State-of-the-art numerical methods for solving complex engineering problems

Great strides in computer technology have been made in the years since the popular first edition of this book was published. Several excellent software packages now help engineers solve complex problems. Making the most of these programs requires a working knowledge of the numerical methods on which the programs are based. Numerical Methods for Engineering Application provides that knowledge.

While it avoids intense mathematical detail, Numerical Methods for Engineering Application supplies more in-depth explanations of methods than found in the typical engineer's numerical "cookbook." It offers complete coverage of most commonly encountered algebraic, interpolation, and integration problems. Ordinary differential equations are examined in great detail, as are three common types of partial differential equations—parabolic, elliptic, and hyperbolic. The author also explores a wide range of methods for solving initial and boundary value problems.

This complete guide to numerical methods for solving engineering problems on computers provides:

• Practical advice on how to select the best method for a given problem
• Valuable insights into how each method works and why it is the best choice
• Complete algorithms and source code for all programs covered
• Code from the book and problem-solving programs designed by the author available from the author's website

Numerical Methods for Engineering Application is a valuable working resource for engineers and applied physicists. It also serves as an excellent upper-level text for physics and engineering students in courses on modern numerical methods.

This book provides theories on non-parametric shape optimization problems, systematically keeping in mind readers with an engineering background. Non-parametric shape optimization problems are defined as problems of finding the shapes of domains in which boundary value problems of partial differential equations are defined. In these problems, optimum shapes are obtained from an arbitrary form without any geometrical parameters previously assigned. In particular, problems in which the optimum shape is sought by making a hole in domain are called topology optimization problems. Moreover, a problem in which the optimum shape is obtained based on domain variation is referred to as a shape optimization problem of domain variation type, or a shape optimization problem in a limited sense. Software has been developed to solve these problems, and it is being used to seek practical optimum shapes. However, there are no books explaining such theories beginning with their foundations. The structure of the book is shown in the Preface. The theorems are built up using mathematical results. Therefore, a mathematical style is introduced, consisting of definitions and theorems to summarize the key points. This method of expression is advanced as provable facts are clearly shown. If something to be investigated is contained in the framework of mathematics, setting up a theory using theorems prepared by great mathematicians is thought to be an extremely effective approach. However, mathematics attempts to heighten the level of abstraction in order to understand many things in a unified fashion. This characteristic may baffle readers with an engineering background. Hence in this book, an attempt has been made to provide explanations in engineering terms, with examples from mechanics, after accurately denoting the provable facts using definitions and theorems.

In this book we gather recent mathematical developments and engineering applications of Trefftz methods, with particular emphasis on the Method of Fundamental Solutions (MFS). These are true meshless methods that have the advantage of avoiding the need to set up a mesh altogether, and therefore going beyond the reduction of the mesh to a boundary. These Trefftz methods have advantages in several engineering applications, for instance in inverse problems where the domain is unknown and some numerical methods would require a remeshing approach. Trefftz methods are also known to perform very well with regular domains and regular data in boundary value problems, achieving exponential convergence. On the other hand, they may also under certain conditions, exhibit instabilities and lead to ill-conditioned systems. This book is divided into ten chapters that illustrate recent advances in Trefftz methods and their application to engineering problems. The first eight chapters are devoted to the MFS and variants whereas the last two chapters are devoted to related meshless engineering applications. Part of these selected contributions were presented in the 9th International Conference on Trefftz Methods and 5th International Conference on the MFS, held in 2019, July 29-31, in Lisbon, Portugal.

This book introduces the reader to the field of jet substructure, starting from the basic considerations for capturing decays of boosted particles in individual jets, to explaining state-of-the-art techniques. Jet substructure methods have become ubiquitous in data analyses at the LHC, with diverse applications stemming from the abundance of jets in proton-proton collisions, the presence of pileup and multiple interactions, and the need to reconstruct and identify decays of highly-Lorentz boosted particles. The last decade has seen a vast increase in our knowledge of all aspects of the field, with a proliferation of new jet substructure algorithms, calculations and measurements which are presented in this book. Recent developments and algorithms are described and put into the larger experimental context. Their usefulness and application are shown in many demonstrative examples and the phenomenological and experimental effects influencing their performance are discussed. A comprehensive overview is given of measurements and searches for new phenomena performed by the ATLAS and CMS Collaborations. This book shows the impressive versatility of jet substructure methods at the LHC.

This volume is part of collection of contributions devoted to analytical and experimental techniques of dynamical systems, presented at the 15th International Conference "Dynamical Systems: Theory and Applications", held in Lodz, Poland on December 2-5, 2019. The wide selection of material has been divided into three volumes, each focusing on a different field of applications of dynamical systems. The broadly outlined focus of both the conference and these books includes bifurcations and chaos in dynamical systems, asymptotic methods in nonlinear dynamics, dynamics in life sciences and bioengineering, original numerical methods of vibration analysis, control in dynamical systems, optimization problems in applied sciences, stability of dynamical systems, experimental and industrial studies, vibrations of lumped and continuous systems, non-smooth systems, engineering systems and differential equations, mathematical approaches to dynamical systems, and mechatronics.

Nonlinearity plays a major role in the understanding of most physical, chemical, biological, and engineering sciences.
Nonlinear problems fascinate scientists and engineers, but often elude exact treatment. However elusive they may be, the solutions do exist-if only one perseveres in seeking them out.

Self-Similarity and Beyond presents a myriad of approaches to finding exact solutions for a diversity of nonlinear problems. These include group-theoretic methods, the direct method of Clarkson and Kruskal, traveling waves, hodograph methods, balancing arguments, embedding special solutions into a more general class, and the infinite series approach.

The author's approach is entirely constructive. Numerical solutions either motivate the analysis or confirm it, therefore they are treated alongside the analysis whenever possible. Many examples drawn from real physical situations-primarily fluid mechanics and nonlinear diffusion-illustrate and emphasize the central points presented.

Accessible to a broad base of readers, Self-Similarity and Beyond illuminates a variety of productive methods for meeting the challenges of nonlinearity. Researchers and graduate students in nonlinearity, partial differential equations, and fluid mechanics, along with mathematical physicists and numerical analysts, will re-discover the importance of exact solutions and find valuable additions to their mathematical toolkits.

"Analyzes algebras of concrete approximation methods detailing prerequisites, local principles, and lifting theorems. Covers fractality and Fredholmness. Explains the phenomena of the asymptotic splitting of the singular values, and more."

Matrix Analysis and Computations introduces the basics of matrix analysis and presents representative methods and their corresponding theories in matrix computations. In this textbook, readers will find: The matrix theory necessary for direct and iterative methods for solving systems of linear equations. Systematic methods and rigorous theory on matrix splitting iteration methods and Krylov subspace iteration methods. Current results on preconditioning and iterative methods for solving standard and generalized saddle-point linear systems. Exercises at the end of each chapter for applying learned methods. This book is intended for graduate students, researchers, and engineers interested in matrix analysis and matrix computations. It is appropriate for the following courses: Advanced Numerical Analysis, Special Topics on Numerical Analysis, Topics on Data Science, Topics on Numerical Optimization, and Topics on Approximation Theory.

This book presents a systematic exposition of the main ideas and methods in treating inverse problems for PDEs arising in basic mathematical models, though it makes no claim to being exhaustive. Mathematical models of most physical phenomena are governed by initial and boundary value problems for PDEs, and inverse problems governed by these equations arise naturally in nearly all branches of science and engineering. The book's content, especially in the Introduction and Part I, is self-contained and is intended to also be accessible for beginning graduate students, whose mathematical background includes only basic courses in advanced calculus, PDEs and functional analysis. Further, the book can be used as the backbone for a lecture course on inverse and ill-posed problems for partial differential equations. In turn, the second part of the book consists of six nearly-independent chapters. The choice of these chapters was motivated by the fact that the inverse coefficient and source problems considered here are based on the basic and commonly used mathematical models governed by PDEs. These chapters describe not only these inverse problems, but also main inversion methods and techniques. Since the most distinctive features of any inverse problems related to PDEs are hidden in the properties of the corresponding solutions to direct problems, special attention is paid to the investigation of these properties. For the second edition, the authors have added two new chapters focusing on real-world applications of inverse problems arising in wave and vibration phenomena. They have also revised the whole text of the first edition.

This book gathers research papers and surveys on the latest advances in Schubert Calculus, presented at the International Festival in Schubert Calculus, held in Guangzhou, China on November 6-10, 2017. With roots in enumerative geometry and Hilbert's 15th problem, modern Schubert Calculus studies classical and quantum intersection rings on spaces with symmetries, such as flag manifolds. The presence of symmetries leads to particularly rich structures, and it connects Schubert Calculus to many branches of mathematics, including algebraic geometry, combinatorics, representation theory, and theoretical physics. For instance, the study of the quantum cohomology ring of a Grassmann manifold combines all these areas in an organic way. The book is useful for researchers and graduate students interested in Schubert Calculus, and more generally in the study of flag manifolds in relation to algebraic geometry, combinatorics, representation theory and mathematical physics.

These are the proceedings of the 25th International Conference on Domain Decomposition Methods in Science and Engineering, which was held in St. John's, Newfoundland, Canada in July 2018. Domain decomposition methods are iterative methods for solving the often very large systems of equations that arise when engineering problems are discretized, frequently using finite elements or other modern techniques. These methods are specifically designed to make effective use of massively parallel, high-performance computing systems. The book presents both theoretical and computational advances in this domain, reflecting the state of art in 2018.

This text presents a comprehensive mathematical theory for elliptic, parabolic, and hyperbolic differential equations. It compares finite element and finite difference methods and illustrates applications of generalized difference methods to elastic bodies, electromagnetic fields, underground water pollution, and coupled sound-heat flows.

This book gathers contributions from the 15th ICOLD Benchmark Workshop on Numerical Analysis of Dams. The workshop provided an opportunity for engineers, researchers and operators to present and exchange their experiences and the latest advances in numerical modelling in the context of the design, performance and monitoring of dams. Covering various aspects of computer analysis tools and safety assessment criteria, and their development over recent decades, the book is a valuable reference resource for those in the engineering community involved in the safety, planning, design, construction, operation and maintenance of dams.

This multidisciplinary volume is the second in the STEAM-H series to feature invited contributions on mathematical applications in naval engineering. Seeking a more holistic approach that transcends current scientific boundaries, leading experts present interdisciplinary instruments and models on a broad range of topics. Each chapter places special emphasis on important methods, research directions, and applications of analysis within the field. Fundamental scientific and mathematical concepts are applied to topics such as microlattice materials in structural dynamics, acoustic transmission in low Mach number liquid flow, differential cavity ventilation on a symmetric airfoil, Kalman smoother, metallic foam metamaterials for vibration damping and isolation, seal whiskers as a bio-inspired model for the reduction of vortex-induced vibrations, multidimensional integral for multivariate weighted generalized Gaussian distributions, minimum uniform search track placement for rectangular regions, antennas in the maritime environment, the destabilizing impact of non-performers in multi-agent groups, inertial navigation accuracy with bias modeling. Carefully peer-reviewed and pedagogically presented for a broad readership, this volume is perfect to graduate and postdoctoral students interested in interdisciplinary research. Researchers in applied mathematics and sciences will find this book an important resource on the latest developments in naval engineering. In keeping with the ideals of the STEAM-H series, this volume will certainly inspire interdisciplinary understanding and collaboration.

This book includes selected contributions on applied mathematics, numerical analysis, numerical simulation and scientific computing related to fluid mechanics problems, presented at the FEF-"Finite Element for Flows" conference, held in Rome in spring 2017. Written by leading international experts and covering state-of-the-art topics in numerical simulation for flows, it provides fascinating insights into and perspectives on current and future methodological and numerical developments in computational science. As such, the book is a valuable resource for researchers, as well as Masters and Ph.D students.

This book covers different, current research directions in the context of variational methods for non-linear geometric data. Each chapter is authored by leading experts in the respective discipline and provides an introduction, an overview and a description of the current state of the art. Non-linear geometric data arises in various applications in science and engineering. Examples of nonlinear data spaces are diverse and include, for instance, nonlinear spaces of matrices, spaces of curves, shapes as well as manifolds of probability measures. Applications can be found in biology, medicine, product engineering, geography and computer vision for instance. Variational methods on the other hand have evolved to being amongst the most powerful tools for applied mathematics. They involve techniques from various branches of mathematics such as statistics, modeling, optimization, numerical mathematics and analysis. The vast majority of research on variational methods, however, is focused on data in linear spaces. Variational methods for non-linear data is currently an emerging research topic. As a result, and since such methods involve various branches of mathematics, there is a plethora of different, recent approaches dealing with different aspects of variational methods for nonlinear geometric data. Research results are rather scattered and appear in journals of different mathematical communities. The main purpose of the book is to account for that by providing, for the first time, a comprehensive collection of different research directions and existing approaches in this context. It is organized in a way that leading researchers from the different fields provide an introductory overview of recent research directions in their respective discipline. As such, the book is a unique reference work for both newcomers in the field of variational methods for non-linear geometric data, as well as for established experts that aim at to exploit new research directions or collaborations. Chapter 9 of this book is available open access under a CC BY 4.0 license at link.springer.com.

Wave phenomena are ubiquitous in nature. Their mathematical modeling, simulation and analysis lead to fascinating and challenging problems in both analysis and numerical mathematics. These challenges and their impact on significant applications have inspired major results and methods about wave-type equations in both fields of mathematics. The Conference on Mathematics of Wave Phenomena 2018 held in Karlsruhe, Germany, was devoted to these topics and attracted internationally renowned experts from a broad range of fields. These conference proceedings present new ideas, results, and techniques from this exciting research area.

This book addresses the global study of finite and infinite singularities of planar polynomial differential systems, with special emphasis on quadratic systems. While results covering the degenerate cases of singularities of quadratic systems have been published elsewhere, the proofs for the remaining harder cases were lengthier. This book covers all cases, with half of the content focusing on the last non-degenerate ones. The book contains the complete bifurcation diagram, in the 12-parameter space, of global geometrical configurations of singularities of quadratic systems. The authors' results provide - for the first time - global information on all singularities of quadratic systems in invariant form and their bifurcations. In addition, a link to a very helpful software package is included. With the help of this software, the study of the algebraic bifurcations becomes much more efficient and less time-consuming. Given its scope, the book will appeal to specialists on polynomial differential systems, pure and applied mathematicians who need to study bifurcation diagrams of families of such systems, Ph.D. students, and postdoctoral fellows.

This is chemical engineering text for graduate students and researchers. It provides a comprehensive and rigorous introduction to the fundamental principles and differential equations that govern the kinematics and dynamics of laminar flow of incompressible Newtonian fluids. The text illustrates the application of numerical methods to computing a variety of flow variables and solving a broad range of problems, and discusses the development of specific computational algorithms. A feature of this book is that it combines both theoretical and computational aspects of Fluid Dynamics in a unified and comprehensive treatment. It also assumes very little prior knowledge or experience of computational fluid dynamics and all the terminology is explained clearly. The material is intended to be instructive in a classroom setting and act as a useful source reference for researchers.

This two-volume book provides an insight into the 10th International Conference on Soft Computing for Problem Solving (SocProS 2020). This international conference is a joint technical collaboration of Soft Computing Research Society and Indian Institute of Technology Indore. The book presents the latest achievements and innovations in the interdisciplinary areas of soft computing. It brings together the researchers, engineers and practitioners to discuss thought-provoking developments and challenges, in order to select potential future directions. It covers original research papers in the areas including but not limited to algorithms (artificial immune system, artificial neural network, genetic algorithm, genetic programming and particle swarm optimization) and applications (control systems, data mining and clustering, finance, weather forecasting, game theory, business and forecasting applications). The book will be beneficial for young as well as experienced researchers dealing across complex and intricate real-world problems for which finding a solution by traditional methods is a difficult task.

This book focuses on mathematical modeling, describes the process of constructing and evaluating models, discusses the challenges and delicacies of the modeling process, and explicitly outlines the required rules and regulations so that the reader will be able to generalize and reuse concepts in other problems by relying on mathematical logic.Undergraduate and postgraduate students of different academic disciplines would find this book a suitable option preparing them for jobs and research fields requiring modeling techniques. Furthermore, this book can be used as a reference book for experts and practitioners requiring advanced skills of model building in their jobs.

This monograph presents the geoscientific context arising in decorrelative gravitational exploration to determine the mass density distribution inside the Earth. First, an insight into the current state of research is given by reducing gravimetry to mathematically accessible, and thus calculable, decorrelated models. In this way, the various unresolved questions and problems of gravimetry are made available to a broad scientific audience and the exploration industry. New theoretical developments will be given, and innovative ways of modeling geologic layers and faults by mollifier regularization techniques are shown. This book is dedicated to surface as well as volume geology with potential data primarily of terrestrial origin. For deep geology, the geomathematical decorrelation methods are to be designed in such a way that depth information (e.g., in boreholes) may be canonically entered. Bridging several different geo-disciplines, this book leads in a cycle from the potential measurements made by geoengineers, to the cleansing of data by geophysicists and geoengineers, to the subsequent theory and model formation, computer-based implementation, and numerical calculation and simulations made by geomathematicians, to interpretation by geologists, and, if necessary, back. It therefore spans the spectrum from geoengineering, especially geodesy, via geophysics to geomathematics and geology, and back. Using the German Saarland area for methodological tests, important new fields of application are opened, particularly for regions with mining-related cavities or dense development in today's geo-exploration.

This book evaluates the seismic performance of concrete gravity dams, considering the effects of strong motion duration, mainshock-aftershock seismic sequence, and near-fault ground motion. It employs both the extended finite element method (XFEM) and concrete damaged plasticity (CDP) models to characterize the mechanical behavior of concrete gravity dams under strong ground motions, including the dam-reservoir-foundation interaction. In addition, it discusses the effects of the initial crack, earthquake direction, and cross-stream seismic excitation on the nonlinear dynamic response to strong ground motions, and on the damage-cracking risk of concrete gravity dams. This book provides a theoretical basis for the seismic performance evaluation of high dams, and can also be used as a reference resource for researchers and graduate students engaged in the seismic design of high dams.

Learn approaches of computational thinking and the art of designing algorithms. Most of the algorithms you will see in this book are used in almost all software that runs on your computer. Learning how to program can be very rewarding. It is a special feeling to seeing a computer translate your thoughts into actions and see it solve your problems for you. To get to that point, however, you must learn to think about computations in a new way-you must learn computational thinking. This book begins by discussing models of the world and how to formalize problems. This leads onto a definition of computational thinking and putting computational thinking in a broader context. The practical coding in the book is carried out in Python; you'll get an introduction to Python programming, including how to set up your development environment. What You Will Learn Think in a computational way Acquire general techniques for problem solving See general and concrete algorithmic techniques Program solutions that are both computationally efficient and maintainable Who This Book Is For Those new to programming and computer science who are interested in learning how to program algorithms and working with other computational aspects of programming.

This book discusses email spam detection and its challenges such as text classification and categorization. The book proposes an efficient spam detection technique that is a combination of Character Segmentation and Recognition and Classification (CSRC). The author describes how this can detect whether an email (text and image based) is a spam mail or not. The book presents four solutions: first, to extract the text character from the image by segmentation process which includes a combination of Discrete Wavelet Transform (DWT) and skew detection. Second, text characters are via text recognition and visual feature extraction approach which relies on contour analysis with improved Local Binary Pattern (LBP). Third, extracted text features are classified using improvised K-Nearest Neighbor search (KNN) and Support Vector Machine (SVM). Fourth, the performance of the proposed method is validated by the measure of metric named as sensitivity, specificity, precision, recall, F-measure, accuracy, error rate and correct rate. Presents solutions to email spam detection and discusses its challenges such as text classification and categorization; Analyzes the proposed techniques' performance using precision, F-measure, recall and accuracy; Evaluates the limitations of the proposed research thereby recommending future research.