Numerisk analyse

The monograph is devoted to the construction of the high-order finite difference and finite element methods for numerical solving multidimensional boundary-value problems (BVPs) for different partial differential equations, in particular, linear Helmholtz and wave equations, nonlinear Burgers¿ equations, and elliptic (Schrödinger) equation. Despite of a long history especially in development of the theoretical background of these methods there are open questions in their constructive implementation in numerical solving the multidimensional BVPs having additional requirement on physical parameters or desirable properties of its approximate solutions. Over the last two decades many papers on this topics have been published, in which new constructive approaches to numerically solving the multidimensional BVPs were proposed, and its highly desirable to systematically collect these results. This motivate us to write thus monograph based on our research results obtainedin collaboration with the co-authors. Since the topic is importance we believe that this book will be useful to readers, graduate students and researchers interested in the field of computational physics, applied mathematics, numerical analysis and applied sciences

This book gathers the latest advances, innovations, and applications in the field of computational engineering, as presented by leading international researchers and engineers at the 29th International Conference on Computational & Experimental Engineering and Sciences (ICCES), held in Shenzhen, China on May 26-29, 2023. ICCES covers all aspects of applied sciences and engineering: theoretical, analytical, computational, and experimental studies and solutions of problems in the physical, chemical, biological, mechanical, electrical, and mathematical sciences. As such, the book discusses highly diverse topics, including composites; bioengineering & biomechanics; geotechnical engineering; offshore & arctic engineering; multi-scale & multi-physics fluid engineering; structural integrity & longevity; materials design & simulation; and computer modeling methods in engineering. The contributions, which were selected by means of a rigorous international peer-review process, highlight numerous exciting ideas that will spur novel research directions and foster multidisciplinary collaborations.

These are the proceedings of the 27th International Conference on Domain Decomposition Methods in Science and Engineering, which was held in Prague, Czech Republic, in July 2022.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 2022.

This book provides an alternative approach to time-independent perturbation theory in non-relativistic quantum mechanics. It allows easy application to any initial condition because it is based on an approximation to the evolution operator and may also be used on unitary evolution operators for the unperturbed Hamiltonian in the case where the eigenvalues cannot be found. This flexibility sets it apart from conventional perturbation theory. The matrix perturbation method also gives new theoretical insights; for example, it provides corrections to the energy and wave function in one operation. Another notable highlight is the facility to readily derive a general expression for the normalization constant at m-th order, a significant difference between the approach within and those already in the literature. Another unique aspect of the matrix perturbation method is that it can be extended directly to the Lindblad master equation. The first and second-order corrections are obtained for this equation and the method is generalized for higher orders. An alternative form of the Dyson series, in matrix form instead of integral form, is also obtained. Throughout the book, several benchmark examples and practical applications underscore the potential, accuracy and good performance of this novel approach. Moreover, the method's applicability extends to some specific time-dependent Hamiltonians. This book represents a valuable addition to the literature on perturbation theory in quantum mechanics and is accessible to students and researchers alike.

This 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.

This book focuses on Krylov subspace methods for solving linear systems, which are known as one of the top 10 algorithms in the twentieth century, such as Fast Fourier Transform and Quick Sort (SIAM News, 2000). Theoretical aspects of Krylov subspace methods developed in the twentieth century are explained and derived in a concise and unified way. Furthermore, some Krylov subspace methods in the twenty-first century are described in detail, such as the COCR method for complex symmetric linear systems, the BiCR method, and the IDR(s) method for non-Hermitian linear systems.The strength of the book is not only in describing principles of Krylov subspace methods but in providing a variety of applications: shifted linear systems and matrix functions from the theoretical point of view, as well as partial differential equations, computational physics, computational particle physics, optimizations, and machine learning from a practical point of view.The book is self-contained in that basic necessary concepts of numerical linear algebra are explained, making it suitable for senior undergraduates, postgraduates, and researchers in mathematics, engineering, and computational science. Readers will find it a useful resource for understanding the principles and properties of Krylov subspace methods and correctly using those methods for solving problems in the future.

This book presents the research outcomes from cooperative projects with industrial partners. It showcases the practical relevance of the research, features the knowledge exchange. The papers cover a wide range of engineering disciplines, highlighting the impact of these collaborations in addressing real-world challenges and advancing technological developments.

This textbook introduces the study of partial differential equations using both analytical and numerical methods. By intertwining the two complementary approaches, the authors create an ideal foundation for further study. Motivating examples from the physical sciences, engineering, and economics complete this integrated approach.A showcase of models begins the book, demonstrating how PDEs arise in practical problems that involve heat, vibration, fluid flow, and financial markets. Several important characterizing properties are used to classify mathematical similarities, then elementary methods are used to solve examples of hyperbolic, elliptic, and parabolic equations. From here, an accessible introduction to Hilbert spaces and the spectral theorem lay the foundation for advanced methods. Sobolev spaces are presented first in dimension one, before being extended to arbitrary dimension for the study of elliptic equations. An extensive chapter on numerical methods focuses onfinite difference and finite element methods. Computer-aided calculation with Maple¿ completes the book. Throughout, three fundamental examples are studied with different tools: Poisson¿s equation, the heat equation, and the wave equation on Euclidean domains. The Black¿Scholes equation from mathematical finance is one of several opportunities for extension.Partial Differential Equations offers an innovative introduction for students new to the area. Analytical and numerical tools combine with modeling to form a versatile toolbox for further study in pure or applied mathematics. Illuminating illustrations and engaging exercises accompany the text throughout. Courses in real analysis and linear algebra at the upper-undergraduate level are assumed.

This book constitutes the refereed proceedings of the 21st International Workshop on Approximation and Online Algorithms, WAOA 2023, held in Amsterdam, The Netherlands, during September 7¿8, 2023The 16 full papers included in this book are carefully reviewed and selected from 43 submissions. The topics of WAOA 2023 were algorithmic game theory, algorithmic trading, coloring and partitioning, competitive analysis, computational advertising, computational finance, cuts and connectivity, FPT-approximation algorithms, geometric problems, graph algorithms, inapproximability results, mechanism design, network design, packing and covering, paradigms for the design and analysis of approximation and online algorithms, resource augmentation, and scheduling problems

This contributed volume explores innovative research in the modeling, simulation, and control of crowd dynamics. Chapter authors approach the topic from the perspectives of mathematics, physics, engineering, and psychology, providing a comprehensive overview of the work carried out in this challenging interdisciplinary research field. The volume begins with an overview of analytical problems related to crowd modeling. Attention is then given to the importance of considering the social and psychological factors that influence crowd behavior ¿ such as emotions, communication, and decision-making processes ¿ in order to create reliable models. Finally, specific features of crowd behavior are explored, including single-file traffic, passenger movement, modeling multiple groups in crowds, and the interplay between crowd dynamics and the spread of disease.Crowd Dynamics, Volume 4 is ideal for mathematicians, engineers, physicists, and other researchers working in the rapidly growing field of modeling and simulation of human crowds.

This book describes recent collaborations combining the expertise of applied mathematicians, engineers and geophysicists within a research training group (RTG) on "Modeling, Simulation and Optimization of Fluid Dynamic Applications¿, funded by the Deutsche Forschungsgemeinschaft (DFG). The focus is on mathematical modeling, adaptive discretization, approximation strategies and shape optimization with PDEs. The balanced research program is based on the guiding principle that mathematics drives applications and is inspired by applications. With this leitmotif the RTG advances research in Modeling, Simulation and Optimization by an interdisciplinary approach, i.e., to stimulate fundamental education and research by highly complex applications and at the simultaneously transfer tailored mathematical methods to applied sciences. The reported research involves nine projects and addresses challenging fluid dynamic problems inspired by applied sciences, such as climate research & meteorology, energy, aerospace & marine engineering, or medicine. More fundamental research concerning analysis, approximation and numerics is also covered.The material represents a successful attempt to exchange research paradigms between different disciplines and thus displays a modern approach to basic research into scientifically and societally relevant contemporary problems.

This Handbook of Numerical Simulation of In-Flight Icing covers an array of methodologies and technologies on numerical simulation of in-flight icing and its applications. Comprised of contributions from internationally recognized experts from the Americas, Asia, and the EU, this authoritative, self-contained reference includes best practices and specification data spanning the gamut of simulation tools available internationally that can be used to speed up the certification of aircraft and make them safer to fly into known icing. The collection features nine sections concentrating on aircraft, rotorcraft, jet engines, UAVs; ice protection systems, including hot-air, electrothermal, and others; sensors and probes, CFD in the aid of testing, flight simulators, and certification process acceleration methods. Incorporating perspectives from academia, commercial, government R&D, the book is ideal for a range of engineers and scientists concerned with in-flight icing applications.

This book offers a careful selection of studies in optimization techniques based on artificial intelligence, applied to inverse problems in radiative transfer. In this book, the reader will find an in-depth exploration of heuristic optimization methods, each meticulously described and accompanied by historical context and natural process analogies.From simulated annealing and genetic algorithms to artificial neural networks, ant colony optimization, and particle swarms, this volume presents a wide range of heuristic methods. Additional approaches such as generalized extreme optimization, particle collision, differential evolution, Luus-Jaakola, and firefly algorithms are also discussed, providing a rich repertoire of tools for tackling challenging problems.While the applications showcased primarily focus on radiative transfer, their potential extends to various domains, particularly nonlinear and large-scale problems where traditional deterministic methods fall short. With clear and comprehensive presentations, this book empowers readers to adapt each method to their specific needs. Furthermore, practical examples of classical optimization problems and application suggestions are included to enhance your understanding.This book is suitable to any researcher or practitioner whose interests lie on optimization techniques based in artificial intelligence and bio-inspired algorithms, in fields like Applied Mathematics, Engineering, Computing, and cross-disciplinary areas.

This book elucidates the fundamental thermomechanical behaviour inherent in the 3D printing process within a laser-based powder bed fusion (L-PBF) system. It presents foundational concepts and provides in-depth derivations of the governing equations. The analysis encompasses arbitrary anisotropic linear viscoelastic materials, accounting for thermal effects. The authors leverage the theory of axially moving materials, a framework previously employed in the analysis of production processes within the process industry. They introduce a coordinate frame that moves in tandem with the printing laser, adopting an Eulerian perspective towards the in-motion solid. Designed for graduate students and researchers, this book is poised to foster a profound comprehension and spur innovative technological advancements in the realm of additive manufacturing.

Vector Quantization, a pioneering discretization method based on nearest neighbor search, emerged in the 1950s primarily in signal processing, electrical engineering, and information theory. Later in the 1960s, it evolved into an automatic classification technique for generating prototypes of extensive datasets. In modern terms, it can be recognized as a seminal contribution to unsupervised learning through the k-means clustering algorithm in data science.In contrast, Functional Quantization, a more recent area of study dating back to the early 2000s, focuses on the quantization of continuous-time stochastic processes viewed as random vectors in Banach function spaces. This book distinguishes itself by delving into the quantization of random vectors with values in a Banach space¿a unique feature of its content. Its main objectives are twofold: first, to offer a comprehensive and cohesive overview of the latest developments as well as several new results in optimal quantization theory, spanning both finite and infinite dimensions, building upon the advancements detailed in Graf and Luschgy's Lecture Notes volume. Secondly, it serves to demonstrate how optimal quantization can be employed as a space discretization method within probability theory and numerical probability, particularly in fields like quantitative finance. The main applications to numerical probability are the controlled approximation of regular and conditional expectations by quantization-based cubature formulas, with applications to time-space discretization of Markov processes, typically Brownian diffusions, by quantization trees.While primarily catering to mathematicians specializing in probability theory and numerical probability, this monograph also holds relevance for data scientists, electrical engineers involved in data transmission, and professionals in economics and logistics who are intrigued by optimal allocation problems.

This book aims to introduce graduate students to the many applications of numerical computation, explaining in detail both how and why the included methods work in practice. The text addresses numerical analysis as a middle ground between practice and theory, addressing both the abstract mathematical analysis and applied computation and programming models instrumental to the field. While the text uses pseudocode, Matlab and Julia codes are available online for students to use, and to demonstrate implementation techniques. The textbook also emphasizes multivariate problems alongside single-variable problems and deals with topics in randomness, including stochastic differential equations and randomized algorithms, and topics in optimization and approximation relevant to machine learning. Ultimately, it seeks to clarify issues in numerical analysis in the context of applications, and presenting accessible methods to students in mathematics and data science. 

This book gathers the latest advances, innovations, and applications in the field of computational engineering, as presented by leading international researchers and engineers at the 29th International Conference on Computational & Experimental Engineering and Sciences (ICCES), held in Shenzhen, China on May 26-29, 2023. ICCES covers all aspects of applied sciences and engineering: theoretical, analytical, computational, and experimental studies and solutions of problems in the physical, chemical, biological, mechanical, electrical, and mathematical sciences. As such, the book discusses highly diverse topics, including composites; bioengineering & biomechanics; geotechnical engineering; offshore & arctic engineering; multi-scale & multi-physics fluid engineering; structural integrity & longevity; materials design & simulation; and computer modeling methods in engineering. The contributions, which were selected by means of a rigorous international peer-review process, highlight numerousexciting ideas that will spur novel research directions and foster multidisciplinary collaborations.

This volume examines current research in mechanics and its applications to various disciplines, with a particular focus on fluid-structure interaction (FSI). The topics have been chosen in commemoration of Dr. Bong Jae Chung and with respect to his wide range of research interests. This volume stands apart because of this diversity of interests, featuring an interdisciplinary and in-depth analysis of FSI that is difficult to find conveniently collected elsewhere in the literature. Contributors include mathematicians, physicists, mechanical and biomechanical engineers, and psychologists. This volume is structured into four thematic areas in order to increase its accessibility: theory, computations, experiments, and applications. Recent Advances in Mechanics and Fluid-Structure Interaction with Applications will appeal to established researchers as well as postdocs and graduate students interested in this active area of research.