchers that need to deepen their knowledge of this technique. Scientists and practitioners from other areas will find chapters 4 to 8 very useful for the wide range of examples and applications. The companion package and the fact that all results (even figures) are reproducible is a real bonus. Thank you Paul and Brian for being truthful to your motto: 'show, don't tell'.' Maria Durbán, University Carlos III de MadridTable of Contents1. Introduction; 2. Bases, penalties, and likelihoods; 3. Optimal smoothing in action; 4. Multidimensional smoothing; 5. Smoothing of scale and shape; 6. Complex counts and composite links; 7. Signal regression; 8. Special subjects; A. P-splines for the impatient; B. P-splines and competitors; C. Computational details; D. Array algorithms; E. Mixed model equations; F. Standard errors in detail; G. The website.

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Book SynopsisDynamical systems are a principal tool in the modeling, prediction, and control of a wide range of complex phenomena. As the need for improved accuracy leads to larger and more complex dynamical systems, direct simulation often becomes the only available strategy for accurate prediction or control, inevitably creating a considerable burden on computational resources. This is the main context where one considers model reduction, seeking to replace large systems of coupled differential and algebraic equations that constitute high fidelity system models with substantially fewer equations that are crafted to control the loss of fidelity that order reduction may induce in the system response. Interpolatory methods are among the most widely used model reduction techniques, and Interpolatory Methods for Model Reduction is the first comprehensive analysis of this approach available in a single, extensive resource. It introduces state-of-the-art methods reflecting significant developments over the past two decades, covering both classical projection frameworks for model reduction and data-driven, nonintrusive frameworks.This textbook is appropriate for a wide audience of engineers and other scientists working in the general areas of large-scale dynamical systems and data-driven modeling of dynamics.

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Book SynopsisThis volume encompasses prototypical, innovative and emerging examples and benchmarks of Differential-Algebraic Equations (DAEs) and their applications, such as electrical networks, chemical reactors, multibody systems, and multiphysics models, to name but a few. Each article begins with an exposition of modelling, explaining whether the model is prototypical and for which applications it is used. This is followed by a mathematical analysis, and if appropriate, a discussion of the numerical aspects including simulation. Additionally, benchmark examples are included throughout the text.Mathematicians, engineers, and other scientists, working in both academia and industry either on differential-algebraic equations and systems or on problems where the tools and insight provided by differential-algebraic equations could be useful, would find this book resourceful. Trade Review“The book can be of special interest to mathematicians, STEM students, and engineers working in multidisciplinary industry settings where the insight provided by differential-algebraic equations can be determinant in decision making.” (Andrzej Sokolowski, MAA Reviews, August 11, 2019)Table of ContentsGeneral Nonlinear Differential Algebraic Equations and Tracking Problems: A Robotics Example.- DAE Aspects in Vehicle Dynamics and Mobile Robotics.- Open-loop Control of Underactuated Mechanical Systems Using Servo-constraints: Analysis and Some Examples.- Systems of Differential Algebraic Equations in Computational Electromagnetics.- Gas Network Benchmark Models.- Topological Index Analysis Applied to Coupled Flow Networks.- Nonsmooth DAEs with Applications in Modeling Phase Changes.- Continuous, Semi-Discrete, and Fully Discretized Navier-Stokes Equations.

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Book SynopsisThis book presents the state-of-the-art in supercomputer simulation. It includes the latest findings from leading researchers using systems from the High Performance Computing Center Stuttgart (HLRS) in 2019. The reports cover all fields of computational science and engineering ranging from CFD to computational physics and from chemistry to computer science with a special emphasis on industrially relevant applications. Presenting findings of one of Europe’s leading systems, this volume covers a wide variety of applications that deliver a high level of sustained performance.The book covers the main methods in high-performance computing. Its outstanding results in achieving the best performance for production codes are of particular interest for both scientists and engineers. The book comes with a wealth of color illustrations and tables of results.Table of ContentsPart 1, Physics.- Part 2, Solid State Physics.- Part 3, Chemistry.- Part 4, Material Science.- Part 5, Reactive Flows.- Part 6, Computational Fluid Dynamics.- Part 7, Transport and Climate.- Part 8, Computer Science.- Part 9, Miscellaneous Topics.

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Book SynopsisThis book presents the state of the art in High Performance Computing on modern supercomputer architectures. It addresses trends in hardware and software development in general. The contributions cover a broad range of topics, from performance evaluations in context with power efficiency to Computational Fluid Dynamics and High Performance Data Analytics. In addition, they explore new topics like the use of High Performance Computers in the field of Artificial Intelligence and Machine Learning. All contributions are based on selected papers presented at the 30th Workshop on Sustained Simulation Performance (WSSP) held at the High Performance Computing Center, University of Stuttgart, Germany in October 2019 and on the papers for the planned Workshop on Sustained Simulation Performance in March 2020, which could not take place due to the Covid-19 pandemic.Table of ContentsPerformance and Power.- Numeric and Optimization.- Data Handling and New Concepts.- Trends in HPC and AI.

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Book SynopsisThis graduate-level textbook aims to give a unified presentation and solution of several commonly used techniques for multivariate data analysis (MDA). Unlike similar texts, it treats the MDA problems as optimization problems on matrix manifolds defined by the MDA model parameters, allowing them to be solved using (free) optimization software Manopt. The book includes numerous in-text examples as well as Manopt codes and software guides, which can be applied directly or used as templates for solving similar and new problems. The first two chapters provide an overview and essential background for studying MDA, giving basic information and notations. Next, it considers several sets of matrices routinely used in MDA as parameter spaces, along with their basic topological properties. A brief introduction to matrix (Riemannian) manifolds and optimization methods on them with Manopt complete the MDA prerequisite. The remaining chapters study individual MDA techniques in depth. The number of exercises complement the main text with additional information and occasionally involve open and/or challenging research questions. Suitable fields include computational statistics, data analysis, data mining and data science, as well as theoretical computer science, machine learning and optimization. It is assumed that the readers have some familiarity with MDA and some experience with matrix analysis, computing, and optimization. Table of ContentsIntroduction.- Matrix analysis and differentiation.- Matrix manifolds in MDA.- Principal component analysis (PCA).- Factor analysis (FA).- Procrustes analysis (PA).- Linear discriminant analysis (LDA).- Canonical correlation analysis (CCA).- Common principal components (CPC).- Metric multidimensional scaling (MDS) and related methods.- Data analysis on simplexes.

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Book SynopsisThis book presents the notes from the seminar on wave phenomena given in 2019 at the Mathematical Research Center in Oberwolfach.The research on wave-type problems is a fascinating and emerging field in mathematical research with many challenging applications in sciences and engineering. Profound investigations on waves require a strong interaction of several mathematical disciplines including functional analysis, partial differential equations, mathematical modeling, mathematical physics, numerical analysis, and scientific computing.The goal of this book is to present a comprehensive introduction to the research on wave phenomena. Starting with basic models for acoustic, elastic, and electro-magnetic waves, topics such as the existence of solutions for linear and some nonlinear material laws, efficient discretizations and solution methods in space and time, and the application to inverse parameter identification problems are covered. The aim of this book is to intertwine analysis and numerical mathematics for wave-type problems promoting thus cooperative research projects in this field.Table of ContentsSpace-time approximations for linear acoustic, elastic, and electro-magnetic wave equations.- Local wellposedness and long-time behavior of quasilinear Maxwell equations.- Error analysis of second-order time integration methods for discontinuous Galerkin discretizations of Friedrichs’ systems.- An abstract framework for inverse wave problems with applications.

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Book SynopsisThis book constitutes the proceedings of the 4th Iberoamerican Conference and third Indo-American Conference on Knowledge Graphs and Semantic Web, KGSWC 2022, which took place in Madrid, Spain, in November 2022.The 22 full and 3 short research papers presented in this volume were carefully reviewed and selected from 63 submissions. The papers cover topics related to software and its engineering, software creation and management, Emerging technologies, Analysis and design of emerging devices and systems, Emerging tools and methodologies and others.Table of ContentsDBkWik++ - Multi Source Matching of Knowledge Graphs.- A Survey on Knowledge Graph-based Methods for Automated Driving.- Physicians’ Brain Digital Twin: Holistic Clinical & Biomedical Knowledge Graphs for Patient Safety and Value-Based Care to Prevent The Post-pandemic Healthcare Ecosystem Crisis.- Combining Ontology and Natural Language Processing methods for Prevention of Falls from Height.- Learning to Automatically Generating Genre-Specific Song Lyrics: A Comparative Study.- DLIME-Graphs: A DLIME Extension based on Triple Embedding for Graphs.- Edge-labelled graphs and property graphs - to the user, more similar than different.- Knowledge Graph supported machine parameterization for the injection moulding industry.- IPR: Integrative Policy Recommendation Framework based on Hybrid Semantics.- Convolutional Neural Networks applied to emotion analysis in texts: Experimentation from the Mexican context.- Proficient Annotation Recommendation in a Biomedical Content Authoring Environment.- DKMI: Diversification of Web Image Search using Knowledge Centric Machine Intelligence.- Does Wikidata Support Analogical Reasoning?.- Flexible Queries over Knowledge Graphs.- Knowledge Graphs for Community Detection in Textual Data.- Framework for Author Name Disambiguation in Scientific Papers Using an Ontological Approach and Deep Learning.- On contrasting and completing YAGO with GPT language models: an experiment for person-related attributes.- Easy and complex: new perspectives for metadata modeling using RDF-star and Named Graphs.- Multi-Aspect Sentiment Analysis using Domain Ontologies.- Popularity Driven Data Integration.- Methodology for Creating a Community Corpus using a Wikibase Knowledge Graph.- Understanding Human Activity Patterns in Smart Homes with Process Mining.- String Matching based Framework for Online Hindi Question Answering System.- Towards an ontological approach to business continuity assessment.- From Ontology to Knowledge Graph Trend: Ontology As Foundation Layer For Knowledge Graph.

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Book SynopsisThis book constitutes the refereed proceedings of the 5th International Conference on Optimization and Learning, OLA 2022, which took place in Syracuse, Sicilia, Italy, in July 2022. The 19 full papers presented in this volume were carefully reviewed and selected from 52 submissions. The papers are organized in the following topical sections: Optimization and Learning; Novel Optimization Techniques; Logistics; and Applications.Table of ContentsOptimization and Learning.- Evolutionary-Based Co-Optimization of DNN and Hardware Configurations on Edge GPU.- Maximum Information Coverage and Monitoring Path Planning With Unmanned Surface Vehicles Using Deep Reinforcement Learning.- Tuning ForestDisc hyperparameters: A sensitivity analysis.- Multi-objective hyperparameter optimization with performance uncertainty.- Novel Optimization Techniques.- A new algorithm for bi-objective problems based on gradient information.- Adaptive Continuous Multi-Objective Optimization using Cooperative Agents.- Integer Linear Programming reformulations for the linear ordering problem.- SHAMan: a versatile auto-tuning framework for costly and noisy HPC systems.- Cooperation-based search of global optima.- Date-driven Simulation-Optimization (DSO): An Efficient Approach to Optimize Simulation Models with Databases.- Logistics.- Sweep Algorithms for the Vehicle Routing Problem with TimeWindows.- Improving the accuracy of vehicle routing problem approximation using the formula for the average distance between a point and a rectangular area.- Optimal Delivery Area Assignment for the Capital Vehicle Routing Problem Based on a Maximum Likelihood Approach.- Neural Order-First Split-Second Algorithm for the Capacitated Vehicle Routing Problem.- Applications.- GRASP-based hybrid search to solve the multi-objective requirements selection problem.- Comparing Parallel Surrogate-based and Surrogate-free Multi-Objective Optimization of COVID-19 vaccines allocation.- Decentralizing and Optimizing Nation-Wide Employee Allocation while Simultaneously Maximizing Employee Satisfaction.- Categorical-Continuous Bayesian optimization applied to chemical reactions.- Assessing Similarity-Based Grammar-Guided Genetic Programming Approaches for Program Synthesis.

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Book SynopsisThis book constitutes the conference proceedings of the 48th International Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2023, held in Nový Smokovec, Slovakia, during January 15–18, 2023.The 22 full papers presented together with 2 best papers and 2 best students papers in this book were carefully reviewed and selected from 43 submissions.This workshop focuses on graphs problems and optimization; graph drawing and visualization; NP-hardness and fixed parameter tractability; communication and temporal graphs; complexity and learning; and robots and strings. Table of ContentsThe Complexity of Finding Tangles.- A spectral algorithm for finding maximum cliques in dense random intersection graphs.- Solving Cut-Problems in Quadratic Time for Graphs With Bounded Treewidth.- More Effort Towards Multiagent Knapsack.- Dominance Drawings for DAGs with Bounded Modular Width.- Morphing Planar Graph Drawings Through 3D.- Visualizing Multispecies Coalescent Trees: Drawing Gene Trees Inside Species Trees.- Parameterized Approaches to Orthogonal Compaction.- Hardness of bounding influence via graph modification.- On the Parameterized Complexity of $s$-club Cluster Deletion Problems.- Balanced Substructures in Bicolored Graphs.- On the Complexity of Scheduling Problems With a Fixed Number of Parallel Identical Machines.- On the 2-Layer Window Width Minimization Problem.- Sequentially Swapping Tokens: Further on Graph Classes.- On the Preservation of Properties when Changing Communication Models.- Introduction to Routing Problems with Mandatory Transitions .- Multi-Parameter Analysis of Finding Minors and Subgraphs in Edge-Periodic Temporal Graphs.- Lower Bounds for Monotone $q$-Multilinear Boolean Circuits.- A faster algorithm for determining the linear feasibility of systems of BTVPI constraints.- Quantum complexity for vector domination problem.- Learning through Imitation by using Formal Verification.- Delivery to Safety with Two Cooperating Robots.- Space-Efficient STR-IC-LCS Computation.- The k-center Problem for Classes of Cyclic Words.

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Book SynopsisThis book constitutes the refereed proceedings of the 21st International Workshop, IWDW 2022, held in Guilin, China, during November 18-19, 2022. The 14 full papers included in this book were carefully reviewed and selected from 30 submissions. They were organized in topical sections as follows: Steganology, Forensics and Security Analysis, Watermarking.Table of ContentsSteganology.- High-Performance Steganographic Coding Based on Sub-Polarized Channel.- High-Capacity Adaptive Steganography Based on Transform Coefficient for HEVC.- Forensics and Security Analysis.- SE-ResNet56: Robust Network Model for Deepfake Detection.- Voice Conversion Using Learnable Similarity-Guided Masked Autoencoder.- Visual Explanations for Exposing Potential Inconsistency of Deepfakes.- Improving the Transferability of Adversarial Attacks through Both Front and Rear Vector Method.- Manipulated Face Detection and Localization Based on Semantic Segmentation.- Deep Learning Image Age Approximation - What is more Relevant: Image Content or Age Information?.- Watermarking.- Physical Anti-Copying Semi-Robust Random Watermarking for QR Code.- Robust and Imperceptible Watermarking Scheme for GWAS Data Traceability.- Adaptive Robust Watermarking Method Based on Deep Neural Networks.- Adaptive Despread Spectrum-Based Image Watermarking for Fast Product Tracking.- Reversible Data Hiding via Arranging Blocks of Bit-Planes in Encrypted Images.- High Capacity Reversible Data Hiding for Encrypted 3D Mesh Models Based on Topology.

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Book SynopsisThis book addresses the state of the art of reduced order methods for modelling and computational reduction of complex parametrised systems, governed by ordinary and/or partial differential equations, with a special emphasis on real time computing techniques and applications in various fields.Consisting of four contributions presented at the CIME summer school, the book presents several points of view and techniques to solve demanding problems of increasing complexity. The focus is on theoretical investigation and applicative algorithm development for reduction in the complexity – the dimension, the degrees of freedom, the data – arising in these models.The book is addressed to graduate students, young researchers and people interested in the field. It is a good companion for graduate/doctoral classes.Table of Contents- 1. The Reduced Basis Method in Space and Time: Challenges, Limits and Perspectives. - 2. Inverse Problems: A Deterministic Approach Using Physics-Based Reduced Models. - 3. Model Order Reduction for Optimal Control Problems. - 4. Machine Learning Methods for Reduced Order Modeling.

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Book SynopsisFocusing on special matrices and matrices which are in some sense `near’ to structured matrices, this volume covers a broad range of topics of current interest in numerical linear algebra. Exploitation of these less obvious structural properties can be of great importance in the design of efficient numerical methods, for example algorithms for matrices with low-rank block structure, matrices with decay, and structured tensor computations. Applications range from quantum chemistry to queuing theory. Structured matrices arise frequently in applications. Examples include banded and sparse matrices, Toeplitz-type matrices, and matrices with semi-separable or quasi-separable structure, as well as Hamiltonian and symplectic matrices. The associated literature is enormous, and many efficient algorithms have been developed for solving problems involving such matrices. The text arose from a C.I.M.E. course held in Cetraro (Italy) in June 2015 which aimed to present this fast growing field to young researchers, exploiting the expertise of five leading lecturers with different theoretical and application perspectives.Table of Contents Preface.-Charles F. Van Loan: Structured Matrix Problems from Tensors.-Dario A. Bini: Matrix Structures in Queuing Models.-. Jonas Ballani and Daniel Kressner: Matrices with Hierarchical Low-Rank Structures.-Michele Benzi: Localization in Matrix Computations: Theory and Applications.-Munthe-Kaas: Groups and Symmetries in Numerical Linear Algebra.

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Book SynopsisThis book, now in a carefully revised second edition, provides an up-to-date account of Oka theory, including the classical Oka-Grauert theory and the wide array of applications to the geometry of Stein manifolds.Oka theory is the field of complex analysis dealing with global problems on Stein manifolds which admit analytic solutions in the absence of topological obstructions. The exposition in the present volume focuses on the notion of an Oka manifold introduced by the author in 2009. It explores connections with elliptic complex geometry initiated by Gromov in 1989, with the Andersén-Lempert theory of holomorphic automorphisms of complex Euclidean spaces and of Stein manifolds with the density property, and with topological methods such as homotopy theory and the Seiberg-Witten theory.Researchers and graduate students interested in the homotopy principle in complex analysis will find this book particularly useful. It is currently the only work that offers a comprehensive introduction to both the Oka theory and the theory of holomorphic automorphisms of complex Euclidean spaces and of other complex manifolds with large automorphism groups.Table of ContentsPart I Stein Manifolds.- 1 Preliminaries.- 2 Stein Manifolds.- 3 Stein Neighborhoods and Approximation.- 4 Automorphisms of Complex Euclidean Spaces.- Part II Oka Theory.- 5 Oka Manifolds.- 6 Elliptic Complex Geometry and Oka Theory.- 7 Flexibility Properties of Complex Manifolds and Holomorphic Maps.- Part III Applications.- 8 Applications of Oka Theory and its Methods.- 9 Embeddings, Immersions and Submersions.- 10 Topological Methods in Stein Geometry.- References.- Index.

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Book SynopsisThis book takes readers on a multi-perspective tour through state-of-the-art mathematical developments related to the numerical treatment of PDEs based on splines, and in particular isogeometric methods. A wide variety of research topics are covered, ranging from approximation theory to structured numerical linear algebra. More precisely, the book provides (i) a self-contained introduction to B-splines, with special focus on approximation and hierarchical refinement, (ii) a broad survey of numerical schemes for control problems based on B-splines and B-spline-type wavelets, (iii) an exhaustive description of methods for computing and analyzing the spectral distribution of discretization matrices, and (iv) a detailed overview of the mathematical and implementational aspects of isogeometric analysis. The text is the outcome of a C.I.M.E. summer school held in Cetraro (Italy), July 2017, featuring four prominent lecturers with different theoretical and application perspectives. The book may serve both as a reference and an entry point into further research.Table of ContentsFoundations of Spline Theory: B-Splines, Spline Approximation, and Hierarchical Refinement.- Adaptive Multiscale Methods for the Numerical Treatment of Systems of PDEs.- Generalized Locally Toeplitz Sequences: A Spectral Analysis Tool for Discretized Differential Equations.- Isogeometric Analysis: Mathematical and Implementational Aspects, with Applications.

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Book SynopsisSince the early 70's, mixed finite elements have been the object of a wide and deep study by the mathematical and engineering communities. The fundamental role of this method for many application fields has been worldwide recognized and its use has been introduced in several commercial codes. An important feature of mixed finite elements is the interplay between theory and application. Discretization spaces for mixed schemes require suitable compatibilities, so that simple minded approximations generally do not work and the design of appropriate stabilizations gives rise to challenging mathematical problems. This volume collects the lecture notes of a C.I.M.E. course held in Summer 2006, when some of the most world recognized experts in the field reviewed the rigorous setting of mixed finite elements and revisited it after more than 30 years of practice. Applications, in this volume, range from traditional ones, like fluid-dynamics or elasticity, to more recent and active fields, like electromagnetism.Table of ContentsMixed Finite Element Methods.- Finite Elements for the Stokes Problem.- Polynomial Exact Sequences and Projection-Based Interpolation with Application to Maxwell Equations.- Finite Element Methods for Linear Elasticity.- Finite Elements for the Reissner–Mindlin Plate.

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Book SynopsisThe main theme is the integration of the theory of linear PDE and the theory of finite difference and finite element methods. For each type of PDE, elliptic, parabolic, and hyperbolic, the text contains one chapter on the mathematical theory of the differential equation, followed by one chapter on finite difference methods and one on finite element methods. The chapters on elliptic equations are preceded by a chapter on the two-point boundary value problem for ordinary differential equations. Similarly, the chapters on time-dependent problems are preceded by a chapter on the initial-value problem for ordinary differential equations. There is also one chapter on the elliptic eigenvalue problem and eigenfunction expansion. The presentation does not presume a deep knowledge of mathematical and functional analysis. The required background on linear functional analysis and Sobolev spaces is reviewed in an appendix. The book is suitable for advanced undergraduate and beginning graduate students of applied mathematics and engineering.Trade ReviewFrom the reviews:"The book under review is an introduction to the field of linear partial differential equations and to standard methods for their numerical solution. … The balanced combination of mathematical theory with numerical analysis is an essential feature of the book. … The book is easily accessible and concentrates on the main ideas while avoiding unnecessary technicalities. It is therefore well suited as a textbook for a beginning graduate course in applied mathematics." (A. Ostermann, IMN - Internationale Mathematische Nachrichten, Vol. 59 (198), 2005)"This book, which is aimed at beginning graduate students of applied mathematics and engineering, provides an up to date synthesis of mathematical analysis, and the corresponding numerical analysis, for elliptic, parabolic and hyperbolic partial differential equations. … This widely applicable material is attractively presented in this impeccably well-organised text. … Partial differential equations with numerical methods covers a lot of ground authoritatively and without ostentation and with a constant focus on the needs of practitioners." (Nick Lord, The Mathematical Gazette, March, 2005)"Larsson and Thomée … discuss numerical solution methods of linear partial differential equations. They explain finite difference and finite element methods and apply these concepts to elliptic, parabolic, and hyperbolic partial differential equations. … The text is enhanced by 13 figures and 150 problems. Also included are appendixes on mathematical analysis preliminaries and a connection to numerical linear algebra. Summing Up: Recommended. Upper-division undergraduates through faculty." (D. P. Turner, CHOICE, March, 2004)"This book presents a very well written and systematic introduction to the finite difference and finite element methods for the numerical solution of the basic types of linear partial differential equations (PDE). … the book is very well written, the exposition is clear, readable and very systematic." (Emil Minchev, Zentralblatt MATH, Vol. 1025, 2003)"The author’s purpose is to give an elementary, relatively short, and readable account of the basic types of linear partial differential equations, their properties, and the most commonly used methods for their numerical solution. … We warmly recommend it to advanced undergraduate and beginning graduate students of applied mathematics and/or engineering at every university of the world." (Ferenc Móricz, Acta Scientiarum Mathematicarum, Vol. 71, 2005)"The presentation of the book is smart and very classical; it is more a reference book for applied mathematicians … . The convergence results, error estimates, variation formulations, all the theorems proofs, are very clear and well presented, the annexes A and B summary the necessary background for the understanding, without redundant generalisation or forgotten matter. The bibliography is presented by theme, well targeted on the topic of the book." (Anne Lemaitre, Physicalia Magazine, Vol. 28 (1), 2006)“Offers basic theory of linear partial differential equations and discusses the most commonly used numerical methods to solve these equations. … There are two appendices providing some extra basic material, useful to help understanding some of the theoretical principles that might be unfamiliar to unexperienced readers and students. The text is elementary and meant for students in mathematics, physics, engineering. … The bibliography is well arranged according to the important issues, which makes it easy to get informed about possible references for further study.” (Paula Bruggen, Bulletin of the Belgian Mathematical Society, Vol. 15 (1), 2008)Table of ContentsA Two-Point Boundary Value Problem.- Elliptic Equations.- Finite Difference Methods for Elliptic Equations.- Finite Element Methods for Elliptic Equations.- The Elliptic Eigenvalue Problem.- Initial-Value Problems for Ordinary Differential Equations.- Parabolic Equations.- Finite Difference Methods for Parabolic Problems.- The Finite Element Method for a Parabolic Problem.- Hyperbolic Equations.- Finite Difference Methods for Hyperbolic Equations.- The Finite Element Method for Hyperbolic Equations.- Some Other Classes of Numerical Methods.

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Book SynopsisThe application of modern methods in numerical mathematics on problems in chemical engineering is essential for designing, analyzing and running chemical processes and even entire plants. Scientific Computing in Chemical Engineering II gives the state of the art from the point of view of numerical mathematicians as well as that of engineers.The present volume as part of a two-volume edition covers topics such as computer-aided process design, combustion and flame, image processing, optimization, control, and neural networks. The volume is aimed at scientists, practitioners and graduate students in chemical engineering, industrial engineering and numerical mathematics.Table of ContentsInvited Presentations.- Combustion and Flame.- Computer Aided Process Design.- Control.- Image Processing.- Optimization.- Neural Network.

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a huge range and FREE tracked UK delivery on ALL orders.

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Table of ContentsInvited papers.- Discrete Differential Forms, Approximation of Eigenvalue Problems, and Application to the p Version of Edge Finite Elements.- Semi-Implicit DGFE Discretization of the Compressible Navier–Stokes Equations: Efficient Solution Strategy.- Some Numerical Approaches for Weakly Random Homogenization.- Goal Oriented, Anisotropic, A Posteriori Error Estimates for the Laplace Equation.- Contributed papers.- Energy Stability of the MUSCL Scheme.- Numerical Stabilization of the Melt Front for Laser Beam Cutting.- Numerical Optimization of a Bioreactor for the Treatment of Eutrophicated Water.- Finite Element Approximation of a Quasi-3D Model for Estuarian River Flows.- Convergence of a Mixed Discontinuous Galerkin and Finite Volume Scheme for the 3 Dimensional Vlasov–Poisson–Fokker–Planck System.- Infrastructure for the Coupling of Dune Grids.- FEM for Flow and Pollution Transport in a Street Canyon.- Stabilized Finite Element Methods with Shock-Capturing for Nonlinear Convection–Diffusion-Reaction Models.- Finite Element Discretization of the Giesekus Model for Polymer Flows.- A dG Method for the Strain-Rate Formulation of the Stokes Problem Related with Nonconforming Finite Element Methods.- Numerical Simulation of the Stratified Flow Past a Body.- A Flexible Updating Framework for Preconditioners in PDE-Based Image Restoration Algorithms.- Stabilized Finite Element Method for Compressible–Incompressible Diphasic Flows.- An Immersed Interface Technique for the Numerical Solution of the Heat Equation on a Moving Domain.- Lid-Driven-Cavity Simulations of Oldroyd-B Models Using Free-Energy-Dissipative Schemes.- Adaptive Multiresolution Simulation of Waves in Electrocardiology.- On the Numerical Approximation of the Laplace Transform Function from Real Samples and Its Inversion.- A Motion-Aided Ultrasound Image Sequence Segmentation.- A High Order Finite Volume Numerical Scheme for Shallow Water System: An Efficient Implementation on GPUs.- Spectral Analysis for Radial Basis Function Collocation Matrices.- Finite Element Solution of the Primitive Equations of the Ocean by the Orthogonal Sub-Scales Method.- Solution of Incompressible Flow Equations by a High-Order Term-by-Term Stabilized Method.- Solving Large Sparse Linear Systems Efficiently on Grid Computers Using an Asynchronous Iterative Method as a Preconditioner.- Hierarchical High Order Finite Element Approximation Spaces for H(div) and H(curl).- Some Theoretical Results About Stability for IMEX Schemes Applied to Hyperbolic Equations with Stiff Reaction Terms.- Stable Perfectly Matched Layers for the Schrödinger Equations.- Domain Decomposition Schemes for Frictionless Multibody Contact Problems of Elasticity.- Analysis and Acceleration of a Fluid-Structure Interaction Coupling Scheme.- Second Order Numerical Operator Splitting for 3D Advection–Diffusion-Reaction Models.- Space-Time DG Method for Nonstationary Convection–Diffusion Problems.- High Order Finite Volume Schemes for Numerical Solution of Unsteady Flows.- Multigrid Finite Element Method on Semi-Structured Grids for the Poroelasticity Problem.- A Posteriori Error Bounds for Discontinuous Galerkin Methods for Quasilinear Parabolic Problems.- An A Posteriori Analysis of Multiscale Operator Decomposition.- Goal-Oriented Error Estimation for the Discontinuous Galerkin Method Applied to the Biharmonic Equation.- Solving Stochastic Collocation Systems with Algebraic Multigrid.- Adaptive Two-Step Peer Methods for Incompressible Navier–Stokes Equations.- On Hierarchical Error Estimators for Time-Discretized Phase Field Models.- Nonlinear Decomposition Methods in Elastodynamics.- An Implementation Framework for Solving High-Dimensional PDEs on Massively Parallel Computers.- Benchmarking FE-Methods for the Brinkman Problem.- Finite Element Based Second Moment Analysis for Elliptic Problems in Stochastic Domains.- On Robust Parallel Preconditioning for Incompressible Flow Problems.- Hybrid Modeling of Plasmas.- A Priori Error Estimates for DGFEM Applied to Nonstationary Nonlinear Convection–Diffusion Equation.- Stable Crank–Nicolson Discretisation for Incompressible Miscible Displacement Problems of Low Regularity.- Simulations of 3D/4D Precipitation Processes in a Turbulent Flow Field.- 2D Finite Volume Lagrangian Scheme in Hyperelasticity and Finite Plasticity.- Local Projection Method for Convection-Diffusion-Reaction Problems with Projection Spaces Defined on Overlapping Sets.- Numerical Solution of Volterra Integral Equations with Weak Singularities.- Non-Conforming Finite Element Method for the Brinkman Problem.- Error Control for Simulations of a Dissociative Quantum System.- A Comparison of Simplicial and Block Finite Elements.- Five-Dimensional Euclidean Space Cannot be Conformly Partitioned into Acute Simplices.- The Discontinuous Galerkin Method for Convection-Diffusion Problems in Time-Dependent Domains.- A Spectral Time-Domain Method for Computational Electrodynamics.- Numerical Simulation of Fluid–Structure Interaction in Human Phonation: Application.- Error Estimation and Anisotropic Mesh Refinement for Aerodynamic Flow Simulations.- A MHD Problem on Unbounded Domains: Coupling of FEM and BEM.- A Stable and High Order Interface Procedure for Conjugate Heat Transfer Problems.- Local Time-Space Mesh Refinement for Finite Difference Simulation of Waves.- Formulation of a Staggered Two-Dimensional Lagrangian Scheme by Means of Cell-Centered Approximate Riemann Solver.- Optimal Control for River Pollution Remediation.- An Anisotropic Micro-Sphere Approach Applied to the Modelling of Soft Biological Tissues.- Anisotropic Adaptation via a Zienkiewicz–Zhu Error Estimator for 2D Elliptic Problems.- On a Sediment Transport Model in Shallow Water Equations with Gravity Effects.- Adaptive SQP Method for Shape Optimization.- Convergence of Path-Conservative Numerical Schemes for Hyperbolic Systems of Balance Laws.- A Two-Level Newton–Krylov–Schwarz Method for the Bidomain Model of Electrocardiology.- On a Shallow Water Model for Non-Newtonian Fluids.- On Stationary Viscous Incompressible Flow Through a Cascade of Profiles with the Modified Boundary Condition on the Outflow and Large Inflow.- Variational and Heterogeneous Multiscale Methods.- Discrete Dislocation Dynamics and Mean Curvature Flow.- Non-Symmetric Algebraic Multigrid Preconditioners for the Bidomain Reaction–Diffusion system.- Efficiency of Shock Capturing Schemes for Burgers’ Equation with Boundary Uncertainty.- FEM Techniques for the LCR Reformulation of Viscoelastic Flow Problems.- A Posteriori Estimates for Variational Inequalities.- Review on Longest Edge Nested Algorithms.- Simulation of Spray Painting in Automotive Industry.- Numerical Simulation of the Electrohydrodynamic Generation of Droplets by the Boundary Element Method.- A General Pricing Technique Based on Theta-Calculus and Sparse Grids.- A Posteriori Error Estimation in Mixed Finite Element Methods for Signorini’s Problem.- Solution of an Inverse Problem for a 2-D Turbulent Flow Around an Airfoil.- On Skew-Symmetric Splitting and Entropy Conservation Schemes for the Euler Equations.- Ideal Curved Elements and the Discontinuous Galerkin Method.- Analysis of the Parallel Finite Volume Solver for the Anisotropic Allen–Cahn Equation in 3D.- Stabilized Finite Element Approximations of Flow Over a Self-Oscillating Airfoil.- Multigrid Methods for Elliptic Optimal Control Problems with Neumann Boundary Control.- Extension of the Complete Flux Scheme to Time-Dependent Conservation Laws.- Solution of Navier–Stokes Equations Using FEM with Stabilizing Subgrid.- Multigrid Methods for Control-Constrained Elliptic Optimal Control Problems.- Modelling the New Soil Improvement Method Biogrout: Extension to 3D.- Angle Conditions for Discrete Maximum Principles in Higher-Order FEM.- Unsteady High Order Residual Distribution Schemes with Applications to Linearised Euler Equations.- Implicit–Explicit Backward Difference Formulae Discontinuous Galerkin Finite Element Methods for Convection–Diffusion Problems.- A Cut-Cell Finite-Element Method for a Discontinuous Switch Model for Wound Closure.

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Book SynopsisThis Finite Element Method offers a fundamental and practical introduction to the finite element method, its variants, and their applications in engineering. Every concept is introduced in the simplest possible setting, while maintaining a level of treatment that is as rigorous as possible without being unnecessarily abstract. Various finite elements in one, two, and three space dimensions are introduced, and their applications to elliptic, parabolic, hyperbolic, and nonlinear equations and to solid mechanics, fluid mechanics, and porous media flow problems are addressed. The variants include the control volume, multipoint flux approximation, nonconforming, mixed, discontinuous, characteristic, adaptive, and multiscale finite element methods. Illustrative computer programs in Fortran and C++ are described. An extensive set of exercises are provided in each chapter. This book serves as a text a for one-semester course for upper-level undergraduates and beginning graduate students and as a professional reference for engineers, mathematicians, and scientists.Table of ContentsOne-Dimensional Model Problems; Two-Dimensional Model Problems; General Variational Formulation; One-Dimensional Elements and Their Properties; Two-Dimensional Elements and Their Properties; Three-Dimensional Elements and Their Properties; Finite Elements for Transient and Nonlinear Problems; Application to Solid Mechanics; Application to Fluid Mechanics; Application to Porous Media Flow; Other Finite Element Methods.

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