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 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.

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.

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 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 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 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 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.

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 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.

Addressing the applications of computational intelligence algorithms in energy, this book presents a systematic procedure that illustrates the practical steps required for applying bio-inspired, meta-heuristic algorithms in energy, such as the prediction of oil consumption and other energy products. Contributions include research findings, projects, surveying work and industrial experiences that describe significant advances in the applications of computational intelligence algorithms in energy. For easy understanding, the text provides practical simulation results, convergence and learning curves as well as illustrations and tables. Providing a valuable resource for undergraduate and postgraduate students alike, it is also intended for researchers in the fields of computational intelligence and energy.

"My absolute favorite for this kind of interview preparation is Steven Skiena's The Algorithm Design Manual. More than any other book it helped me understand just how astonishingly commonplace ... graph problems are -- they should be part of every working programmer's toolkit. The book also covers basic data structures and sorting algorithms, which is a nice bonus. ... every 1 - pager has a simple picture, making it easy to remember. This is a great way to learn how to identify hundreds of problem types." (Steve Yegge, Get that Job at Google) "Steven Skiena's Algorithm Design Manual retains its title as the best and most comprehensive practical algorithm guide to help identify and solve problems. ... Every programmer should read this book, and anyone working in the field should keep it close to hand. ... This is the best investment ... a programmer or aspiring programmer can make." (Harold Thimbleby, Times Higher Education) "It is wonderful to open to a random spot and discover an interesting algorithm. This is the only textbook I felt compelled to bring with me out of my student days.... The color really adds a lot of energy to the new edition of the book!" (Cory Bart, University of Delaware) "The is the most approachable book on algorithms I have." (Megan Squire, Elon University) --- This newly expanded and updated third edition of the best-selling classic continues to take the "mystery" out of designing algorithms, and analyzing their efficiency. It serves as the primary textbook of choice for algorithm design courses and interview self-study, while maintaining its status as the premier practical reference guide to algorithms for programmers, researchers, and students. The reader-friendly Algorithm Design Manual provides straightforward access to combinatorial algorithms technology, stressing design over analysis. The first part, Practical Algorithm Design, provides accessible instruction on methods for designing and analyzing computer algorithms. The second part, the Hitchhiker's Guide to Algorithms, is intended for browsing and reference, and comprises the catalog of algorithmic resources, implementations, and an extensive bibliography. NEW to the third edition: -- New and expanded coverage of randomized algorithms, hashing, divide and conquer, approximation algorithms, and quantum computing -- Provides full online support for lecturers, including an improved website component with lecture slides and videos -- Full color illustrations and code instantly clarify difficult concepts -- Includes several new "war stories" relating experiences from real-world applications -- Over 100 new problems, including programming-challenge problems from LeetCode and Hackerrank. -- Provides up-to-date links leading to the best implementations available in C, C++, and Java Additional Learning Tools: -- Contains a unique catalog identifying the 75 algorithmic problems that arise most often in practice, leading the reader down the right path to solve them -- Exercises include "job interview problems" from major software companies -- Highlighted "take home lessons" emphasize essential concepts -- The "no theorem-proof" style provides a uniquely accessible and intuitive approach to a challenging subject -- Many algorithms are presented with actual code (written in C) -- Provides comprehensive references to both survey articles and the primary literature Written by a well-known algorithms researcher who received the IEEE Computer Science and Engineering Teaching Award, this substantially enhanced third edition of The Algorithm Design Manual is an essential learning tool for students and professionals needed a solid grounding in algorithms. Professor Skiena is also the author of the popular Springer texts, The Data Science Design Manual and Programming Challenges: The Programming Contest Training Manual.

This book describes the development of a constitutive modeling platform for soil testing, which is one of the key components in geomechanics and geotechnics. It discusses the fundamentals of the constitutive modeling of soils and illustrates the use of these models to simulate various laboratory tests. To help readers understand the fundamentals and modeling of soil behaviors, it first introduces the general stress-strain relationship of soils and the principles and modeling approaches of various laboratory tests, before examining the ideas and formulations of constitutive models of soils. Moving on to the application of constitutive models, it presents a modeling platform with a practical, simple interface, which includes various kinds of tests and constitutive models ranging from clay to sand, that is used for simulating most kinds of laboratory tests. The book is intended for undergraduate and graduate-level teaching in soil mechanics and geotechnical engineering and other related engineering specialties. Thanks to the inclusion of real-world applications, it is also of use to industry practitioners, opening the door to advanced courses on modeling within the industrial engineering and operations research fields.

This monograph presents the geoscientific context arising in decorrelative geomagnetic exploration. First, an insight into the current state of research is given by reducing magnetometry to mathematically accessible, and thus calculable, decorrelated models. In this way, various questions and problems of magnetometry are made available to a broad scientific audience and the exploration industry. New stimuli are given, and innovative ways of modeling geologic strata by mollifier magnetometric techniques are shown. Potential data sets primarily of terrestrial origin constitute the main data basis in the book. For deep geology, the geomathematical decorrelation methods are designed in such a way that depth information (e.g., in boreholes) may be canonically entered. Overall, this book provides pioneering and ground-breaking innovative mathematical knowledge as a transfer methodology from the "reality space" of magnetometric measurements into the "virtual space" of mathematical-numerical modeling structures and mollifier solutions with novel geological application areas. It pursues a double goal: On the one hand, it represents a geoscientific set of rules for today's geoengineering, interested in the application of innovative modelling and simulation techniques to promising data sets and structures occurring in geomagnetics. On the other hand, the book serves as a collection of current material in Applied Mathematics to offer alternative methodologies in the theory of inverse problems.

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.

Address vector and matrix methods necessary in numerical methods and optimization of linear systems in engineering with this unified text. Treats the mathematical models that describe and predict the evolution of our processes and systems, and the numerical methods required to obtain approximate solutions. Explores the dynamical systems theory used to describe and characterize system behaviour, alongside the techniques used to optimize their performance. Integrates and unifies matrix and eigenfunction methods with their applications in numerical and optimization methods. Consolidating, generalizing, and unifying these topics into a single coherent subject, this practical resource is suitable for advanced undergraduate students and graduate students in engineering, physical sciences, and applied mathematics.

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 volume gathers papers presented at the international conference BAIL, which was held at the University of Strathclyde, Scotland from the 14th to the 22nd of June 2018. The conference gathered specialists in the asymptotic and numerical analysis of problems which exhibit layers and interfaces. Covering a wide range of topics and sharing a wealth of insights, the papers in this volume provide an overview of the latest research into the theory and numerical approximation of problems involving boundary and interior layers.

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.

Over the past 50 years, strain gradient material theories have been developed for the continuum modeling of size effects in materials and structures in terms of their elasticity, plasticity and fracturing. This book puts forward a unifying perspective to combine existing theories involving the higher order gradient of the strain tensor, or of plastic strain. It begins by reviewing experimental findings on the existence (or non-existence) of size effects on the mechanics of materials. In turn, the book devises first, second and higher order strain gradient theories from general principles, and presents constitutive frameworks that satisfy thermodynamic requirements. The special case of strain gradient plasticity is then developed and illustrated via computational analyses of size effects on the plasticity of metals at small scales. In closing, the book explains the origin of gradient effects in the case of lattice structures by drawing on homogenization theory.

This book explores four guiding themes - reduced order modelling, high dimensional problems, efficient algorithms, and applications - by reviewing recent algorithmic and mathematical advances and the development of new research directions for uncertainty quantification in the context of partial differential equations with random inputs. Highlighting the most promising approaches for (near-) future improvements in the way uncertainty quantification problems in the partial differential equation setting are solved, and gathering contributions by leading international experts, the book's content will impact the scientific, engineering, financial, economic, environmental, social, and commercial sectors.

This book constitutes refereed proceedings of the 4th Maple Conference, MC 2020, held in Waterloo, Ontario, Canada, in November 2020. The 25 revised full papers and 3 short papers were carefully reviewed and selected out of 75 submissions, one invited paper is also presented in the volume. The papers included in this book cover topics in education, algorithms, and applciations of the mathematical software Maple.