Numerisk analyse

This book constitutes revised selected papers from the thoroughly refereed workshop proceedings of the 20th International Workshop on Approximation and Online Algorithms, WAOA 2022, which was colocated with ALGO 2022 and took place in Potsdam, Germany, in September 2022.The 12 papers included in these proceedings were carefully reviewed and selected from21 submissions. They focus on topics such as graph algorithms, network design, algorithmic game theory, approximation and online algorithms, etc.

This textbook covers the basic concepts and applications of finite element analysis. It is specifically aimed at introducing this advanced topic to undergraduate-level engineering students and practicing engineers in a lucid manner. It also introduces a structural and heat transfer analysis software FEASTSMT which has wide applications in civil, mechanical, nuclear and automobile engineering domains. This software has been developed by generations of scientists and engineers of Vikram Sarabhai Space Centre and Indian Space Research Organisation. Supported with many illustrative examples, the textbook covers the classical methods of estimating solutions of mathematical models. The book is written in an easy-to-understand manner. This textbook also contains numeral exercise problems to aid self-learning of the students. The solutions to these problems are demonstrated using finite element software. Furthermore, the textbook contains several tutorials and associated onlineresources on usage of the FEASTSMT software. Given the contents, this textbook is highly useful for the undergraduate students of various disciplines of engineering. It is also a good reference book for the practicing engineers.

The main objective of this work is to represent the behaviors of weighted automata by expressively equivalent formalisms: rational operations on formal power series, linear representations by means of matrices, and weighted monadic second-order logic. First, we exhibit the classical results of Kleene, Buchi, Elgot and Trakhtenbrot, which concentrate on the expressive power of finite automata. We further derive a generalization of the Buchi-Elgot-Trakhtenbrot Theorem addressing formulas, whereas the original statement concerns only sentences. Then we use the language-theoretic methods as starting point for our investigations regarding power series. We establish Schutzenberger's extension of Kleene's Theorem, referred to as Kleene-Schutzenberger Theorem. Moreover, we introduce a weighted version of monadic second-order logic, which is due to Droste and Gastin. By means of this weighted logic, we derive an extension of the Buchi-Elgot-Trakhtenbrot Theorem. Thus, we point out relations among the different specification approaches for formal power series. Further, we relate the notions and results concerning power series to their counterparts in Language Theory. Overall, our investigations shed light on the interplay between languages, formal power series, automata and monadic second-order logic.

This book provides an accessible overview concerning the stochastic numerical methods inheriting long-time dynamical behaviours of finite and infinite-dimensional stochastic Hamiltonian systems. The long-time dynamical behaviours under study involve symplectic structure, invariants, ergodicity and invariant measure. The emphasis is placed on the systematic construction and the probabilistic superiority of stochastic symplectic methods, which preserve the geometric structure of the stochastic flow of stochastic Hamiltonian systems.The problems considered in this book are related to several fascinating research hotspots: numerical analysis, stochastic analysis, ergodic theory, stochastic ordinary and partial differential equations, and rough path theory. This book will appeal to researchers who are interested in these topics.

This book presents the latest research into CSS methods, uses, and results, as presented at the 2019 annual conference of the CSSSA.  This conference was held in Santa Fe, New Mexico, October 24 - 27, 2019, at the Drury Plaza Hotel.  What follows is a diverse representation of new results and approaches for using the tools of CSS and agent-based modeling (ABM) for exploring complex phenomena across many different domains. Readers will therefore not only have the results of these specific projects on which to build, but will also gain a greater appreciation for the broad scope of CSS, and have a wealth of case-study examples that can serve as meaningful exemplars for new research projects and activities. The Computational Social Science Society of the Americas (CSSSA) is a professional society that aims to advance the field of CSS in all its areas, from fundamental principles to real-world applications, by holding conferences and workshops, promoting standards of scientific excellence in research and teaching, and publishing novel research findings.

This LNCS 13453 constitutes the thoroughly refereed proceedings of the 48th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2022.The 32 full papers presented in this volume were carefully reviewed and selected from a total of 96 submissions. The WG 2022 workshop aims to merge theory and practice by demonstrating how concepts from Graph Theory can be applied to various areas in Computer Science, or by extracting new graph theoretic problems from applications.

The book is devoted to the study of constrained minimization  problems on closed and convex sets in Banach spaces with a Frechet differentiable objective function. Such  problems are well studied in a  finite-dimensional space and in an infinite-dimensional Hilbert space. When the space is Hilbert there are many algorithms for solving optimization problems including the gradient projection algorithm which  is one of the most important tools in the optimization theory, nonlinear analysis and their applications. An optimization problem is described by an  objective function  and a set of feasible points. For the gradient projection algorithm each iteration consists of two steps. The first step is a calculation of a gradient of the objective function while in the second one  we calculate a projection on the feasible  set. In each of these two steps there is a computational error. In our recent research we show that the gradient projection algorithm generates a good approximate solution, if all the computational errors are bounded from above by a small positive constant. It should be mentioned that  the properties of a Hilbert space play an important role. When we consider an optimization problem in a general Banach space the situation becomes more difficult and less understood. On the other hand such problems arise in the approximation theory. The book is of interest for mathematicians working in  optimization. It also can be useful in preparation courses for graduate students.  The main feature of the book which appeals specifically to this audience is the study of algorithms for convex and nonconvex minimization problems in a general Banach space. The book is of interest for experts in applications of optimization to the approximation theory.In this book the goal is to obtain a good approximate solution of the constrained optimization problem in a general Banach space under  the presence of computational errors.  It is shown that the algorithm generates a good approximate solution, if the sequence of computational errors is bounded from above by a small constant. The book consists of four chapters. In the first we discuss several algorithms which are studied in the book and  prove a convergence result for an unconstrained problem which is a prototype of our results for the constrained problem. In Chapter 2 we analyze convex optimization problems. Nonconvex optimization problems  are studied in Chapter 3. In Chapter 4 we study  continuous   algorithms for minimization problems under the presence of computational errors. The algorithm generates a good approximate solution, if the sequence of computational errors is bounded from above by a small constant. The book consists of four chapters. In the first we discuss several algorithms which are studied in the book and  prove a convergence result for an unconstrained problem which is a prototype of our results for the constrained problem. In Chapter 2 we analyze convex optimization problems. Nonconvex optimization problems  are studied in Chapter 3. In Chapter 4 we study  continuous   algorithms for minimization problems under the presence of computational errors.

This book focuses on iterative solvers and preconditioners for mixed finite element methods. It provides an overview of some of the state-of-the-art solvers for discrete systems with constraints such as those which arise from mixed formulations.Starting by recalling the basic theory of mixed finite element methods, the book goes on to discuss the augmented Lagrangian method and gives a summary of the standard iterative methods, describing their usage for mixed methods. Here, preconditioners are built from an approximate factorisation of the mixed system.A first set of applications is considered for incompressible elasticity problems and flow problems, including non-linear models.An account of the mixed formulation for Dirichlet's boundary conditions is then given before turning to contact problems, where contact between incompressible bodies leads to problems with two constraints.This book is aimed at graduate students and researchers in the field of numerical methods and scientific computing.

Richard Earl describes the nascent evolution of mathematical analysis, its development as a subject in its own right, and its wide-ranging applications in mathematics and science, modelling reality from acoustics to fluid dynamics, from biological systems to quantum theory.

This book puts forward a new mathematical theory to study chaotic phenomenon. The uniform theory is established on the basis of two elementary concept of circle and externally tangent square in mathematics. The author studies the uniformity of a finite set of points distributed in space by uniform theory. This book also illustrates that uniform theory performs better than other indices such as entropy and Lyapunov exponent in chaos measurement by numerous examples. This book develops a new mathematical tool for studying chaos so it will be appealing to students and researchers interested in theory of chaos. It also has potential applications in various fields such as Engineering, Forestry and Ecology.

The idea of structure-preserving algorithms appeared in the 1980's. The new paradigm brought many innovative changes. The new paradigm wanted to identify the long-time behaviour of the solutions or the existence of conservation laws or some other qualitative feature of the dynamics. Another area that has kept growing in importance within Geometric Numerical Integration is the study of highly-oscillatory problems: problems where the solutions are periodic or quasiperiodic and have to be studied in time intervals that include an extremely large number of periods. As is known, these equations cannot be solved efficiently using conventional methods. A further study of novel geometric integrators has become increasingly important in recent years. The objective of this monograph is to explore further geometric integrators for highly oscillatory problems that can be formulated as systems of ordinary and partial differential equations.Facing challenging scientific computational problems, this book presents some new perspectives of the subject matter based on theoretical derivations and mathematical analysis, and provides high-performance numerical simulations. In order to show the long-time numerical behaviour of the simulation, all the integrators presented in this monograph have been tested and verified on highly oscillatory systems from a wide range of applications in the field of science and engineering. They are more efficient than existing schemes in the literature for differential equations that have highly oscillatory solutions. This book is useful to researchers, teachers, students and engineers who are interested in Geometric Integrators and their long-time behaviour analysis for differential equations with highly oscillatory solutions. 

This book deals with magnetic anomaly maps and their properties. These properties are essential to modeling the elimination of the uncertainty problem of buried archaeological structure locations and depths. To this end, several models are presented and their quantitative properties are studied. Numerical simulations have been created, confirming theoretical results that were obtained.

This book develops a class of graded finite element methods to solve singular elliptic boundary value problems in two- and three-dimensional domains. It provides an approachable and self-contained presentation of the topic, including both the mathematical theory and numerical tools necessary to address the major challenges imposed by the singular solution. Moreover, by focusing upon second-order equations with constant coefficients, it manages to derive explicit results that are accessible to the broader computation community. Although written with mathematics graduate students and researchers in mind, this book is also relevant to applied and computational mathematicians, scientists, and engineers in numerical methods who may encounter singular problems.

This book gathers a selection of peer-reviewed papers presented at the 3rd International Conference on Experimental and Computational Mechanics in Engineering (ICECME 2021), held as a virtual conference and organized by Universitas Syiah Kuala, Banda Aceh, Indonesia, on October 11-12, 2021.This book, prepared by international scientists and engineers, covers the latest advances in computational mechanics, metallurgy and material science, energy systems, manufacturing processing systems, industrial and system engineering, biomechanics, artificial intelligence, micro-/nano-engineering, micro-electro-mechanical system, machine learning, mechatronics, and engineering design. This book is intended for academics, including graduate students and researchers, as well as industrial practitioners working in the areas of experimental and computational mechanics.